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7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 120
The
Asia
SpoSpoSpoSpo
Hosted b
D
30303030t tt t
YYYY
013 ACM ICPC
egional Contest
Dhaka Site
nsored by IBMnsored by IBMnsored by IBMnsored by IBM
y North South University
aka Bangladesh
hhhh November 2013November 2013November 2013November 2013u get 20 Pagesu get 20 Pagesu get 20 Pagesu get 20 Pages
11 Problems11 Problems11 Problems11 Problemsampampampamp
300 Minutes300 Minutes300 Minutes300 Minutes
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 220
2
983122983157983148983141983155 983142983151983154 983105983107983117983085983113983107983120983107 983090983088983089983091 983105983155983145983137 983122983141983143983145983151983150983137983148 983108983144983137983147983137 983123983145983156983141983098
a) Solutions to problems submitted for judging are called runs Each run is judged as accepted orrejected by the judge and the team is notified of the results Submitted codes should not contain
team or University name and the file name should not have any white space
b) Notification of accepted runs will NOT be suspended at the last one hour of the contest time to keepthe final results secret Notification of rejected runs will also continue until the end of the contest Butthe teams will not be given any balloon and the public rank list will not be updated in the last onehour
c) A contestant may submit a clarification request to judges If the judges agree that an ambiguity orerror exists a clarification will be issued to all contestants
d) Contestants are not to converse with anyone except members of their team and personnel designatedby the organizing committee while seated at the team desk But they cannot even talk with theirteam members when they are walking around the contest floor to have food or any otherpurpose Systems support staff may advise contestants on system-related problems such as explainingsystem error messages Coaches should not try to enter the contest area under any
circumstances
e) While the contest is scheduled for a particular time length (five hours) the contest director has theauthority to alter the duration of the contest in the event of unforeseen difficulties Should the contestduration be altered every attempt will be made to notify contestants in a timely and uniform manner
f) A team may be disqualified by the Contest Director for any activity that jeopardizes the contestsuch as dislodging extension cords unauthorized modification of contest materials distractingbehavior of communicating with other teams
g) Nine ten or eleven problems will be posed So far as possible problems will avoid dependence ondetailed knowledge of a particular applications area or particular contest language Of these problemsat least two will be solvable by a first year computer science student another two will be solvable by asecond year computer science student and rest will determine the winner
h) Contestants will have foods available in their contest room during the contest So they cannot leavethe contest room during the contest without permission The contestants are not allowed tocommunicate with any contestant (Even contestants of his own team) or coach while are outsidethe contest floor
i) Team can bring up to 200 pages of printed materials with them but they can also bring threeadditional books But they are not allowed to bring calculators mobile phones or any machine-readabledevices like CD DVD Pen-drive IPOD MP3MP4 players floppy disks etc
j) With the help of the volunteers the contestants can have printouts of their codes for debuggingpurposes Passing of printed codes to other teams is strictly prohibited
k) The decision of the judges is final
l) Teams should inform the volunteers if they donrsquot get reply from the judges within 10 minutesof submission Volunteers will inform the judges for further action Teams should also notify thevolunteers if they cannot log in into the PC^2 system This sort of complains will not beentertained after the contest
m) If you want to assume that judge data is weaker than what is stated then do it at your ownrisk )
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 320
A
In general small objects have less
areavolume compared to larger objec
volume is 1 So the ratio is 61 and for
the ratio is 610 Given the shape of
of gravitation on it
For simplicity we will assume the fol
problem
1 All ants are described as a box sshaped object is described with three i
which denotes the length width and
So the volume of the ant is ( W L timestimes
2 The density (Mass per unit volume)
the above mentioned ant is also ( Ltimes
weight is g H W L timestimestimes )( (Here
caused by gravitation)
3 When an ant freely falls four sides a
faces at the top and bottom are paral
So the area of the plane facing botto
For any ant the upward force put by t
to the area of the of the bottom face
proved that the downward acceleratio
solely on the value of H (as g is same
Falling AntsInput Standard Inpututput Standard Output
Ants make up 10 of the total world
total biomass of all the ants on Earth is
total biomass of all the people on Eart
the people on Earth when they fall from
die for two reasons
- They have so little mass relative to the
they fall slowly and therefore hav
dissipate when they hit the ground
- Their bodies are tiny deformable tan
absorb blows
impact of gravitation on them because they
ts For example consider a (1x1x1) cube Its s
a (10x10x10) cube the surface area is 600 and
any ants you will have to find out which ant h
lowing things in this
aped object A boxntegers L W and H
height of the object
) H
is 1 So the mass of
) H W times and so the
is the acceleration
re upright and so the
lel with the horizon
is always W Ltimes
e air is proportional
o be specific it is2
gW L timestimes
After some ma
n H
gg f
2minus= So the downward accelerati
or all ants)
animal tissue The
oughly equal to the
h However unlike
a height they do not
ir air resistance that
e little energy to
s well designed to
have more surface
rface area is 6 and
volume is 1000 So
s the highest effect
nipulation it can be
n actually depends
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 420
4
Given the dimension of several ants report the volume of the ant that has the highest downward
acceleration If there is a tie report the one with the largest volume
InputThe input file contains at most 500 test cases The description of each test case is given below
First line of each test case contains an integer T (T le 100) which denotes the total number of ants to
consider Each of the next T lines contains three integers which denote the value of L W and H (1 le L
W H le 50) of an ant respectively
Input is terminated by a line containing a single zero
OutputFor each set of input produce one line of output This line contains the volume of the ant that has the
highest downward acceleration If there is a tie report the ant with the highest volume
Sample Input Output for Sample Input3
3 4 5
12 1 5
20 10 4
3
3 4 5
20 30 5
1 2 4
0
60
3000
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 520
BM and J are playing a game The desc
several digits will be shown There ar
ith
button of a display once the value
displays has one fault in common T
button is broken
Each of these displays can be describ
the number of digits shown by the di
side (we can consider it like a 3-digit
Firstly it limits the number of times
display will be interpreted as a B-ba
numbers shown by the display will b
can press each of the three working
display is shown in Figure 1
Figure 1M and J have N of these displays Ea
playing goes like this
1 M plays first J plays second
2 In each move a player selects
only be selected if it hasnrsquot re
is a digit which can be selec
broken you can not choose thi
3 After a move if the summati
displays is divisible by 3 then
4 If there is no move possible th
Given description of N displays you
optimally Initially every digit of ever
Game of MJInput Standard Inpututput Standard Output
ription of the game is very simple They have a
buttons under each digit of every display If s
of the ith
digit of that display will increase by
e 0th
digit (least significant digit) canrsquot be in
d using two parameters L and B L is the len
play If L is 3 then the display can show thr
umber) B is the base of the display It is impo
you can press a button Secondly the numb
sed number with L digits Suppose B is 8 an
octal numbers and the length of the numbers
(not broken) buttons at most seven (7) times
A display with L = 4 and B = 8 h of the display has its own L and B Now th
fter that they alternate moves
a display Then selects a digit And presses its
ched its limit B-1 already A display can only
ed However since the switch for the rightm
button for any display
n of numbers (After converting it to decimal
he player making that move loses and the other
n the game ends in draw
need to find out the outcome of the game
display is set to 0 (zero)
few displays where
omeone presses the
one Each of these
creased because its
th of the display or
e (3) digits side by
tant in two aspects
er displayed in the
d L is 4 Then the
will be 4 Also you
Example of such a
game M and J are
button A digit can
be selected if there
ost digit is already
base) shown in the
player wins
and J both plays
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 620
6
InputFirst line of input consists of an integer T (T le 100) the number of test cases Each test case starts with
an integer N (0 lt N lt10) the number of displays Next N line each contains two integers L (0 lt L lt 109)
and B (1 lt B lt 109) which are the parameters that describes the i
th display
OutputFor each case print one line ldquoCase X Srdquo where X is the case number S is either ldquoMrdquo ldquoJrdquo or
ldquoDrawrdquo based on the outcome of the game in that case
Sample Input Output for Sample Input3 1 5 2 2 3 2 2 6 1 2 2
Case 1 M
Case 2 J
Case 3 Draw
Explanation
Case 1
00000 =gt 00010 =gt 01010 =gt 01110 =gt 11110 which is 30 in decimal and divisible by 3 So J loses and
M wins However this is one possible valid game sequence But if two players play optimally J will
always lose and thus M will always win
Case 2
(00000) =gt (00010) Sum = 0 + 6 = 6
(00000) =gt (10000) =gt (10010) =gt (11010) Sum = 6 + 6 = 12
(00000) =gt (10000) =gt (10010) =gt (10020) =gt (10030) =gt (10040) =gt (10050) =gt (11050) Sum = 6
+ 30 = 36
In this way in every game sequence M is doomed to reach such a configuration where the sum will be
divisible by 3 Hence in this scenario J will win and M will lose
Case 3
(00) =gt (10) which is 2 in decimal and not divisible by 3 There is no move left So the game ends in a
draw
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 720
C G
General Broken Arrow and Lieutenant
year they fought several wars toget
happily until one day the king of G
Shadow Coder wants to become the
become king of a country at the same
other in the Great Chaos Jam (GCJ) fi
Colonel Dragoon friend of both Bro
war and comes up with a great soluti
into two disjoint sets of cities called
Shadow Coder will rule the rest of th
with these divisions To make peoples
build a sub-country of Gigaland calle
Gigaland so that peoples from set A
and B are disjoint cities might not be
set B Broken Arrow and Shadow Cod
The country of Gigaland consists of
which connects two different cities an
every city is connected to each other
le K le min(N 21)) cities 1 2 hellip K set B
Though the warriors have agreed to
Each city of set A should be incident
be incident to even number (It can
Megaland should be minimum that i
cities of Megaland may or may not be
In terms of graph theory you are give
and B = K+1 K+2 hellip N You ha
each node in A should have odd degreof S is sum of all the edge cost in S
Given N M K and description of M
Megaland
me of ThroneInput Standard Input
Output Standard Output
General Shadow Coder are two great warriors
er like ICPC NCPC etc The peoples of Gi
igaland General Rem (RIP) died Now both
new king of Gigaland As this is not possible
time they leave it to the field of war They d
ld and the winner will become the new king
en Arrow and Shadow Coder wants to avoid
n According to his proposed solution the cou
A and B Broken Arrow will rule the cities i
e cities But the people of Gigaland will get f
remain calm and happy Dragoon gave another
d Megaland that consists of some cities and
nd B can have some access to other cities Th
disjoint between Megaland and set A and bet
r both agreed with the idea of Dragoon
(numbered from 1 to N) cities and M bidirec
each road has a cost to travel Gigaland was b
ith sequence of one or more roads Set A will c
umbered cities of Gigaland and rest N ndash K citi
uild the new sub-country Megaland they ha
o odd number of roads of Megaland and each
e zero also) of roads of Megaland The cost
sum of all the road cost of Megaland should
connected to each other
a weighted graph G = (N M) two set of nod
e to find the minimum cost sub-graph S (subs
e in S and each node in B should have even de
roads of Gigaland find the minimum possible
of Gigaland Every
galand were living
Broken Arrow and
for two persons to
cided to fight each
the blood shedding
try will be divided
n the set of A and
rustrated and angry
proposal They will
onnecting roads of
ugh cities of set A
een Megaland and
ional roads each of
uilt such a way that
onsists of first K (2
s will belong to the
e some conditions
city of set B should
of road system in
be minimized The
s A = 1 2 hellip K
et of edges) where
gree in S Here cost
cost of sub-country
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 820
8
InputInput starts with a positive integer T (T le 250) denoting the number of test cases Each case starts with
three integers N (2 le N le 100) M (N-1 le M le N(N-1)2) and K (2 le K le min(N 21)) Each of the next
M lines contains three integers u v and c (1 le uv le N u ne v 0 lt c lt 10000) meaning that there is a bi-
directional road between city u and v of cost c No two roads will be same Please also note that for 90 of the test cases K is less than 20
OutputFor each test case print the test case number (starting from 1) and the minimum possible cost of
Megaland if it is possible to build the sub-country according to the conditions described above otherwise
print ldquoImpossiblerdquo (without the quotes)
Sample Input Output for Sample Input2
7 7 4
1 7 101 5 1
2 5 2
3 6 3
4 6 1
5 6 4
3 7 8
4 4 3
1 2 1
1 3 1
2 4 1
3 4 1
Case 1 7
Case 2 Impossible
Warning The judge input file is around 25 MB So use faster IO functionsExplanation
For test case 1
In Megaland degree of each node in set A = 1234 is 1 and degree nodes in set B = 5 6 7 are 2 2
and 0 respectively
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 920
D
P
Mr Anderson is in a relationship wit
Andersons phone logs and texts to fin
he decided to put a pattern locker on hi
This pattern locker comes with a 9 dot
several dots to record a pattern The
recorded before If we assume that ea
than a sequence of digits The patter
once
Here is an example of such a pattern l
Even after recording a hard to crack p
that his girlfriend might try all possi
different pattern sequences are possib
recorded in patterns
You have to help Mr Anderson in cou
ttern LockerInput Standard Input
Output Standard Output
a very suspicious and jealous girlfriend She
d out he is up to Feeling that his private spac
s phone
s arranged on a 3x3 square grid by default One
n to unlock the phone one needs to replicat
h dot is assigned a unique number then a patt
locker requires that no digit appears in the
cker and some valid and invalid recorded patte
attern Mr Anderson doesnt feel quite comfor
le sequences to break his pattern He wants t
le for a given grid size minimum and maxim
nting the number of possible such sequences
is always checking
is getting violated
has to drag through
e the same pattern
rn is nothing more
equence more than
rn
able He is worried
o know how many
m numbers of dots
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1020
10
InputThe first line of the input will give the number of test cases T (1 le T le 10000) Then T test cases follow
in separate lines Each test case consists of three numbers L M N separated by a single space in between
two numbers The first number L (1 lt L le 100) denotes the number of rows and columns in the grid The
second number M (1le
Mle
LL) denotes minimum number of dots to be included in a pattern and thethird number N (M le N le LL) denotes the maximum number of dots to be included in the pattern
OutputFor each test case you need to print the test case number X in the format ldquoCase X rdquo This will be
followed by the count of possible sequences for the given grid size minimum and maximum number of
dots in a sequence Since the count can be pretty big you need to print the value of the count modulo
10000000000007 (1 followed by 12 zeros followed by 7)
Sample Input Output for Sample Input2
3 4 9
3 1 9
Case 1 985824
Case 2 986409
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1120
EYou have pearl of 3 types
bull Type 1 pearl can be of color fr
bull Type 2 pearl can be of color fr
bull Type 3 pearl can be of color fr
You have unlimited supply of pearls
But you have 2 more additional constr
bull
The total number of Type 1 anbull The total number of Type 2 an
Given A B X Y and Z calculate ho
they have different length or there is a
InputFirst line of the input contains T (1 le
A B X Y and Z All of these 5 intege
OutputFor each test case output an integer d
huge output the result modulo 100000
Sample Input5
1 1 1 1 1
2 3 1 1 1
1 1 1 2 1
10 10 10 10 10
100 100 100 100 100
earl ChainsInput Standard Inpututput Standard Output
m 1 to X
m X+1 to X+Y
m X+Y+1 to X+Y+Z
of each type and each color You want to buil
ints
Type 3 pearls will be exactly AType 3 pearls will be exactly B
many different pearl chains are possible 2 c
position in which they have different colored p
le 100) the number of test cases Each test cas
rs are between 1 and 1017
inclusive
noting the number of possible pearl chains Si
Output for Sample Inp3
25
5
77069
329672
some pearl chain
ains are different if
arl
contains 5 integers
nce the result is too
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1220
F Two PI
O
Itrsquos a common phenomenon to mix u
that they just look at sky and can tell y
whole way they travelled ldquoFirst we
and so this one is helliprdquo and thus end u
each other and they do not always run
ends up with some ridiculous answer a
The city we are talking about is a sq
Although the city is nice square shape
rail track and it is a straight one
perpendicular to the existing one The
or not they just need location of twconnecting these two stations the line
you have to build the stations in intege
So to sum it up you will be given co-
to give any two distinct integer co-or
co-ordinates may coincide with the gi
Input
First line of input will contain an integ
be a line of four integers X1 Y1 X2
ordinates of two stations on the alread
You may assume that these two points
OutputFor each test case produce one line
integers where the first two integers
integers are the x and y co-ordinate
possible value of S and the line pa
(may not necessarily intersect the
answers you may output any of the
coordinates does not exceed9
102times F
Sample Input2
4 4 5 5
9 0 10 0
oints Revisitednput Standard Inputtput Standard Output
direction when you go to a new place Some
ou which one is north And some dumb people
ere east facing then we turned left then right
with a direction But the roads are not always
from north to south or from east to west So thi
lmost all the times
uare shaped one with vertices at (0 0) (S 0)
one the road network is already messed up
o city corporation decides to build another
do not care if the new track intersects with th
rail stations so that if a rail track is built alowould be perpendicular to the existing rail tr
r co-ordinates
rdinates of two stations on the already existing
inates within the city for building new rail tra
en co-ordinates if you want it to
er T the number of test cases (T le 15000) For
2 (0 le X1 Y1 X2 Y2 le 109) Here (X1 Y1) and
existing rail track
are different and within the city
of output This line contains the case numbe
are the x and y co-ordinate of the first statio
of the second station They should be withi
sing through them must be perpendicular
previous track within the city) Since the
but you have to make sure that absolute va
or details please go through the explanation of t
Output for Sample ICase 1 1 0 0 1
Case 2 10 0 10 2
eople are so clever
try to remember the
then again righthellip
in 90 degrees with
kind of calculation
(S S) and (0 S)
ut there is only one
rail track which is
previous rail track
ng the straight lineck The problem is
rail track you have
ck One of the new
each case there will
(X2 Y2) are the co-
r followed by four
n and the next two
the city for any
o the existing line
re can be multiple
lue of any of these
he sample cases
put
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1320
13
Explanation
First Sample
In the first sample the existing rail track goes through points (4 4) and (5 5) If you establish two new
rail stations at (1 0) and (0 1) the rail track passing through them will be perpendicular to the existingrail track Note if you output something like (5 5) and (6 4) you will get Wrong Answer since if S = 5
point (6 4) will not be within the city But for any value of S such that (4 4) and (5 5) is within the city
points (1 0) and (0 1) will also be within the city
Second Sample
In this case there are many correct answers One of them is (10 0) and (10 2) Note that unlike first
sample here the rail tracks intersect
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1420
G
Watc
Day by day number of Kangaroos is d
Now for the convenience of the spect
ldquoKangaroo appears in Screen 7rdquo an
position of Kangaroos and inform th
screen to display that animal based on
as follows
If the position x is outside the rangeOtherwise the coverage is minimum(
An example will make it clear
Suppose there are four screens coveri
Kangaroo appears at x = 10
First screen has coverage of 3 unit aro
15 ndash 10) = minimum(3 5) = 3
Second screen has coverage of 0 unit
100)
Third screen has coverage of 0 unit
minimum(10 ndash 8 10 ndash 10) = 0
Fourth screen has coverage of 1 unit a
1 11 ndash 10) = 1
ing the KangarooInput Standard Input
Output Standard Output
ecreasing just like tiger whale or lions So I de
a sanctuary where they will live peac
visitors go near them So I planted s
outside the sanctuary For this proble
the sanctuary to be a long line of 10000
The leftmost position is marked with
position with 1000000000 There ar
cameras on this line Each of the camer
(L R) which means that camera coposition L to position R inclusive Each
their associated display screens outside
can see the Kangaroos
ators we announce time to time ldquoKangaroo a
so on I have some employees who contin
system (here position is a marker) The syste
the coverage The coverage of a screen for a
of that screen (ie x lt L or x gt R) then thndash L R ndash x)
ng the range (7 15) (14 100) (8 10) and (1
nd x = 10 Because x = 10 is within (7 15) an
around x = 10 Because x = 10 does not belo
around x = 10 Because though x = 10 is
round x = 10 Because x = 10 is within (1 11)
cided to make them
fully I do not let
me display screen
you may assume
0000 unit distance
and the rightmost
at most 100000
as is described with
vers a range fromof the cameras has
where the visitors
pears in Screen 3rdquo
ously monitor the
m chooses the best
osition x is defined
coverage is zero
11) Now say one
minimum(10 ndash 7
g to the range (14
within (8 10) but
and minimum(10 ndash
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1520
15
So which one is better Obviously the first one as it has the maximum coverage
So you are given the ranges of the screens and the positions the kangaroo appears For each position of
the Kangaroo you are to tell me the maximum coverage you can have with any of the screens
Input
First line of the test file contains T (T le 3) number of test cases Hence T cases follow For each case
you are given N M in the first line N is the number of screens and M is the number of Kangaroo
appearance ( 1 le N M le 100000) In the next N lines you are given the range of screens L R ( 0 le L le R
le 1000000000 ) Next M lines contain the position of the Kangaroo- an integer x (0 le x le 1000000000)
OutputFor each case print the case number Hence print M lines ith containing the maximum coverage you can
have around irsquoth Kangaroo
Sample Input Output for Sample Input1
3 2
7 15
14 100
1 11
10
120
Case 1
3
0
Warning The judge input file is around 6 MB So use faster IO functions
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1620
HGiven an integer N find how many pa
A le N
Here gcd (A B) means the greatest c
of the bitwise xor operation on the bin
InputThe first line of the input contains a
following T lines contain an integer N
OutputFor each test case print the case nu
input) followed by a space and then th
Sample Input2
7
20000000
Explanation
Sample 1
For N=7 there are four valid pairs (3
GCD XORInput Standard Inpututput Standard Output
irs (A B) are there such that gcd (A B) = A x
mmon divisor of the numbers A and B And
ary representation of A and B
n integer T(T le 10000) denoting the number
1 le N le 30000000)
ber first in the format Case X (here X
answer for that case
Output for Sample InpCase 1 4
Case 2 34866117
2) (5 4) (6 4) and (7 6)
or B where 1 le B le
xor B is the value
of test cases The
is the serial of the
ut
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1720
INatasha always mixes up things in her
classical problem - finding shortest p
that in another class the professor t
looking but does very different things
to the Primrsquos algorithm (actually w
Pseudocode of her algorithm looks as
FiascoInput Standard Input
Output Standard Output
algorithm classes Last week Prof Chhaya Mu
th to all nodes from a specific node of a wei
aught them Primrsquos and Dijkstrarsquos algorithms
Always confused poor Natasha submitted so
should call it Natasharsquos algorithm) she did
ollows
thy gave the class a
hted graph Before
which are similar
ething very similar
rsquot test it properly
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1820
18
After submission she showed the code to a friend who is good at algorithms That friend immediately
found the flaw Natasha was really terrified and started to cry Then there came the guys the guys who
liked her They jumped at the opportunity and got hold of the dataset to be used to test the solutions Your
friend Rehan is one of those guys He really wanted to impress Natasha He asked you to change the
dataset in such a way that Natasharsquos algorithm gives the right result After the change Rehan will
somehow be able to put the modified data with the old timestamp Rehan told you that
1 The dataset has T test cases
2 Each case contains a connected weighted undirected graph with n nodes and m edges
3 Each case will contain a source node source
4 Edge weights are positive and distinct
To avoid suspicion Rehan asked you not to change which vertices the edges connect or the overall set of
edge weights You may only reorder which weights are assigned to which edges
InputThe first line of the input denotes the number of datasets T (1 le T le 15) T sets of case will follow Eachcase will start with a triplet of numbers n (2 le n le 2500) m (1 le m le 25000) and source (1 le source le
n) - the number of nodes the number of edges and the starting node respectively Each of the next m
lines will contain a triplet of numbers (u v w) meaning that there is an edge between node u and node v
with weight w (1 le w le m) Nodes are numbered from 1 to n It is guaranteed that there is no duplicate or
self-edges in the input and the graph is connected In each given graph all edge weights will be distinct
OutputFor each set of input print one set of output First line of a set should be of the format ldquoCase Xrdquo
where X is the case number Then print each edge triplet - one triplet ( u v and w) in each line separated
by a single space The edges should be printed in the order given in the input If there is more than one
solution to a dataset any one of them will do
Sample Input Output for Sample Input1
7 9 5
2 4 2
1 4 8
7 2 6
3 4 7
5 7 5
7 3 9
6 1 1
6 3 4
5 6 3
Case 1
2 4 7
1 4 9
7 2 3
3 4 8
5 7 1
7 3 4
6 1 5
6 3 6
5 6 2
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1920
J Drom
Lets first define some terms
bull A string is palindromic if it re
madam and toot
bull A string is a dromicpalin if we
dromicpalin string is mmaad becau
palindrome
bull A substring is any contiguous
a c i icp acmicpc but acpc
empty substring so that means there a
Given a string you have to figure out
InputThe first line of input is an integer T
containing a string The strings will c
be positive and not greater than 1000
OutputFor each case first output the case n
Follow the samples for exact format
Sample Input4
acmicpc
aaaaa
isyoursolutionfastenough
abbabababbaba
cpalin SubstringsInput Standard Input
Output Standard Output
ds the same forward and backward Examples
can rearrange its letters to make it a palindro
e we can rearrange the letters to make it
equence of characters of a string Some substri
is not a substring For this problem we are
e2
)1( +nn substrings of a string of length n
ow many of its substrings are dromicpalin
(T lt 100) indicating the number of test cases
ntain only lowercase letters [a - z] The lengt
mber followed by the number of substrings t
Output for Sample InpCase 1 8
Case 2 15
Case 3 24
Case 4 67
of palindromes are
e An example of a
adam which is a
ngs of acmicpc are
not considering the
Each case is a line
of each string will
at are dromicpalin
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 2020
KCan you fill an (abc) cuboid with e
cell inside the (abc) cuboid should
dimensions and for each positive integ
a (223) cuboid can be filled with fi
filled with twelve (111) cubes
To make this problem slightly more di
filled by another cube Your job is to f
the cuboid can be filled by exactly n c
InputThere will be at most 300 test cases
abc le 125 0 le m lt abc)
Each of the next m lines contains thre
(x y z) is already filled
No cell will be mentioned twice Ther
The input is terminated by a line conta
OutputFor each test case print the case num
single space before each number in the
Sample Input2 2 3 0
2 2 3 2
1 1 1
2 2 3
0 0 0 0
ill the CuboidInput Standard Input
Output Standard Output
actly n cubes The cubes may touch but cann
be covered by exactly one cube You may us
er p you can use as many (ppp) cubes as yo
e cubes four (111) cubes and one (222)
fficult m of the cells in the cuboid are already
ind out the possible values of n such that the re
ubes
ach test case begins with four integers a b c
integers x y z (1 le x le a 1 le y le b 1 le z le c)
will be at least one non-filled cell
ining four zeroes
ber and the list of possible answers in increasi
output Look at the output for sample input for
Output for Sample InpCase 1 5 12
Case 2 10
ot overlap and each
cubes of different
like For example
cube It can also be
illed and cannot be
maining cells inside
(2 le a b c le 20
that means the cell
ng order There is a
details
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 220
2
983122983157983148983141983155 983142983151983154 983105983107983117983085983113983107983120983107 983090983088983089983091 983105983155983145983137 983122983141983143983145983151983150983137983148 983108983144983137983147983137 983123983145983156983141983098
a) Solutions to problems submitted for judging are called runs Each run is judged as accepted orrejected by the judge and the team is notified of the results Submitted codes should not contain
team or University name and the file name should not have any white space
b) Notification of accepted runs will NOT be suspended at the last one hour of the contest time to keepthe final results secret Notification of rejected runs will also continue until the end of the contest Butthe teams will not be given any balloon and the public rank list will not be updated in the last onehour
c) A contestant may submit a clarification request to judges If the judges agree that an ambiguity orerror exists a clarification will be issued to all contestants
d) Contestants are not to converse with anyone except members of their team and personnel designatedby the organizing committee while seated at the team desk But they cannot even talk with theirteam members when they are walking around the contest floor to have food or any otherpurpose Systems support staff may advise contestants on system-related problems such as explainingsystem error messages Coaches should not try to enter the contest area under any
circumstances
e) While the contest is scheduled for a particular time length (five hours) the contest director has theauthority to alter the duration of the contest in the event of unforeseen difficulties Should the contestduration be altered every attempt will be made to notify contestants in a timely and uniform manner
f) A team may be disqualified by the Contest Director for any activity that jeopardizes the contestsuch as dislodging extension cords unauthorized modification of contest materials distractingbehavior of communicating with other teams
g) Nine ten or eleven problems will be posed So far as possible problems will avoid dependence ondetailed knowledge of a particular applications area or particular contest language Of these problemsat least two will be solvable by a first year computer science student another two will be solvable by asecond year computer science student and rest will determine the winner
h) Contestants will have foods available in their contest room during the contest So they cannot leavethe contest room during the contest without permission The contestants are not allowed tocommunicate with any contestant (Even contestants of his own team) or coach while are outsidethe contest floor
i) Team can bring up to 200 pages of printed materials with them but they can also bring threeadditional books But they are not allowed to bring calculators mobile phones or any machine-readabledevices like CD DVD Pen-drive IPOD MP3MP4 players floppy disks etc
j) With the help of the volunteers the contestants can have printouts of their codes for debuggingpurposes Passing of printed codes to other teams is strictly prohibited
k) The decision of the judges is final
l) Teams should inform the volunteers if they donrsquot get reply from the judges within 10 minutesof submission Volunteers will inform the judges for further action Teams should also notify thevolunteers if they cannot log in into the PC^2 system This sort of complains will not beentertained after the contest
m) If you want to assume that judge data is weaker than what is stated then do it at your ownrisk )
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 320
A
In general small objects have less
areavolume compared to larger objec
volume is 1 So the ratio is 61 and for
the ratio is 610 Given the shape of
of gravitation on it
For simplicity we will assume the fol
problem
1 All ants are described as a box sshaped object is described with three i
which denotes the length width and
So the volume of the ant is ( W L timestimes
2 The density (Mass per unit volume)
the above mentioned ant is also ( Ltimes
weight is g H W L timestimestimes )( (Here
caused by gravitation)
3 When an ant freely falls four sides a
faces at the top and bottom are paral
So the area of the plane facing botto
For any ant the upward force put by t
to the area of the of the bottom face
proved that the downward acceleratio
solely on the value of H (as g is same
Falling AntsInput Standard Inpututput Standard Output
Ants make up 10 of the total world
total biomass of all the ants on Earth is
total biomass of all the people on Eart
the people on Earth when they fall from
die for two reasons
- They have so little mass relative to the
they fall slowly and therefore hav
dissipate when they hit the ground
- Their bodies are tiny deformable tan
absorb blows
impact of gravitation on them because they
ts For example consider a (1x1x1) cube Its s
a (10x10x10) cube the surface area is 600 and
any ants you will have to find out which ant h
lowing things in this
aped object A boxntegers L W and H
height of the object
) H
is 1 So the mass of
) H W times and so the
is the acceleration
re upright and so the
lel with the horizon
is always W Ltimes
e air is proportional
o be specific it is2
gW L timestimes
After some ma
n H
gg f
2minus= So the downward accelerati
or all ants)
animal tissue The
oughly equal to the
h However unlike
a height they do not
ir air resistance that
e little energy to
s well designed to
have more surface
rface area is 6 and
volume is 1000 So
s the highest effect
nipulation it can be
n actually depends
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 420
4
Given the dimension of several ants report the volume of the ant that has the highest downward
acceleration If there is a tie report the one with the largest volume
InputThe input file contains at most 500 test cases The description of each test case is given below
First line of each test case contains an integer T (T le 100) which denotes the total number of ants to
consider Each of the next T lines contains three integers which denote the value of L W and H (1 le L
W H le 50) of an ant respectively
Input is terminated by a line containing a single zero
OutputFor each set of input produce one line of output This line contains the volume of the ant that has the
highest downward acceleration If there is a tie report the ant with the highest volume
Sample Input Output for Sample Input3
3 4 5
12 1 5
20 10 4
3
3 4 5
20 30 5
1 2 4
0
60
3000
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 520
BM and J are playing a game The desc
several digits will be shown There ar
ith
button of a display once the value
displays has one fault in common T
button is broken
Each of these displays can be describ
the number of digits shown by the di
side (we can consider it like a 3-digit
Firstly it limits the number of times
display will be interpreted as a B-ba
numbers shown by the display will b
can press each of the three working
display is shown in Figure 1
Figure 1M and J have N of these displays Ea
playing goes like this
1 M plays first J plays second
2 In each move a player selects
only be selected if it hasnrsquot re
is a digit which can be selec
broken you can not choose thi
3 After a move if the summati
displays is divisible by 3 then
4 If there is no move possible th
Given description of N displays you
optimally Initially every digit of ever
Game of MJInput Standard Inpututput Standard Output
ription of the game is very simple They have a
buttons under each digit of every display If s
of the ith
digit of that display will increase by
e 0th
digit (least significant digit) canrsquot be in
d using two parameters L and B L is the len
play If L is 3 then the display can show thr
umber) B is the base of the display It is impo
you can press a button Secondly the numb
sed number with L digits Suppose B is 8 an
octal numbers and the length of the numbers
(not broken) buttons at most seven (7) times
A display with L = 4 and B = 8 h of the display has its own L and B Now th
fter that they alternate moves
a display Then selects a digit And presses its
ched its limit B-1 already A display can only
ed However since the switch for the rightm
button for any display
n of numbers (After converting it to decimal
he player making that move loses and the other
n the game ends in draw
need to find out the outcome of the game
display is set to 0 (zero)
few displays where
omeone presses the
one Each of these
creased because its
th of the display or
e (3) digits side by
tant in two aspects
er displayed in the
d L is 4 Then the
will be 4 Also you
Example of such a
game M and J are
button A digit can
be selected if there
ost digit is already
base) shown in the
player wins
and J both plays
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 620
6
InputFirst line of input consists of an integer T (T le 100) the number of test cases Each test case starts with
an integer N (0 lt N lt10) the number of displays Next N line each contains two integers L (0 lt L lt 109)
and B (1 lt B lt 109) which are the parameters that describes the i
th display
OutputFor each case print one line ldquoCase X Srdquo where X is the case number S is either ldquoMrdquo ldquoJrdquo or
ldquoDrawrdquo based on the outcome of the game in that case
Sample Input Output for Sample Input3 1 5 2 2 3 2 2 6 1 2 2
Case 1 M
Case 2 J
Case 3 Draw
Explanation
Case 1
00000 =gt 00010 =gt 01010 =gt 01110 =gt 11110 which is 30 in decimal and divisible by 3 So J loses and
M wins However this is one possible valid game sequence But if two players play optimally J will
always lose and thus M will always win
Case 2
(00000) =gt (00010) Sum = 0 + 6 = 6
(00000) =gt (10000) =gt (10010) =gt (11010) Sum = 6 + 6 = 12
(00000) =gt (10000) =gt (10010) =gt (10020) =gt (10030) =gt (10040) =gt (10050) =gt (11050) Sum = 6
+ 30 = 36
In this way in every game sequence M is doomed to reach such a configuration where the sum will be
divisible by 3 Hence in this scenario J will win and M will lose
Case 3
(00) =gt (10) which is 2 in decimal and not divisible by 3 There is no move left So the game ends in a
draw
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 720
C G
General Broken Arrow and Lieutenant
year they fought several wars toget
happily until one day the king of G
Shadow Coder wants to become the
become king of a country at the same
other in the Great Chaos Jam (GCJ) fi
Colonel Dragoon friend of both Bro
war and comes up with a great soluti
into two disjoint sets of cities called
Shadow Coder will rule the rest of th
with these divisions To make peoples
build a sub-country of Gigaland calle
Gigaland so that peoples from set A
and B are disjoint cities might not be
set B Broken Arrow and Shadow Cod
The country of Gigaland consists of
which connects two different cities an
every city is connected to each other
le K le min(N 21)) cities 1 2 hellip K set B
Though the warriors have agreed to
Each city of set A should be incident
be incident to even number (It can
Megaland should be minimum that i
cities of Megaland may or may not be
In terms of graph theory you are give
and B = K+1 K+2 hellip N You ha
each node in A should have odd degreof S is sum of all the edge cost in S
Given N M K and description of M
Megaland
me of ThroneInput Standard Input
Output Standard Output
General Shadow Coder are two great warriors
er like ICPC NCPC etc The peoples of Gi
igaland General Rem (RIP) died Now both
new king of Gigaland As this is not possible
time they leave it to the field of war They d
ld and the winner will become the new king
en Arrow and Shadow Coder wants to avoid
n According to his proposed solution the cou
A and B Broken Arrow will rule the cities i
e cities But the people of Gigaland will get f
remain calm and happy Dragoon gave another
d Megaland that consists of some cities and
nd B can have some access to other cities Th
disjoint between Megaland and set A and bet
r both agreed with the idea of Dragoon
(numbered from 1 to N) cities and M bidirec
each road has a cost to travel Gigaland was b
ith sequence of one or more roads Set A will c
umbered cities of Gigaland and rest N ndash K citi
uild the new sub-country Megaland they ha
o odd number of roads of Megaland and each
e zero also) of roads of Megaland The cost
sum of all the road cost of Megaland should
connected to each other
a weighted graph G = (N M) two set of nod
e to find the minimum cost sub-graph S (subs
e in S and each node in B should have even de
roads of Gigaland find the minimum possible
of Gigaland Every
galand were living
Broken Arrow and
for two persons to
cided to fight each
the blood shedding
try will be divided
n the set of A and
rustrated and angry
proposal They will
onnecting roads of
ugh cities of set A
een Megaland and
ional roads each of
uilt such a way that
onsists of first K (2
s will belong to the
e some conditions
city of set B should
of road system in
be minimized The
s A = 1 2 hellip K
et of edges) where
gree in S Here cost
cost of sub-country
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 820
8
InputInput starts with a positive integer T (T le 250) denoting the number of test cases Each case starts with
three integers N (2 le N le 100) M (N-1 le M le N(N-1)2) and K (2 le K le min(N 21)) Each of the next
M lines contains three integers u v and c (1 le uv le N u ne v 0 lt c lt 10000) meaning that there is a bi-
directional road between city u and v of cost c No two roads will be same Please also note that for 90 of the test cases K is less than 20
OutputFor each test case print the test case number (starting from 1) and the minimum possible cost of
Megaland if it is possible to build the sub-country according to the conditions described above otherwise
print ldquoImpossiblerdquo (without the quotes)
Sample Input Output for Sample Input2
7 7 4
1 7 101 5 1
2 5 2
3 6 3
4 6 1
5 6 4
3 7 8
4 4 3
1 2 1
1 3 1
2 4 1
3 4 1
Case 1 7
Case 2 Impossible
Warning The judge input file is around 25 MB So use faster IO functionsExplanation
For test case 1
In Megaland degree of each node in set A = 1234 is 1 and degree nodes in set B = 5 6 7 are 2 2
and 0 respectively
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 920
D
P
Mr Anderson is in a relationship wit
Andersons phone logs and texts to fin
he decided to put a pattern locker on hi
This pattern locker comes with a 9 dot
several dots to record a pattern The
recorded before If we assume that ea
than a sequence of digits The patter
once
Here is an example of such a pattern l
Even after recording a hard to crack p
that his girlfriend might try all possi
different pattern sequences are possib
recorded in patterns
You have to help Mr Anderson in cou
ttern LockerInput Standard Input
Output Standard Output
a very suspicious and jealous girlfriend She
d out he is up to Feeling that his private spac
s phone
s arranged on a 3x3 square grid by default One
n to unlock the phone one needs to replicat
h dot is assigned a unique number then a patt
locker requires that no digit appears in the
cker and some valid and invalid recorded patte
attern Mr Anderson doesnt feel quite comfor
le sequences to break his pattern He wants t
le for a given grid size minimum and maxim
nting the number of possible such sequences
is always checking
is getting violated
has to drag through
e the same pattern
rn is nothing more
equence more than
rn
able He is worried
o know how many
m numbers of dots
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1020
10
InputThe first line of the input will give the number of test cases T (1 le T le 10000) Then T test cases follow
in separate lines Each test case consists of three numbers L M N separated by a single space in between
two numbers The first number L (1 lt L le 100) denotes the number of rows and columns in the grid The
second number M (1le
Mle
LL) denotes minimum number of dots to be included in a pattern and thethird number N (M le N le LL) denotes the maximum number of dots to be included in the pattern
OutputFor each test case you need to print the test case number X in the format ldquoCase X rdquo This will be
followed by the count of possible sequences for the given grid size minimum and maximum number of
dots in a sequence Since the count can be pretty big you need to print the value of the count modulo
10000000000007 (1 followed by 12 zeros followed by 7)
Sample Input Output for Sample Input2
3 4 9
3 1 9
Case 1 985824
Case 2 986409
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1120
EYou have pearl of 3 types
bull Type 1 pearl can be of color fr
bull Type 2 pearl can be of color fr
bull Type 3 pearl can be of color fr
You have unlimited supply of pearls
But you have 2 more additional constr
bull
The total number of Type 1 anbull The total number of Type 2 an
Given A B X Y and Z calculate ho
they have different length or there is a
InputFirst line of the input contains T (1 le
A B X Y and Z All of these 5 intege
OutputFor each test case output an integer d
huge output the result modulo 100000
Sample Input5
1 1 1 1 1
2 3 1 1 1
1 1 1 2 1
10 10 10 10 10
100 100 100 100 100
earl ChainsInput Standard Inpututput Standard Output
m 1 to X
m X+1 to X+Y
m X+Y+1 to X+Y+Z
of each type and each color You want to buil
ints
Type 3 pearls will be exactly AType 3 pearls will be exactly B
many different pearl chains are possible 2 c
position in which they have different colored p
le 100) the number of test cases Each test cas
rs are between 1 and 1017
inclusive
noting the number of possible pearl chains Si
Output for Sample Inp3
25
5
77069
329672
some pearl chain
ains are different if
arl
contains 5 integers
nce the result is too
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1220
F Two PI
O
Itrsquos a common phenomenon to mix u
that they just look at sky and can tell y
whole way they travelled ldquoFirst we
and so this one is helliprdquo and thus end u
each other and they do not always run
ends up with some ridiculous answer a
The city we are talking about is a sq
Although the city is nice square shape
rail track and it is a straight one
perpendicular to the existing one The
or not they just need location of twconnecting these two stations the line
you have to build the stations in intege
So to sum it up you will be given co-
to give any two distinct integer co-or
co-ordinates may coincide with the gi
Input
First line of input will contain an integ
be a line of four integers X1 Y1 X2
ordinates of two stations on the alread
You may assume that these two points
OutputFor each test case produce one line
integers where the first two integers
integers are the x and y co-ordinate
possible value of S and the line pa
(may not necessarily intersect the
answers you may output any of the
coordinates does not exceed9
102times F
Sample Input2
4 4 5 5
9 0 10 0
oints Revisitednput Standard Inputtput Standard Output
direction when you go to a new place Some
ou which one is north And some dumb people
ere east facing then we turned left then right
with a direction But the roads are not always
from north to south or from east to west So thi
lmost all the times
uare shaped one with vertices at (0 0) (S 0)
one the road network is already messed up
o city corporation decides to build another
do not care if the new track intersects with th
rail stations so that if a rail track is built alowould be perpendicular to the existing rail tr
r co-ordinates
rdinates of two stations on the already existing
inates within the city for building new rail tra
en co-ordinates if you want it to
er T the number of test cases (T le 15000) For
2 (0 le X1 Y1 X2 Y2 le 109) Here (X1 Y1) and
existing rail track
are different and within the city
of output This line contains the case numbe
are the x and y co-ordinate of the first statio
of the second station They should be withi
sing through them must be perpendicular
previous track within the city) Since the
but you have to make sure that absolute va
or details please go through the explanation of t
Output for Sample ICase 1 1 0 0 1
Case 2 10 0 10 2
eople are so clever
try to remember the
then again righthellip
in 90 degrees with
kind of calculation
(S S) and (0 S)
ut there is only one
rail track which is
previous rail track
ng the straight lineck The problem is
rail track you have
ck One of the new
each case there will
(X2 Y2) are the co-
r followed by four
n and the next two
the city for any
o the existing line
re can be multiple
lue of any of these
he sample cases
put
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1320
13
Explanation
First Sample
In the first sample the existing rail track goes through points (4 4) and (5 5) If you establish two new
rail stations at (1 0) and (0 1) the rail track passing through them will be perpendicular to the existingrail track Note if you output something like (5 5) and (6 4) you will get Wrong Answer since if S = 5
point (6 4) will not be within the city But for any value of S such that (4 4) and (5 5) is within the city
points (1 0) and (0 1) will also be within the city
Second Sample
In this case there are many correct answers One of them is (10 0) and (10 2) Note that unlike first
sample here the rail tracks intersect
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1420
G
Watc
Day by day number of Kangaroos is d
Now for the convenience of the spect
ldquoKangaroo appears in Screen 7rdquo an
position of Kangaroos and inform th
screen to display that animal based on
as follows
If the position x is outside the rangeOtherwise the coverage is minimum(
An example will make it clear
Suppose there are four screens coveri
Kangaroo appears at x = 10
First screen has coverage of 3 unit aro
15 ndash 10) = minimum(3 5) = 3
Second screen has coverage of 0 unit
100)
Third screen has coverage of 0 unit
minimum(10 ndash 8 10 ndash 10) = 0
Fourth screen has coverage of 1 unit a
1 11 ndash 10) = 1
ing the KangarooInput Standard Input
Output Standard Output
ecreasing just like tiger whale or lions So I de
a sanctuary where they will live peac
visitors go near them So I planted s
outside the sanctuary For this proble
the sanctuary to be a long line of 10000
The leftmost position is marked with
position with 1000000000 There ar
cameras on this line Each of the camer
(L R) which means that camera coposition L to position R inclusive Each
their associated display screens outside
can see the Kangaroos
ators we announce time to time ldquoKangaroo a
so on I have some employees who contin
system (here position is a marker) The syste
the coverage The coverage of a screen for a
of that screen (ie x lt L or x gt R) then thndash L R ndash x)
ng the range (7 15) (14 100) (8 10) and (1
nd x = 10 Because x = 10 is within (7 15) an
around x = 10 Because x = 10 does not belo
around x = 10 Because though x = 10 is
round x = 10 Because x = 10 is within (1 11)
cided to make them
fully I do not let
me display screen
you may assume
0000 unit distance
and the rightmost
at most 100000
as is described with
vers a range fromof the cameras has
where the visitors
pears in Screen 3rdquo
ously monitor the
m chooses the best
osition x is defined
coverage is zero
11) Now say one
minimum(10 ndash 7
g to the range (14
within (8 10) but
and minimum(10 ndash
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1520
15
So which one is better Obviously the first one as it has the maximum coverage
So you are given the ranges of the screens and the positions the kangaroo appears For each position of
the Kangaroo you are to tell me the maximum coverage you can have with any of the screens
Input
First line of the test file contains T (T le 3) number of test cases Hence T cases follow For each case
you are given N M in the first line N is the number of screens and M is the number of Kangaroo
appearance ( 1 le N M le 100000) In the next N lines you are given the range of screens L R ( 0 le L le R
le 1000000000 ) Next M lines contain the position of the Kangaroo- an integer x (0 le x le 1000000000)
OutputFor each case print the case number Hence print M lines ith containing the maximum coverage you can
have around irsquoth Kangaroo
Sample Input Output for Sample Input1
3 2
7 15
14 100
1 11
10
120
Case 1
3
0
Warning The judge input file is around 6 MB So use faster IO functions
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1620
HGiven an integer N find how many pa
A le N
Here gcd (A B) means the greatest c
of the bitwise xor operation on the bin
InputThe first line of the input contains a
following T lines contain an integer N
OutputFor each test case print the case nu
input) followed by a space and then th
Sample Input2
7
20000000
Explanation
Sample 1
For N=7 there are four valid pairs (3
GCD XORInput Standard Inpututput Standard Output
irs (A B) are there such that gcd (A B) = A x
mmon divisor of the numbers A and B And
ary representation of A and B
n integer T(T le 10000) denoting the number
1 le N le 30000000)
ber first in the format Case X (here X
answer for that case
Output for Sample InpCase 1 4
Case 2 34866117
2) (5 4) (6 4) and (7 6)
or B where 1 le B le
xor B is the value
of test cases The
is the serial of the
ut
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1720
INatasha always mixes up things in her
classical problem - finding shortest p
that in another class the professor t
looking but does very different things
to the Primrsquos algorithm (actually w
Pseudocode of her algorithm looks as
FiascoInput Standard Input
Output Standard Output
algorithm classes Last week Prof Chhaya Mu
th to all nodes from a specific node of a wei
aught them Primrsquos and Dijkstrarsquos algorithms
Always confused poor Natasha submitted so
should call it Natasharsquos algorithm) she did
ollows
thy gave the class a
hted graph Before
which are similar
ething very similar
rsquot test it properly
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1820
18
After submission she showed the code to a friend who is good at algorithms That friend immediately
found the flaw Natasha was really terrified and started to cry Then there came the guys the guys who
liked her They jumped at the opportunity and got hold of the dataset to be used to test the solutions Your
friend Rehan is one of those guys He really wanted to impress Natasha He asked you to change the
dataset in such a way that Natasharsquos algorithm gives the right result After the change Rehan will
somehow be able to put the modified data with the old timestamp Rehan told you that
1 The dataset has T test cases
2 Each case contains a connected weighted undirected graph with n nodes and m edges
3 Each case will contain a source node source
4 Edge weights are positive and distinct
To avoid suspicion Rehan asked you not to change which vertices the edges connect or the overall set of
edge weights You may only reorder which weights are assigned to which edges
InputThe first line of the input denotes the number of datasets T (1 le T le 15) T sets of case will follow Eachcase will start with a triplet of numbers n (2 le n le 2500) m (1 le m le 25000) and source (1 le source le
n) - the number of nodes the number of edges and the starting node respectively Each of the next m
lines will contain a triplet of numbers (u v w) meaning that there is an edge between node u and node v
with weight w (1 le w le m) Nodes are numbered from 1 to n It is guaranteed that there is no duplicate or
self-edges in the input and the graph is connected In each given graph all edge weights will be distinct
OutputFor each set of input print one set of output First line of a set should be of the format ldquoCase Xrdquo
where X is the case number Then print each edge triplet - one triplet ( u v and w) in each line separated
by a single space The edges should be printed in the order given in the input If there is more than one
solution to a dataset any one of them will do
Sample Input Output for Sample Input1
7 9 5
2 4 2
1 4 8
7 2 6
3 4 7
5 7 5
7 3 9
6 1 1
6 3 4
5 6 3
Case 1
2 4 7
1 4 9
7 2 3
3 4 8
5 7 1
7 3 4
6 1 5
6 3 6
5 6 2
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1920
J Drom
Lets first define some terms
bull A string is palindromic if it re
madam and toot
bull A string is a dromicpalin if we
dromicpalin string is mmaad becau
palindrome
bull A substring is any contiguous
a c i icp acmicpc but acpc
empty substring so that means there a
Given a string you have to figure out
InputThe first line of input is an integer T
containing a string The strings will c
be positive and not greater than 1000
OutputFor each case first output the case n
Follow the samples for exact format
Sample Input4
acmicpc
aaaaa
isyoursolutionfastenough
abbabababbaba
cpalin SubstringsInput Standard Input
Output Standard Output
ds the same forward and backward Examples
can rearrange its letters to make it a palindro
e we can rearrange the letters to make it
equence of characters of a string Some substri
is not a substring For this problem we are
e2
)1( +nn substrings of a string of length n
ow many of its substrings are dromicpalin
(T lt 100) indicating the number of test cases
ntain only lowercase letters [a - z] The lengt
mber followed by the number of substrings t
Output for Sample InpCase 1 8
Case 2 15
Case 3 24
Case 4 67
of palindromes are
e An example of a
adam which is a
ngs of acmicpc are
not considering the
Each case is a line
of each string will
at are dromicpalin
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 2020
KCan you fill an (abc) cuboid with e
cell inside the (abc) cuboid should
dimensions and for each positive integ
a (223) cuboid can be filled with fi
filled with twelve (111) cubes
To make this problem slightly more di
filled by another cube Your job is to f
the cuboid can be filled by exactly n c
InputThere will be at most 300 test cases
abc le 125 0 le m lt abc)
Each of the next m lines contains thre
(x y z) is already filled
No cell will be mentioned twice Ther
The input is terminated by a line conta
OutputFor each test case print the case num
single space before each number in the
Sample Input2 2 3 0
2 2 3 2
1 1 1
2 2 3
0 0 0 0
ill the CuboidInput Standard Input
Output Standard Output
actly n cubes The cubes may touch but cann
be covered by exactly one cube You may us
er p you can use as many (ppp) cubes as yo
e cubes four (111) cubes and one (222)
fficult m of the cells in the cuboid are already
ind out the possible values of n such that the re
ubes
ach test case begins with four integers a b c
integers x y z (1 le x le a 1 le y le b 1 le z le c)
will be at least one non-filled cell
ining four zeroes
ber and the list of possible answers in increasi
output Look at the output for sample input for
Output for Sample InpCase 1 5 12
Case 2 10
ot overlap and each
cubes of different
like For example
cube It can also be
illed and cannot be
maining cells inside
(2 le a b c le 20
that means the cell
ng order There is a
details
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 320
A
In general small objects have less
areavolume compared to larger objec
volume is 1 So the ratio is 61 and for
the ratio is 610 Given the shape of
of gravitation on it
For simplicity we will assume the fol
problem
1 All ants are described as a box sshaped object is described with three i
which denotes the length width and
So the volume of the ant is ( W L timestimes
2 The density (Mass per unit volume)
the above mentioned ant is also ( Ltimes
weight is g H W L timestimestimes )( (Here
caused by gravitation)
3 When an ant freely falls four sides a
faces at the top and bottom are paral
So the area of the plane facing botto
For any ant the upward force put by t
to the area of the of the bottom face
proved that the downward acceleratio
solely on the value of H (as g is same
Falling AntsInput Standard Inpututput Standard Output
Ants make up 10 of the total world
total biomass of all the ants on Earth is
total biomass of all the people on Eart
the people on Earth when they fall from
die for two reasons
- They have so little mass relative to the
they fall slowly and therefore hav
dissipate when they hit the ground
- Their bodies are tiny deformable tan
absorb blows
impact of gravitation on them because they
ts For example consider a (1x1x1) cube Its s
a (10x10x10) cube the surface area is 600 and
any ants you will have to find out which ant h
lowing things in this
aped object A boxntegers L W and H
height of the object
) H
is 1 So the mass of
) H W times and so the
is the acceleration
re upright and so the
lel with the horizon
is always W Ltimes
e air is proportional
o be specific it is2
gW L timestimes
After some ma
n H
gg f
2minus= So the downward accelerati
or all ants)
animal tissue The
oughly equal to the
h However unlike
a height they do not
ir air resistance that
e little energy to
s well designed to
have more surface
rface area is 6 and
volume is 1000 So
s the highest effect
nipulation it can be
n actually depends
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 420
4
Given the dimension of several ants report the volume of the ant that has the highest downward
acceleration If there is a tie report the one with the largest volume
InputThe input file contains at most 500 test cases The description of each test case is given below
First line of each test case contains an integer T (T le 100) which denotes the total number of ants to
consider Each of the next T lines contains three integers which denote the value of L W and H (1 le L
W H le 50) of an ant respectively
Input is terminated by a line containing a single zero
OutputFor each set of input produce one line of output This line contains the volume of the ant that has the
highest downward acceleration If there is a tie report the ant with the highest volume
Sample Input Output for Sample Input3
3 4 5
12 1 5
20 10 4
3
3 4 5
20 30 5
1 2 4
0
60
3000
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 520
BM and J are playing a game The desc
several digits will be shown There ar
ith
button of a display once the value
displays has one fault in common T
button is broken
Each of these displays can be describ
the number of digits shown by the di
side (we can consider it like a 3-digit
Firstly it limits the number of times
display will be interpreted as a B-ba
numbers shown by the display will b
can press each of the three working
display is shown in Figure 1
Figure 1M and J have N of these displays Ea
playing goes like this
1 M plays first J plays second
2 In each move a player selects
only be selected if it hasnrsquot re
is a digit which can be selec
broken you can not choose thi
3 After a move if the summati
displays is divisible by 3 then
4 If there is no move possible th
Given description of N displays you
optimally Initially every digit of ever
Game of MJInput Standard Inpututput Standard Output
ription of the game is very simple They have a
buttons under each digit of every display If s
of the ith
digit of that display will increase by
e 0th
digit (least significant digit) canrsquot be in
d using two parameters L and B L is the len
play If L is 3 then the display can show thr
umber) B is the base of the display It is impo
you can press a button Secondly the numb
sed number with L digits Suppose B is 8 an
octal numbers and the length of the numbers
(not broken) buttons at most seven (7) times
A display with L = 4 and B = 8 h of the display has its own L and B Now th
fter that they alternate moves
a display Then selects a digit And presses its
ched its limit B-1 already A display can only
ed However since the switch for the rightm
button for any display
n of numbers (After converting it to decimal
he player making that move loses and the other
n the game ends in draw
need to find out the outcome of the game
display is set to 0 (zero)
few displays where
omeone presses the
one Each of these
creased because its
th of the display or
e (3) digits side by
tant in two aspects
er displayed in the
d L is 4 Then the
will be 4 Also you
Example of such a
game M and J are
button A digit can
be selected if there
ost digit is already
base) shown in the
player wins
and J both plays
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 620
6
InputFirst line of input consists of an integer T (T le 100) the number of test cases Each test case starts with
an integer N (0 lt N lt10) the number of displays Next N line each contains two integers L (0 lt L lt 109)
and B (1 lt B lt 109) which are the parameters that describes the i
th display
OutputFor each case print one line ldquoCase X Srdquo where X is the case number S is either ldquoMrdquo ldquoJrdquo or
ldquoDrawrdquo based on the outcome of the game in that case
Sample Input Output for Sample Input3 1 5 2 2 3 2 2 6 1 2 2
Case 1 M
Case 2 J
Case 3 Draw
Explanation
Case 1
00000 =gt 00010 =gt 01010 =gt 01110 =gt 11110 which is 30 in decimal and divisible by 3 So J loses and
M wins However this is one possible valid game sequence But if two players play optimally J will
always lose and thus M will always win
Case 2
(00000) =gt (00010) Sum = 0 + 6 = 6
(00000) =gt (10000) =gt (10010) =gt (11010) Sum = 6 + 6 = 12
(00000) =gt (10000) =gt (10010) =gt (10020) =gt (10030) =gt (10040) =gt (10050) =gt (11050) Sum = 6
+ 30 = 36
In this way in every game sequence M is doomed to reach such a configuration where the sum will be
divisible by 3 Hence in this scenario J will win and M will lose
Case 3
(00) =gt (10) which is 2 in decimal and not divisible by 3 There is no move left So the game ends in a
draw
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 720
C G
General Broken Arrow and Lieutenant
year they fought several wars toget
happily until one day the king of G
Shadow Coder wants to become the
become king of a country at the same
other in the Great Chaos Jam (GCJ) fi
Colonel Dragoon friend of both Bro
war and comes up with a great soluti
into two disjoint sets of cities called
Shadow Coder will rule the rest of th
with these divisions To make peoples
build a sub-country of Gigaland calle
Gigaland so that peoples from set A
and B are disjoint cities might not be
set B Broken Arrow and Shadow Cod
The country of Gigaland consists of
which connects two different cities an
every city is connected to each other
le K le min(N 21)) cities 1 2 hellip K set B
Though the warriors have agreed to
Each city of set A should be incident
be incident to even number (It can
Megaland should be minimum that i
cities of Megaland may or may not be
In terms of graph theory you are give
and B = K+1 K+2 hellip N You ha
each node in A should have odd degreof S is sum of all the edge cost in S
Given N M K and description of M
Megaland
me of ThroneInput Standard Input
Output Standard Output
General Shadow Coder are two great warriors
er like ICPC NCPC etc The peoples of Gi
igaland General Rem (RIP) died Now both
new king of Gigaland As this is not possible
time they leave it to the field of war They d
ld and the winner will become the new king
en Arrow and Shadow Coder wants to avoid
n According to his proposed solution the cou
A and B Broken Arrow will rule the cities i
e cities But the people of Gigaland will get f
remain calm and happy Dragoon gave another
d Megaland that consists of some cities and
nd B can have some access to other cities Th
disjoint between Megaland and set A and bet
r both agreed with the idea of Dragoon
(numbered from 1 to N) cities and M bidirec
each road has a cost to travel Gigaland was b
ith sequence of one or more roads Set A will c
umbered cities of Gigaland and rest N ndash K citi
uild the new sub-country Megaland they ha
o odd number of roads of Megaland and each
e zero also) of roads of Megaland The cost
sum of all the road cost of Megaland should
connected to each other
a weighted graph G = (N M) two set of nod
e to find the minimum cost sub-graph S (subs
e in S and each node in B should have even de
roads of Gigaland find the minimum possible
of Gigaland Every
galand were living
Broken Arrow and
for two persons to
cided to fight each
the blood shedding
try will be divided
n the set of A and
rustrated and angry
proposal They will
onnecting roads of
ugh cities of set A
een Megaland and
ional roads each of
uilt such a way that
onsists of first K (2
s will belong to the
e some conditions
city of set B should
of road system in
be minimized The
s A = 1 2 hellip K
et of edges) where
gree in S Here cost
cost of sub-country
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 820
8
InputInput starts with a positive integer T (T le 250) denoting the number of test cases Each case starts with
three integers N (2 le N le 100) M (N-1 le M le N(N-1)2) and K (2 le K le min(N 21)) Each of the next
M lines contains three integers u v and c (1 le uv le N u ne v 0 lt c lt 10000) meaning that there is a bi-
directional road between city u and v of cost c No two roads will be same Please also note that for 90 of the test cases K is less than 20
OutputFor each test case print the test case number (starting from 1) and the minimum possible cost of
Megaland if it is possible to build the sub-country according to the conditions described above otherwise
print ldquoImpossiblerdquo (without the quotes)
Sample Input Output for Sample Input2
7 7 4
1 7 101 5 1
2 5 2
3 6 3
4 6 1
5 6 4
3 7 8
4 4 3
1 2 1
1 3 1
2 4 1
3 4 1
Case 1 7
Case 2 Impossible
Warning The judge input file is around 25 MB So use faster IO functionsExplanation
For test case 1
In Megaland degree of each node in set A = 1234 is 1 and degree nodes in set B = 5 6 7 are 2 2
and 0 respectively
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 920
D
P
Mr Anderson is in a relationship wit
Andersons phone logs and texts to fin
he decided to put a pattern locker on hi
This pattern locker comes with a 9 dot
several dots to record a pattern The
recorded before If we assume that ea
than a sequence of digits The patter
once
Here is an example of such a pattern l
Even after recording a hard to crack p
that his girlfriend might try all possi
different pattern sequences are possib
recorded in patterns
You have to help Mr Anderson in cou
ttern LockerInput Standard Input
Output Standard Output
a very suspicious and jealous girlfriend She
d out he is up to Feeling that his private spac
s phone
s arranged on a 3x3 square grid by default One
n to unlock the phone one needs to replicat
h dot is assigned a unique number then a patt
locker requires that no digit appears in the
cker and some valid and invalid recorded patte
attern Mr Anderson doesnt feel quite comfor
le sequences to break his pattern He wants t
le for a given grid size minimum and maxim
nting the number of possible such sequences
is always checking
is getting violated
has to drag through
e the same pattern
rn is nothing more
equence more than
rn
able He is worried
o know how many
m numbers of dots
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1020
10
InputThe first line of the input will give the number of test cases T (1 le T le 10000) Then T test cases follow
in separate lines Each test case consists of three numbers L M N separated by a single space in between
two numbers The first number L (1 lt L le 100) denotes the number of rows and columns in the grid The
second number M (1le
Mle
LL) denotes minimum number of dots to be included in a pattern and thethird number N (M le N le LL) denotes the maximum number of dots to be included in the pattern
OutputFor each test case you need to print the test case number X in the format ldquoCase X rdquo This will be
followed by the count of possible sequences for the given grid size minimum and maximum number of
dots in a sequence Since the count can be pretty big you need to print the value of the count modulo
10000000000007 (1 followed by 12 zeros followed by 7)
Sample Input Output for Sample Input2
3 4 9
3 1 9
Case 1 985824
Case 2 986409
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1120
EYou have pearl of 3 types
bull Type 1 pearl can be of color fr
bull Type 2 pearl can be of color fr
bull Type 3 pearl can be of color fr
You have unlimited supply of pearls
But you have 2 more additional constr
bull
The total number of Type 1 anbull The total number of Type 2 an
Given A B X Y and Z calculate ho
they have different length or there is a
InputFirst line of the input contains T (1 le
A B X Y and Z All of these 5 intege
OutputFor each test case output an integer d
huge output the result modulo 100000
Sample Input5
1 1 1 1 1
2 3 1 1 1
1 1 1 2 1
10 10 10 10 10
100 100 100 100 100
earl ChainsInput Standard Inpututput Standard Output
m 1 to X
m X+1 to X+Y
m X+Y+1 to X+Y+Z
of each type and each color You want to buil
ints
Type 3 pearls will be exactly AType 3 pearls will be exactly B
many different pearl chains are possible 2 c
position in which they have different colored p
le 100) the number of test cases Each test cas
rs are between 1 and 1017
inclusive
noting the number of possible pearl chains Si
Output for Sample Inp3
25
5
77069
329672
some pearl chain
ains are different if
arl
contains 5 integers
nce the result is too
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1220
F Two PI
O
Itrsquos a common phenomenon to mix u
that they just look at sky and can tell y
whole way they travelled ldquoFirst we
and so this one is helliprdquo and thus end u
each other and they do not always run
ends up with some ridiculous answer a
The city we are talking about is a sq
Although the city is nice square shape
rail track and it is a straight one
perpendicular to the existing one The
or not they just need location of twconnecting these two stations the line
you have to build the stations in intege
So to sum it up you will be given co-
to give any two distinct integer co-or
co-ordinates may coincide with the gi
Input
First line of input will contain an integ
be a line of four integers X1 Y1 X2
ordinates of two stations on the alread
You may assume that these two points
OutputFor each test case produce one line
integers where the first two integers
integers are the x and y co-ordinate
possible value of S and the line pa
(may not necessarily intersect the
answers you may output any of the
coordinates does not exceed9
102times F
Sample Input2
4 4 5 5
9 0 10 0
oints Revisitednput Standard Inputtput Standard Output
direction when you go to a new place Some
ou which one is north And some dumb people
ere east facing then we turned left then right
with a direction But the roads are not always
from north to south or from east to west So thi
lmost all the times
uare shaped one with vertices at (0 0) (S 0)
one the road network is already messed up
o city corporation decides to build another
do not care if the new track intersects with th
rail stations so that if a rail track is built alowould be perpendicular to the existing rail tr
r co-ordinates
rdinates of two stations on the already existing
inates within the city for building new rail tra
en co-ordinates if you want it to
er T the number of test cases (T le 15000) For
2 (0 le X1 Y1 X2 Y2 le 109) Here (X1 Y1) and
existing rail track
are different and within the city
of output This line contains the case numbe
are the x and y co-ordinate of the first statio
of the second station They should be withi
sing through them must be perpendicular
previous track within the city) Since the
but you have to make sure that absolute va
or details please go through the explanation of t
Output for Sample ICase 1 1 0 0 1
Case 2 10 0 10 2
eople are so clever
try to remember the
then again righthellip
in 90 degrees with
kind of calculation
(S S) and (0 S)
ut there is only one
rail track which is
previous rail track
ng the straight lineck The problem is
rail track you have
ck One of the new
each case there will
(X2 Y2) are the co-
r followed by four
n and the next two
the city for any
o the existing line
re can be multiple
lue of any of these
he sample cases
put
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1320
13
Explanation
First Sample
In the first sample the existing rail track goes through points (4 4) and (5 5) If you establish two new
rail stations at (1 0) and (0 1) the rail track passing through them will be perpendicular to the existingrail track Note if you output something like (5 5) and (6 4) you will get Wrong Answer since if S = 5
point (6 4) will not be within the city But for any value of S such that (4 4) and (5 5) is within the city
points (1 0) and (0 1) will also be within the city
Second Sample
In this case there are many correct answers One of them is (10 0) and (10 2) Note that unlike first
sample here the rail tracks intersect
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1420
G
Watc
Day by day number of Kangaroos is d
Now for the convenience of the spect
ldquoKangaroo appears in Screen 7rdquo an
position of Kangaroos and inform th
screen to display that animal based on
as follows
If the position x is outside the rangeOtherwise the coverage is minimum(
An example will make it clear
Suppose there are four screens coveri
Kangaroo appears at x = 10
First screen has coverage of 3 unit aro
15 ndash 10) = minimum(3 5) = 3
Second screen has coverage of 0 unit
100)
Third screen has coverage of 0 unit
minimum(10 ndash 8 10 ndash 10) = 0
Fourth screen has coverage of 1 unit a
1 11 ndash 10) = 1
ing the KangarooInput Standard Input
Output Standard Output
ecreasing just like tiger whale or lions So I de
a sanctuary where they will live peac
visitors go near them So I planted s
outside the sanctuary For this proble
the sanctuary to be a long line of 10000
The leftmost position is marked with
position with 1000000000 There ar
cameras on this line Each of the camer
(L R) which means that camera coposition L to position R inclusive Each
their associated display screens outside
can see the Kangaroos
ators we announce time to time ldquoKangaroo a
so on I have some employees who contin
system (here position is a marker) The syste
the coverage The coverage of a screen for a
of that screen (ie x lt L or x gt R) then thndash L R ndash x)
ng the range (7 15) (14 100) (8 10) and (1
nd x = 10 Because x = 10 is within (7 15) an
around x = 10 Because x = 10 does not belo
around x = 10 Because though x = 10 is
round x = 10 Because x = 10 is within (1 11)
cided to make them
fully I do not let
me display screen
you may assume
0000 unit distance
and the rightmost
at most 100000
as is described with
vers a range fromof the cameras has
where the visitors
pears in Screen 3rdquo
ously monitor the
m chooses the best
osition x is defined
coverage is zero
11) Now say one
minimum(10 ndash 7
g to the range (14
within (8 10) but
and minimum(10 ndash
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1520
15
So which one is better Obviously the first one as it has the maximum coverage
So you are given the ranges of the screens and the positions the kangaroo appears For each position of
the Kangaroo you are to tell me the maximum coverage you can have with any of the screens
Input
First line of the test file contains T (T le 3) number of test cases Hence T cases follow For each case
you are given N M in the first line N is the number of screens and M is the number of Kangaroo
appearance ( 1 le N M le 100000) In the next N lines you are given the range of screens L R ( 0 le L le R
le 1000000000 ) Next M lines contain the position of the Kangaroo- an integer x (0 le x le 1000000000)
OutputFor each case print the case number Hence print M lines ith containing the maximum coverage you can
have around irsquoth Kangaroo
Sample Input Output for Sample Input1
3 2
7 15
14 100
1 11
10
120
Case 1
3
0
Warning The judge input file is around 6 MB So use faster IO functions
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1620
HGiven an integer N find how many pa
A le N
Here gcd (A B) means the greatest c
of the bitwise xor operation on the bin
InputThe first line of the input contains a
following T lines contain an integer N
OutputFor each test case print the case nu
input) followed by a space and then th
Sample Input2
7
20000000
Explanation
Sample 1
For N=7 there are four valid pairs (3
GCD XORInput Standard Inpututput Standard Output
irs (A B) are there such that gcd (A B) = A x
mmon divisor of the numbers A and B And
ary representation of A and B
n integer T(T le 10000) denoting the number
1 le N le 30000000)
ber first in the format Case X (here X
answer for that case
Output for Sample InpCase 1 4
Case 2 34866117
2) (5 4) (6 4) and (7 6)
or B where 1 le B le
xor B is the value
of test cases The
is the serial of the
ut
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1720
INatasha always mixes up things in her
classical problem - finding shortest p
that in another class the professor t
looking but does very different things
to the Primrsquos algorithm (actually w
Pseudocode of her algorithm looks as
FiascoInput Standard Input
Output Standard Output
algorithm classes Last week Prof Chhaya Mu
th to all nodes from a specific node of a wei
aught them Primrsquos and Dijkstrarsquos algorithms
Always confused poor Natasha submitted so
should call it Natasharsquos algorithm) she did
ollows
thy gave the class a
hted graph Before
which are similar
ething very similar
rsquot test it properly
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1820
18
After submission she showed the code to a friend who is good at algorithms That friend immediately
found the flaw Natasha was really terrified and started to cry Then there came the guys the guys who
liked her They jumped at the opportunity and got hold of the dataset to be used to test the solutions Your
friend Rehan is one of those guys He really wanted to impress Natasha He asked you to change the
dataset in such a way that Natasharsquos algorithm gives the right result After the change Rehan will
somehow be able to put the modified data with the old timestamp Rehan told you that
1 The dataset has T test cases
2 Each case contains a connected weighted undirected graph with n nodes and m edges
3 Each case will contain a source node source
4 Edge weights are positive and distinct
To avoid suspicion Rehan asked you not to change which vertices the edges connect or the overall set of
edge weights You may only reorder which weights are assigned to which edges
InputThe first line of the input denotes the number of datasets T (1 le T le 15) T sets of case will follow Eachcase will start with a triplet of numbers n (2 le n le 2500) m (1 le m le 25000) and source (1 le source le
n) - the number of nodes the number of edges and the starting node respectively Each of the next m
lines will contain a triplet of numbers (u v w) meaning that there is an edge between node u and node v
with weight w (1 le w le m) Nodes are numbered from 1 to n It is guaranteed that there is no duplicate or
self-edges in the input and the graph is connected In each given graph all edge weights will be distinct
OutputFor each set of input print one set of output First line of a set should be of the format ldquoCase Xrdquo
where X is the case number Then print each edge triplet - one triplet ( u v and w) in each line separated
by a single space The edges should be printed in the order given in the input If there is more than one
solution to a dataset any one of them will do
Sample Input Output for Sample Input1
7 9 5
2 4 2
1 4 8
7 2 6
3 4 7
5 7 5
7 3 9
6 1 1
6 3 4
5 6 3
Case 1
2 4 7
1 4 9
7 2 3
3 4 8
5 7 1
7 3 4
6 1 5
6 3 6
5 6 2
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1920
J Drom
Lets first define some terms
bull A string is palindromic if it re
madam and toot
bull A string is a dromicpalin if we
dromicpalin string is mmaad becau
palindrome
bull A substring is any contiguous
a c i icp acmicpc but acpc
empty substring so that means there a
Given a string you have to figure out
InputThe first line of input is an integer T
containing a string The strings will c
be positive and not greater than 1000
OutputFor each case first output the case n
Follow the samples for exact format
Sample Input4
acmicpc
aaaaa
isyoursolutionfastenough
abbabababbaba
cpalin SubstringsInput Standard Input
Output Standard Output
ds the same forward and backward Examples
can rearrange its letters to make it a palindro
e we can rearrange the letters to make it
equence of characters of a string Some substri
is not a substring For this problem we are
e2
)1( +nn substrings of a string of length n
ow many of its substrings are dromicpalin
(T lt 100) indicating the number of test cases
ntain only lowercase letters [a - z] The lengt
mber followed by the number of substrings t
Output for Sample InpCase 1 8
Case 2 15
Case 3 24
Case 4 67
of palindromes are
e An example of a
adam which is a
ngs of acmicpc are
not considering the
Each case is a line
of each string will
at are dromicpalin
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 2020
KCan you fill an (abc) cuboid with e
cell inside the (abc) cuboid should
dimensions and for each positive integ
a (223) cuboid can be filled with fi
filled with twelve (111) cubes
To make this problem slightly more di
filled by another cube Your job is to f
the cuboid can be filled by exactly n c
InputThere will be at most 300 test cases
abc le 125 0 le m lt abc)
Each of the next m lines contains thre
(x y z) is already filled
No cell will be mentioned twice Ther
The input is terminated by a line conta
OutputFor each test case print the case num
single space before each number in the
Sample Input2 2 3 0
2 2 3 2
1 1 1
2 2 3
0 0 0 0
ill the CuboidInput Standard Input
Output Standard Output
actly n cubes The cubes may touch but cann
be covered by exactly one cube You may us
er p you can use as many (ppp) cubes as yo
e cubes four (111) cubes and one (222)
fficult m of the cells in the cuboid are already
ind out the possible values of n such that the re
ubes
ach test case begins with four integers a b c
integers x y z (1 le x le a 1 le y le b 1 le z le c)
will be at least one non-filled cell
ining four zeroes
ber and the list of possible answers in increasi
output Look at the output for sample input for
Output for Sample InpCase 1 5 12
Case 2 10
ot overlap and each
cubes of different
like For example
cube It can also be
illed and cannot be
maining cells inside
(2 le a b c le 20
that means the cell
ng order There is a
details
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 420
4
Given the dimension of several ants report the volume of the ant that has the highest downward
acceleration If there is a tie report the one with the largest volume
InputThe input file contains at most 500 test cases The description of each test case is given below
First line of each test case contains an integer T (T le 100) which denotes the total number of ants to
consider Each of the next T lines contains three integers which denote the value of L W and H (1 le L
W H le 50) of an ant respectively
Input is terminated by a line containing a single zero
OutputFor each set of input produce one line of output This line contains the volume of the ant that has the
highest downward acceleration If there is a tie report the ant with the highest volume
Sample Input Output for Sample Input3
3 4 5
12 1 5
20 10 4
3
3 4 5
20 30 5
1 2 4
0
60
3000
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 520
BM and J are playing a game The desc
several digits will be shown There ar
ith
button of a display once the value
displays has one fault in common T
button is broken
Each of these displays can be describ
the number of digits shown by the di
side (we can consider it like a 3-digit
Firstly it limits the number of times
display will be interpreted as a B-ba
numbers shown by the display will b
can press each of the three working
display is shown in Figure 1
Figure 1M and J have N of these displays Ea
playing goes like this
1 M plays first J plays second
2 In each move a player selects
only be selected if it hasnrsquot re
is a digit which can be selec
broken you can not choose thi
3 After a move if the summati
displays is divisible by 3 then
4 If there is no move possible th
Given description of N displays you
optimally Initially every digit of ever
Game of MJInput Standard Inpututput Standard Output
ription of the game is very simple They have a
buttons under each digit of every display If s
of the ith
digit of that display will increase by
e 0th
digit (least significant digit) canrsquot be in
d using two parameters L and B L is the len
play If L is 3 then the display can show thr
umber) B is the base of the display It is impo
you can press a button Secondly the numb
sed number with L digits Suppose B is 8 an
octal numbers and the length of the numbers
(not broken) buttons at most seven (7) times
A display with L = 4 and B = 8 h of the display has its own L and B Now th
fter that they alternate moves
a display Then selects a digit And presses its
ched its limit B-1 already A display can only
ed However since the switch for the rightm
button for any display
n of numbers (After converting it to decimal
he player making that move loses and the other
n the game ends in draw
need to find out the outcome of the game
display is set to 0 (zero)
few displays where
omeone presses the
one Each of these
creased because its
th of the display or
e (3) digits side by
tant in two aspects
er displayed in the
d L is 4 Then the
will be 4 Also you
Example of such a
game M and J are
button A digit can
be selected if there
ost digit is already
base) shown in the
player wins
and J both plays
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 620
6
InputFirst line of input consists of an integer T (T le 100) the number of test cases Each test case starts with
an integer N (0 lt N lt10) the number of displays Next N line each contains two integers L (0 lt L lt 109)
and B (1 lt B lt 109) which are the parameters that describes the i
th display
OutputFor each case print one line ldquoCase X Srdquo where X is the case number S is either ldquoMrdquo ldquoJrdquo or
ldquoDrawrdquo based on the outcome of the game in that case
Sample Input Output for Sample Input3 1 5 2 2 3 2 2 6 1 2 2
Case 1 M
Case 2 J
Case 3 Draw
Explanation
Case 1
00000 =gt 00010 =gt 01010 =gt 01110 =gt 11110 which is 30 in decimal and divisible by 3 So J loses and
M wins However this is one possible valid game sequence But if two players play optimally J will
always lose and thus M will always win
Case 2
(00000) =gt (00010) Sum = 0 + 6 = 6
(00000) =gt (10000) =gt (10010) =gt (11010) Sum = 6 + 6 = 12
(00000) =gt (10000) =gt (10010) =gt (10020) =gt (10030) =gt (10040) =gt (10050) =gt (11050) Sum = 6
+ 30 = 36
In this way in every game sequence M is doomed to reach such a configuration where the sum will be
divisible by 3 Hence in this scenario J will win and M will lose
Case 3
(00) =gt (10) which is 2 in decimal and not divisible by 3 There is no move left So the game ends in a
draw
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 720
C G
General Broken Arrow and Lieutenant
year they fought several wars toget
happily until one day the king of G
Shadow Coder wants to become the
become king of a country at the same
other in the Great Chaos Jam (GCJ) fi
Colonel Dragoon friend of both Bro
war and comes up with a great soluti
into two disjoint sets of cities called
Shadow Coder will rule the rest of th
with these divisions To make peoples
build a sub-country of Gigaland calle
Gigaland so that peoples from set A
and B are disjoint cities might not be
set B Broken Arrow and Shadow Cod
The country of Gigaland consists of
which connects two different cities an
every city is connected to each other
le K le min(N 21)) cities 1 2 hellip K set B
Though the warriors have agreed to
Each city of set A should be incident
be incident to even number (It can
Megaland should be minimum that i
cities of Megaland may or may not be
In terms of graph theory you are give
and B = K+1 K+2 hellip N You ha
each node in A should have odd degreof S is sum of all the edge cost in S
Given N M K and description of M
Megaland
me of ThroneInput Standard Input
Output Standard Output
General Shadow Coder are two great warriors
er like ICPC NCPC etc The peoples of Gi
igaland General Rem (RIP) died Now both
new king of Gigaland As this is not possible
time they leave it to the field of war They d
ld and the winner will become the new king
en Arrow and Shadow Coder wants to avoid
n According to his proposed solution the cou
A and B Broken Arrow will rule the cities i
e cities But the people of Gigaland will get f
remain calm and happy Dragoon gave another
d Megaland that consists of some cities and
nd B can have some access to other cities Th
disjoint between Megaland and set A and bet
r both agreed with the idea of Dragoon
(numbered from 1 to N) cities and M bidirec
each road has a cost to travel Gigaland was b
ith sequence of one or more roads Set A will c
umbered cities of Gigaland and rest N ndash K citi
uild the new sub-country Megaland they ha
o odd number of roads of Megaland and each
e zero also) of roads of Megaland The cost
sum of all the road cost of Megaland should
connected to each other
a weighted graph G = (N M) two set of nod
e to find the minimum cost sub-graph S (subs
e in S and each node in B should have even de
roads of Gigaland find the minimum possible
of Gigaland Every
galand were living
Broken Arrow and
for two persons to
cided to fight each
the blood shedding
try will be divided
n the set of A and
rustrated and angry
proposal They will
onnecting roads of
ugh cities of set A
een Megaland and
ional roads each of
uilt such a way that
onsists of first K (2
s will belong to the
e some conditions
city of set B should
of road system in
be minimized The
s A = 1 2 hellip K
et of edges) where
gree in S Here cost
cost of sub-country
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 820
8
InputInput starts with a positive integer T (T le 250) denoting the number of test cases Each case starts with
three integers N (2 le N le 100) M (N-1 le M le N(N-1)2) and K (2 le K le min(N 21)) Each of the next
M lines contains three integers u v and c (1 le uv le N u ne v 0 lt c lt 10000) meaning that there is a bi-
directional road between city u and v of cost c No two roads will be same Please also note that for 90 of the test cases K is less than 20
OutputFor each test case print the test case number (starting from 1) and the minimum possible cost of
Megaland if it is possible to build the sub-country according to the conditions described above otherwise
print ldquoImpossiblerdquo (without the quotes)
Sample Input Output for Sample Input2
7 7 4
1 7 101 5 1
2 5 2
3 6 3
4 6 1
5 6 4
3 7 8
4 4 3
1 2 1
1 3 1
2 4 1
3 4 1
Case 1 7
Case 2 Impossible
Warning The judge input file is around 25 MB So use faster IO functionsExplanation
For test case 1
In Megaland degree of each node in set A = 1234 is 1 and degree nodes in set B = 5 6 7 are 2 2
and 0 respectively
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 920
D
P
Mr Anderson is in a relationship wit
Andersons phone logs and texts to fin
he decided to put a pattern locker on hi
This pattern locker comes with a 9 dot
several dots to record a pattern The
recorded before If we assume that ea
than a sequence of digits The patter
once
Here is an example of such a pattern l
Even after recording a hard to crack p
that his girlfriend might try all possi
different pattern sequences are possib
recorded in patterns
You have to help Mr Anderson in cou
ttern LockerInput Standard Input
Output Standard Output
a very suspicious and jealous girlfriend She
d out he is up to Feeling that his private spac
s phone
s arranged on a 3x3 square grid by default One
n to unlock the phone one needs to replicat
h dot is assigned a unique number then a patt
locker requires that no digit appears in the
cker and some valid and invalid recorded patte
attern Mr Anderson doesnt feel quite comfor
le sequences to break his pattern He wants t
le for a given grid size minimum and maxim
nting the number of possible such sequences
is always checking
is getting violated
has to drag through
e the same pattern
rn is nothing more
equence more than
rn
able He is worried
o know how many
m numbers of dots
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1020
10
InputThe first line of the input will give the number of test cases T (1 le T le 10000) Then T test cases follow
in separate lines Each test case consists of three numbers L M N separated by a single space in between
two numbers The first number L (1 lt L le 100) denotes the number of rows and columns in the grid The
second number M (1le
Mle
LL) denotes minimum number of dots to be included in a pattern and thethird number N (M le N le LL) denotes the maximum number of dots to be included in the pattern
OutputFor each test case you need to print the test case number X in the format ldquoCase X rdquo This will be
followed by the count of possible sequences for the given grid size minimum and maximum number of
dots in a sequence Since the count can be pretty big you need to print the value of the count modulo
10000000000007 (1 followed by 12 zeros followed by 7)
Sample Input Output for Sample Input2
3 4 9
3 1 9
Case 1 985824
Case 2 986409
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1120
EYou have pearl of 3 types
bull Type 1 pearl can be of color fr
bull Type 2 pearl can be of color fr
bull Type 3 pearl can be of color fr
You have unlimited supply of pearls
But you have 2 more additional constr
bull
The total number of Type 1 anbull The total number of Type 2 an
Given A B X Y and Z calculate ho
they have different length or there is a
InputFirst line of the input contains T (1 le
A B X Y and Z All of these 5 intege
OutputFor each test case output an integer d
huge output the result modulo 100000
Sample Input5
1 1 1 1 1
2 3 1 1 1
1 1 1 2 1
10 10 10 10 10
100 100 100 100 100
earl ChainsInput Standard Inpututput Standard Output
m 1 to X
m X+1 to X+Y
m X+Y+1 to X+Y+Z
of each type and each color You want to buil
ints
Type 3 pearls will be exactly AType 3 pearls will be exactly B
many different pearl chains are possible 2 c
position in which they have different colored p
le 100) the number of test cases Each test cas
rs are between 1 and 1017
inclusive
noting the number of possible pearl chains Si
Output for Sample Inp3
25
5
77069
329672
some pearl chain
ains are different if
arl
contains 5 integers
nce the result is too
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1220
F Two PI
O
Itrsquos a common phenomenon to mix u
that they just look at sky and can tell y
whole way they travelled ldquoFirst we
and so this one is helliprdquo and thus end u
each other and they do not always run
ends up with some ridiculous answer a
The city we are talking about is a sq
Although the city is nice square shape
rail track and it is a straight one
perpendicular to the existing one The
or not they just need location of twconnecting these two stations the line
you have to build the stations in intege
So to sum it up you will be given co-
to give any two distinct integer co-or
co-ordinates may coincide with the gi
Input
First line of input will contain an integ
be a line of four integers X1 Y1 X2
ordinates of two stations on the alread
You may assume that these two points
OutputFor each test case produce one line
integers where the first two integers
integers are the x and y co-ordinate
possible value of S and the line pa
(may not necessarily intersect the
answers you may output any of the
coordinates does not exceed9
102times F
Sample Input2
4 4 5 5
9 0 10 0
oints Revisitednput Standard Inputtput Standard Output
direction when you go to a new place Some
ou which one is north And some dumb people
ere east facing then we turned left then right
with a direction But the roads are not always
from north to south or from east to west So thi
lmost all the times
uare shaped one with vertices at (0 0) (S 0)
one the road network is already messed up
o city corporation decides to build another
do not care if the new track intersects with th
rail stations so that if a rail track is built alowould be perpendicular to the existing rail tr
r co-ordinates
rdinates of two stations on the already existing
inates within the city for building new rail tra
en co-ordinates if you want it to
er T the number of test cases (T le 15000) For
2 (0 le X1 Y1 X2 Y2 le 109) Here (X1 Y1) and
existing rail track
are different and within the city
of output This line contains the case numbe
are the x and y co-ordinate of the first statio
of the second station They should be withi
sing through them must be perpendicular
previous track within the city) Since the
but you have to make sure that absolute va
or details please go through the explanation of t
Output for Sample ICase 1 1 0 0 1
Case 2 10 0 10 2
eople are so clever
try to remember the
then again righthellip
in 90 degrees with
kind of calculation
(S S) and (0 S)
ut there is only one
rail track which is
previous rail track
ng the straight lineck The problem is
rail track you have
ck One of the new
each case there will
(X2 Y2) are the co-
r followed by four
n and the next two
the city for any
o the existing line
re can be multiple
lue of any of these
he sample cases
put
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1320
13
Explanation
First Sample
In the first sample the existing rail track goes through points (4 4) and (5 5) If you establish two new
rail stations at (1 0) and (0 1) the rail track passing through them will be perpendicular to the existingrail track Note if you output something like (5 5) and (6 4) you will get Wrong Answer since if S = 5
point (6 4) will not be within the city But for any value of S such that (4 4) and (5 5) is within the city
points (1 0) and (0 1) will also be within the city
Second Sample
In this case there are many correct answers One of them is (10 0) and (10 2) Note that unlike first
sample here the rail tracks intersect
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1420
G
Watc
Day by day number of Kangaroos is d
Now for the convenience of the spect
ldquoKangaroo appears in Screen 7rdquo an
position of Kangaroos and inform th
screen to display that animal based on
as follows
If the position x is outside the rangeOtherwise the coverage is minimum(
An example will make it clear
Suppose there are four screens coveri
Kangaroo appears at x = 10
First screen has coverage of 3 unit aro
15 ndash 10) = minimum(3 5) = 3
Second screen has coverage of 0 unit
100)
Third screen has coverage of 0 unit
minimum(10 ndash 8 10 ndash 10) = 0
Fourth screen has coverage of 1 unit a
1 11 ndash 10) = 1
ing the KangarooInput Standard Input
Output Standard Output
ecreasing just like tiger whale or lions So I de
a sanctuary where they will live peac
visitors go near them So I planted s
outside the sanctuary For this proble
the sanctuary to be a long line of 10000
The leftmost position is marked with
position with 1000000000 There ar
cameras on this line Each of the camer
(L R) which means that camera coposition L to position R inclusive Each
their associated display screens outside
can see the Kangaroos
ators we announce time to time ldquoKangaroo a
so on I have some employees who contin
system (here position is a marker) The syste
the coverage The coverage of a screen for a
of that screen (ie x lt L or x gt R) then thndash L R ndash x)
ng the range (7 15) (14 100) (8 10) and (1
nd x = 10 Because x = 10 is within (7 15) an
around x = 10 Because x = 10 does not belo
around x = 10 Because though x = 10 is
round x = 10 Because x = 10 is within (1 11)
cided to make them
fully I do not let
me display screen
you may assume
0000 unit distance
and the rightmost
at most 100000
as is described with
vers a range fromof the cameras has
where the visitors
pears in Screen 3rdquo
ously monitor the
m chooses the best
osition x is defined
coverage is zero
11) Now say one
minimum(10 ndash 7
g to the range (14
within (8 10) but
and minimum(10 ndash
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1520
15
So which one is better Obviously the first one as it has the maximum coverage
So you are given the ranges of the screens and the positions the kangaroo appears For each position of
the Kangaroo you are to tell me the maximum coverage you can have with any of the screens
Input
First line of the test file contains T (T le 3) number of test cases Hence T cases follow For each case
you are given N M in the first line N is the number of screens and M is the number of Kangaroo
appearance ( 1 le N M le 100000) In the next N lines you are given the range of screens L R ( 0 le L le R
le 1000000000 ) Next M lines contain the position of the Kangaroo- an integer x (0 le x le 1000000000)
OutputFor each case print the case number Hence print M lines ith containing the maximum coverage you can
have around irsquoth Kangaroo
Sample Input Output for Sample Input1
3 2
7 15
14 100
1 11
10
120
Case 1
3
0
Warning The judge input file is around 6 MB So use faster IO functions
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1620
HGiven an integer N find how many pa
A le N
Here gcd (A B) means the greatest c
of the bitwise xor operation on the bin
InputThe first line of the input contains a
following T lines contain an integer N
OutputFor each test case print the case nu
input) followed by a space and then th
Sample Input2
7
20000000
Explanation
Sample 1
For N=7 there are four valid pairs (3
GCD XORInput Standard Inpututput Standard Output
irs (A B) are there such that gcd (A B) = A x
mmon divisor of the numbers A and B And
ary representation of A and B
n integer T(T le 10000) denoting the number
1 le N le 30000000)
ber first in the format Case X (here X
answer for that case
Output for Sample InpCase 1 4
Case 2 34866117
2) (5 4) (6 4) and (7 6)
or B where 1 le B le
xor B is the value
of test cases The
is the serial of the
ut
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1720
INatasha always mixes up things in her
classical problem - finding shortest p
that in another class the professor t
looking but does very different things
to the Primrsquos algorithm (actually w
Pseudocode of her algorithm looks as
FiascoInput Standard Input
Output Standard Output
algorithm classes Last week Prof Chhaya Mu
th to all nodes from a specific node of a wei
aught them Primrsquos and Dijkstrarsquos algorithms
Always confused poor Natasha submitted so
should call it Natasharsquos algorithm) she did
ollows
thy gave the class a
hted graph Before
which are similar
ething very similar
rsquot test it properly
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1820
18
After submission she showed the code to a friend who is good at algorithms That friend immediately
found the flaw Natasha was really terrified and started to cry Then there came the guys the guys who
liked her They jumped at the opportunity and got hold of the dataset to be used to test the solutions Your
friend Rehan is one of those guys He really wanted to impress Natasha He asked you to change the
dataset in such a way that Natasharsquos algorithm gives the right result After the change Rehan will
somehow be able to put the modified data with the old timestamp Rehan told you that
1 The dataset has T test cases
2 Each case contains a connected weighted undirected graph with n nodes and m edges
3 Each case will contain a source node source
4 Edge weights are positive and distinct
To avoid suspicion Rehan asked you not to change which vertices the edges connect or the overall set of
edge weights You may only reorder which weights are assigned to which edges
InputThe first line of the input denotes the number of datasets T (1 le T le 15) T sets of case will follow Eachcase will start with a triplet of numbers n (2 le n le 2500) m (1 le m le 25000) and source (1 le source le
n) - the number of nodes the number of edges and the starting node respectively Each of the next m
lines will contain a triplet of numbers (u v w) meaning that there is an edge between node u and node v
with weight w (1 le w le m) Nodes are numbered from 1 to n It is guaranteed that there is no duplicate or
self-edges in the input and the graph is connected In each given graph all edge weights will be distinct
OutputFor each set of input print one set of output First line of a set should be of the format ldquoCase Xrdquo
where X is the case number Then print each edge triplet - one triplet ( u v and w) in each line separated
by a single space The edges should be printed in the order given in the input If there is more than one
solution to a dataset any one of them will do
Sample Input Output for Sample Input1
7 9 5
2 4 2
1 4 8
7 2 6
3 4 7
5 7 5
7 3 9
6 1 1
6 3 4
5 6 3
Case 1
2 4 7
1 4 9
7 2 3
3 4 8
5 7 1
7 3 4
6 1 5
6 3 6
5 6 2
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1920
J Drom
Lets first define some terms
bull A string is palindromic if it re
madam and toot
bull A string is a dromicpalin if we
dromicpalin string is mmaad becau
palindrome
bull A substring is any contiguous
a c i icp acmicpc but acpc
empty substring so that means there a
Given a string you have to figure out
InputThe first line of input is an integer T
containing a string The strings will c
be positive and not greater than 1000
OutputFor each case first output the case n
Follow the samples for exact format
Sample Input4
acmicpc
aaaaa
isyoursolutionfastenough
abbabababbaba
cpalin SubstringsInput Standard Input
Output Standard Output
ds the same forward and backward Examples
can rearrange its letters to make it a palindro
e we can rearrange the letters to make it
equence of characters of a string Some substri
is not a substring For this problem we are
e2
)1( +nn substrings of a string of length n
ow many of its substrings are dromicpalin
(T lt 100) indicating the number of test cases
ntain only lowercase letters [a - z] The lengt
mber followed by the number of substrings t
Output for Sample InpCase 1 8
Case 2 15
Case 3 24
Case 4 67
of palindromes are
e An example of a
adam which is a
ngs of acmicpc are
not considering the
Each case is a line
of each string will
at are dromicpalin
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 2020
KCan you fill an (abc) cuboid with e
cell inside the (abc) cuboid should
dimensions and for each positive integ
a (223) cuboid can be filled with fi
filled with twelve (111) cubes
To make this problem slightly more di
filled by another cube Your job is to f
the cuboid can be filled by exactly n c
InputThere will be at most 300 test cases
abc le 125 0 le m lt abc)
Each of the next m lines contains thre
(x y z) is already filled
No cell will be mentioned twice Ther
The input is terminated by a line conta
OutputFor each test case print the case num
single space before each number in the
Sample Input2 2 3 0
2 2 3 2
1 1 1
2 2 3
0 0 0 0
ill the CuboidInput Standard Input
Output Standard Output
actly n cubes The cubes may touch but cann
be covered by exactly one cube You may us
er p you can use as many (ppp) cubes as yo
e cubes four (111) cubes and one (222)
fficult m of the cells in the cuboid are already
ind out the possible values of n such that the re
ubes
ach test case begins with four integers a b c
integers x y z (1 le x le a 1 le y le b 1 le z le c)
will be at least one non-filled cell
ining four zeroes
ber and the list of possible answers in increasi
output Look at the output for sample input for
Output for Sample InpCase 1 5 12
Case 2 10
ot overlap and each
cubes of different
like For example
cube It can also be
illed and cannot be
maining cells inside
(2 le a b c le 20
that means the cell
ng order There is a
details
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 520
BM and J are playing a game The desc
several digits will be shown There ar
ith
button of a display once the value
displays has one fault in common T
button is broken
Each of these displays can be describ
the number of digits shown by the di
side (we can consider it like a 3-digit
Firstly it limits the number of times
display will be interpreted as a B-ba
numbers shown by the display will b
can press each of the three working
display is shown in Figure 1
Figure 1M and J have N of these displays Ea
playing goes like this
1 M plays first J plays second
2 In each move a player selects
only be selected if it hasnrsquot re
is a digit which can be selec
broken you can not choose thi
3 After a move if the summati
displays is divisible by 3 then
4 If there is no move possible th
Given description of N displays you
optimally Initially every digit of ever
Game of MJInput Standard Inpututput Standard Output
ription of the game is very simple They have a
buttons under each digit of every display If s
of the ith
digit of that display will increase by
e 0th
digit (least significant digit) canrsquot be in
d using two parameters L and B L is the len
play If L is 3 then the display can show thr
umber) B is the base of the display It is impo
you can press a button Secondly the numb
sed number with L digits Suppose B is 8 an
octal numbers and the length of the numbers
(not broken) buttons at most seven (7) times
A display with L = 4 and B = 8 h of the display has its own L and B Now th
fter that they alternate moves
a display Then selects a digit And presses its
ched its limit B-1 already A display can only
ed However since the switch for the rightm
button for any display
n of numbers (After converting it to decimal
he player making that move loses and the other
n the game ends in draw
need to find out the outcome of the game
display is set to 0 (zero)
few displays where
omeone presses the
one Each of these
creased because its
th of the display or
e (3) digits side by
tant in two aspects
er displayed in the
d L is 4 Then the
will be 4 Also you
Example of such a
game M and J are
button A digit can
be selected if there
ost digit is already
base) shown in the
player wins
and J both plays
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 620
6
InputFirst line of input consists of an integer T (T le 100) the number of test cases Each test case starts with
an integer N (0 lt N lt10) the number of displays Next N line each contains two integers L (0 lt L lt 109)
and B (1 lt B lt 109) which are the parameters that describes the i
th display
OutputFor each case print one line ldquoCase X Srdquo where X is the case number S is either ldquoMrdquo ldquoJrdquo or
ldquoDrawrdquo based on the outcome of the game in that case
Sample Input Output for Sample Input3 1 5 2 2 3 2 2 6 1 2 2
Case 1 M
Case 2 J
Case 3 Draw
Explanation
Case 1
00000 =gt 00010 =gt 01010 =gt 01110 =gt 11110 which is 30 in decimal and divisible by 3 So J loses and
M wins However this is one possible valid game sequence But if two players play optimally J will
always lose and thus M will always win
Case 2
(00000) =gt (00010) Sum = 0 + 6 = 6
(00000) =gt (10000) =gt (10010) =gt (11010) Sum = 6 + 6 = 12
(00000) =gt (10000) =gt (10010) =gt (10020) =gt (10030) =gt (10040) =gt (10050) =gt (11050) Sum = 6
+ 30 = 36
In this way in every game sequence M is doomed to reach such a configuration where the sum will be
divisible by 3 Hence in this scenario J will win and M will lose
Case 3
(00) =gt (10) which is 2 in decimal and not divisible by 3 There is no move left So the game ends in a
draw
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 720
C G
General Broken Arrow and Lieutenant
year they fought several wars toget
happily until one day the king of G
Shadow Coder wants to become the
become king of a country at the same
other in the Great Chaos Jam (GCJ) fi
Colonel Dragoon friend of both Bro
war and comes up with a great soluti
into two disjoint sets of cities called
Shadow Coder will rule the rest of th
with these divisions To make peoples
build a sub-country of Gigaland calle
Gigaland so that peoples from set A
and B are disjoint cities might not be
set B Broken Arrow and Shadow Cod
The country of Gigaland consists of
which connects two different cities an
every city is connected to each other
le K le min(N 21)) cities 1 2 hellip K set B
Though the warriors have agreed to
Each city of set A should be incident
be incident to even number (It can
Megaland should be minimum that i
cities of Megaland may or may not be
In terms of graph theory you are give
and B = K+1 K+2 hellip N You ha
each node in A should have odd degreof S is sum of all the edge cost in S
Given N M K and description of M
Megaland
me of ThroneInput Standard Input
Output Standard Output
General Shadow Coder are two great warriors
er like ICPC NCPC etc The peoples of Gi
igaland General Rem (RIP) died Now both
new king of Gigaland As this is not possible
time they leave it to the field of war They d
ld and the winner will become the new king
en Arrow and Shadow Coder wants to avoid
n According to his proposed solution the cou
A and B Broken Arrow will rule the cities i
e cities But the people of Gigaland will get f
remain calm and happy Dragoon gave another
d Megaland that consists of some cities and
nd B can have some access to other cities Th
disjoint between Megaland and set A and bet
r both agreed with the idea of Dragoon
(numbered from 1 to N) cities and M bidirec
each road has a cost to travel Gigaland was b
ith sequence of one or more roads Set A will c
umbered cities of Gigaland and rest N ndash K citi
uild the new sub-country Megaland they ha
o odd number of roads of Megaland and each
e zero also) of roads of Megaland The cost
sum of all the road cost of Megaland should
connected to each other
a weighted graph G = (N M) two set of nod
e to find the minimum cost sub-graph S (subs
e in S and each node in B should have even de
roads of Gigaland find the minimum possible
of Gigaland Every
galand were living
Broken Arrow and
for two persons to
cided to fight each
the blood shedding
try will be divided
n the set of A and
rustrated and angry
proposal They will
onnecting roads of
ugh cities of set A
een Megaland and
ional roads each of
uilt such a way that
onsists of first K (2
s will belong to the
e some conditions
city of set B should
of road system in
be minimized The
s A = 1 2 hellip K
et of edges) where
gree in S Here cost
cost of sub-country
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 820
8
InputInput starts with a positive integer T (T le 250) denoting the number of test cases Each case starts with
three integers N (2 le N le 100) M (N-1 le M le N(N-1)2) and K (2 le K le min(N 21)) Each of the next
M lines contains three integers u v and c (1 le uv le N u ne v 0 lt c lt 10000) meaning that there is a bi-
directional road between city u and v of cost c No two roads will be same Please also note that for 90 of the test cases K is less than 20
OutputFor each test case print the test case number (starting from 1) and the minimum possible cost of
Megaland if it is possible to build the sub-country according to the conditions described above otherwise
print ldquoImpossiblerdquo (without the quotes)
Sample Input Output for Sample Input2
7 7 4
1 7 101 5 1
2 5 2
3 6 3
4 6 1
5 6 4
3 7 8
4 4 3
1 2 1
1 3 1
2 4 1
3 4 1
Case 1 7
Case 2 Impossible
Warning The judge input file is around 25 MB So use faster IO functionsExplanation
For test case 1
In Megaland degree of each node in set A = 1234 is 1 and degree nodes in set B = 5 6 7 are 2 2
and 0 respectively
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 920
D
P
Mr Anderson is in a relationship wit
Andersons phone logs and texts to fin
he decided to put a pattern locker on hi
This pattern locker comes with a 9 dot
several dots to record a pattern The
recorded before If we assume that ea
than a sequence of digits The patter
once
Here is an example of such a pattern l
Even after recording a hard to crack p
that his girlfriend might try all possi
different pattern sequences are possib
recorded in patterns
You have to help Mr Anderson in cou
ttern LockerInput Standard Input
Output Standard Output
a very suspicious and jealous girlfriend She
d out he is up to Feeling that his private spac
s phone
s arranged on a 3x3 square grid by default One
n to unlock the phone one needs to replicat
h dot is assigned a unique number then a patt
locker requires that no digit appears in the
cker and some valid and invalid recorded patte
attern Mr Anderson doesnt feel quite comfor
le sequences to break his pattern He wants t
le for a given grid size minimum and maxim
nting the number of possible such sequences
is always checking
is getting violated
has to drag through
e the same pattern
rn is nothing more
equence more than
rn
able He is worried
o know how many
m numbers of dots
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1020
10
InputThe first line of the input will give the number of test cases T (1 le T le 10000) Then T test cases follow
in separate lines Each test case consists of three numbers L M N separated by a single space in between
two numbers The first number L (1 lt L le 100) denotes the number of rows and columns in the grid The
second number M (1le
Mle
LL) denotes minimum number of dots to be included in a pattern and thethird number N (M le N le LL) denotes the maximum number of dots to be included in the pattern
OutputFor each test case you need to print the test case number X in the format ldquoCase X rdquo This will be
followed by the count of possible sequences for the given grid size minimum and maximum number of
dots in a sequence Since the count can be pretty big you need to print the value of the count modulo
10000000000007 (1 followed by 12 zeros followed by 7)
Sample Input Output for Sample Input2
3 4 9
3 1 9
Case 1 985824
Case 2 986409
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1120
EYou have pearl of 3 types
bull Type 1 pearl can be of color fr
bull Type 2 pearl can be of color fr
bull Type 3 pearl can be of color fr
You have unlimited supply of pearls
But you have 2 more additional constr
bull
The total number of Type 1 anbull The total number of Type 2 an
Given A B X Y and Z calculate ho
they have different length or there is a
InputFirst line of the input contains T (1 le
A B X Y and Z All of these 5 intege
OutputFor each test case output an integer d
huge output the result modulo 100000
Sample Input5
1 1 1 1 1
2 3 1 1 1
1 1 1 2 1
10 10 10 10 10
100 100 100 100 100
earl ChainsInput Standard Inpututput Standard Output
m 1 to X
m X+1 to X+Y
m X+Y+1 to X+Y+Z
of each type and each color You want to buil
ints
Type 3 pearls will be exactly AType 3 pearls will be exactly B
many different pearl chains are possible 2 c
position in which they have different colored p
le 100) the number of test cases Each test cas
rs are between 1 and 1017
inclusive
noting the number of possible pearl chains Si
Output for Sample Inp3
25
5
77069
329672
some pearl chain
ains are different if
arl
contains 5 integers
nce the result is too
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1220
F Two PI
O
Itrsquos a common phenomenon to mix u
that they just look at sky and can tell y
whole way they travelled ldquoFirst we
and so this one is helliprdquo and thus end u
each other and they do not always run
ends up with some ridiculous answer a
The city we are talking about is a sq
Although the city is nice square shape
rail track and it is a straight one
perpendicular to the existing one The
or not they just need location of twconnecting these two stations the line
you have to build the stations in intege
So to sum it up you will be given co-
to give any two distinct integer co-or
co-ordinates may coincide with the gi
Input
First line of input will contain an integ
be a line of four integers X1 Y1 X2
ordinates of two stations on the alread
You may assume that these two points
OutputFor each test case produce one line
integers where the first two integers
integers are the x and y co-ordinate
possible value of S and the line pa
(may not necessarily intersect the
answers you may output any of the
coordinates does not exceed9
102times F
Sample Input2
4 4 5 5
9 0 10 0
oints Revisitednput Standard Inputtput Standard Output
direction when you go to a new place Some
ou which one is north And some dumb people
ere east facing then we turned left then right
with a direction But the roads are not always
from north to south or from east to west So thi
lmost all the times
uare shaped one with vertices at (0 0) (S 0)
one the road network is already messed up
o city corporation decides to build another
do not care if the new track intersects with th
rail stations so that if a rail track is built alowould be perpendicular to the existing rail tr
r co-ordinates
rdinates of two stations on the already existing
inates within the city for building new rail tra
en co-ordinates if you want it to
er T the number of test cases (T le 15000) For
2 (0 le X1 Y1 X2 Y2 le 109) Here (X1 Y1) and
existing rail track
are different and within the city
of output This line contains the case numbe
are the x and y co-ordinate of the first statio
of the second station They should be withi
sing through them must be perpendicular
previous track within the city) Since the
but you have to make sure that absolute va
or details please go through the explanation of t
Output for Sample ICase 1 1 0 0 1
Case 2 10 0 10 2
eople are so clever
try to remember the
then again righthellip
in 90 degrees with
kind of calculation
(S S) and (0 S)
ut there is only one
rail track which is
previous rail track
ng the straight lineck The problem is
rail track you have
ck One of the new
each case there will
(X2 Y2) are the co-
r followed by four
n and the next two
the city for any
o the existing line
re can be multiple
lue of any of these
he sample cases
put
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1320
13
Explanation
First Sample
In the first sample the existing rail track goes through points (4 4) and (5 5) If you establish two new
rail stations at (1 0) and (0 1) the rail track passing through them will be perpendicular to the existingrail track Note if you output something like (5 5) and (6 4) you will get Wrong Answer since if S = 5
point (6 4) will not be within the city But for any value of S such that (4 4) and (5 5) is within the city
points (1 0) and (0 1) will also be within the city
Second Sample
In this case there are many correct answers One of them is (10 0) and (10 2) Note that unlike first
sample here the rail tracks intersect
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1420
G
Watc
Day by day number of Kangaroos is d
Now for the convenience of the spect
ldquoKangaroo appears in Screen 7rdquo an
position of Kangaroos and inform th
screen to display that animal based on
as follows
If the position x is outside the rangeOtherwise the coverage is minimum(
An example will make it clear
Suppose there are four screens coveri
Kangaroo appears at x = 10
First screen has coverage of 3 unit aro
15 ndash 10) = minimum(3 5) = 3
Second screen has coverage of 0 unit
100)
Third screen has coverage of 0 unit
minimum(10 ndash 8 10 ndash 10) = 0
Fourth screen has coverage of 1 unit a
1 11 ndash 10) = 1
ing the KangarooInput Standard Input
Output Standard Output
ecreasing just like tiger whale or lions So I de
a sanctuary where they will live peac
visitors go near them So I planted s
outside the sanctuary For this proble
the sanctuary to be a long line of 10000
The leftmost position is marked with
position with 1000000000 There ar
cameras on this line Each of the camer
(L R) which means that camera coposition L to position R inclusive Each
their associated display screens outside
can see the Kangaroos
ators we announce time to time ldquoKangaroo a
so on I have some employees who contin
system (here position is a marker) The syste
the coverage The coverage of a screen for a
of that screen (ie x lt L or x gt R) then thndash L R ndash x)
ng the range (7 15) (14 100) (8 10) and (1
nd x = 10 Because x = 10 is within (7 15) an
around x = 10 Because x = 10 does not belo
around x = 10 Because though x = 10 is
round x = 10 Because x = 10 is within (1 11)
cided to make them
fully I do not let
me display screen
you may assume
0000 unit distance
and the rightmost
at most 100000
as is described with
vers a range fromof the cameras has
where the visitors
pears in Screen 3rdquo
ously monitor the
m chooses the best
osition x is defined
coverage is zero
11) Now say one
minimum(10 ndash 7
g to the range (14
within (8 10) but
and minimum(10 ndash
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1520
15
So which one is better Obviously the first one as it has the maximum coverage
So you are given the ranges of the screens and the positions the kangaroo appears For each position of
the Kangaroo you are to tell me the maximum coverage you can have with any of the screens
Input
First line of the test file contains T (T le 3) number of test cases Hence T cases follow For each case
you are given N M in the first line N is the number of screens and M is the number of Kangaroo
appearance ( 1 le N M le 100000) In the next N lines you are given the range of screens L R ( 0 le L le R
le 1000000000 ) Next M lines contain the position of the Kangaroo- an integer x (0 le x le 1000000000)
OutputFor each case print the case number Hence print M lines ith containing the maximum coverage you can
have around irsquoth Kangaroo
Sample Input Output for Sample Input1
3 2
7 15
14 100
1 11
10
120
Case 1
3
0
Warning The judge input file is around 6 MB So use faster IO functions
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1620
HGiven an integer N find how many pa
A le N
Here gcd (A B) means the greatest c
of the bitwise xor operation on the bin
InputThe first line of the input contains a
following T lines contain an integer N
OutputFor each test case print the case nu
input) followed by a space and then th
Sample Input2
7
20000000
Explanation
Sample 1
For N=7 there are four valid pairs (3
GCD XORInput Standard Inpututput Standard Output
irs (A B) are there such that gcd (A B) = A x
mmon divisor of the numbers A and B And
ary representation of A and B
n integer T(T le 10000) denoting the number
1 le N le 30000000)
ber first in the format Case X (here X
answer for that case
Output for Sample InpCase 1 4
Case 2 34866117
2) (5 4) (6 4) and (7 6)
or B where 1 le B le
xor B is the value
of test cases The
is the serial of the
ut
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1720
INatasha always mixes up things in her
classical problem - finding shortest p
that in another class the professor t
looking but does very different things
to the Primrsquos algorithm (actually w
Pseudocode of her algorithm looks as
FiascoInput Standard Input
Output Standard Output
algorithm classes Last week Prof Chhaya Mu
th to all nodes from a specific node of a wei
aught them Primrsquos and Dijkstrarsquos algorithms
Always confused poor Natasha submitted so
should call it Natasharsquos algorithm) she did
ollows
thy gave the class a
hted graph Before
which are similar
ething very similar
rsquot test it properly
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1820
18
After submission she showed the code to a friend who is good at algorithms That friend immediately
found the flaw Natasha was really terrified and started to cry Then there came the guys the guys who
liked her They jumped at the opportunity and got hold of the dataset to be used to test the solutions Your
friend Rehan is one of those guys He really wanted to impress Natasha He asked you to change the
dataset in such a way that Natasharsquos algorithm gives the right result After the change Rehan will
somehow be able to put the modified data with the old timestamp Rehan told you that
1 The dataset has T test cases
2 Each case contains a connected weighted undirected graph with n nodes and m edges
3 Each case will contain a source node source
4 Edge weights are positive and distinct
To avoid suspicion Rehan asked you not to change which vertices the edges connect or the overall set of
edge weights You may only reorder which weights are assigned to which edges
InputThe first line of the input denotes the number of datasets T (1 le T le 15) T sets of case will follow Eachcase will start with a triplet of numbers n (2 le n le 2500) m (1 le m le 25000) and source (1 le source le
n) - the number of nodes the number of edges and the starting node respectively Each of the next m
lines will contain a triplet of numbers (u v w) meaning that there is an edge between node u and node v
with weight w (1 le w le m) Nodes are numbered from 1 to n It is guaranteed that there is no duplicate or
self-edges in the input and the graph is connected In each given graph all edge weights will be distinct
OutputFor each set of input print one set of output First line of a set should be of the format ldquoCase Xrdquo
where X is the case number Then print each edge triplet - one triplet ( u v and w) in each line separated
by a single space The edges should be printed in the order given in the input If there is more than one
solution to a dataset any one of them will do
Sample Input Output for Sample Input1
7 9 5
2 4 2
1 4 8
7 2 6
3 4 7
5 7 5
7 3 9
6 1 1
6 3 4
5 6 3
Case 1
2 4 7
1 4 9
7 2 3
3 4 8
5 7 1
7 3 4
6 1 5
6 3 6
5 6 2
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1920
J Drom
Lets first define some terms
bull A string is palindromic if it re
madam and toot
bull A string is a dromicpalin if we
dromicpalin string is mmaad becau
palindrome
bull A substring is any contiguous
a c i icp acmicpc but acpc
empty substring so that means there a
Given a string you have to figure out
InputThe first line of input is an integer T
containing a string The strings will c
be positive and not greater than 1000
OutputFor each case first output the case n
Follow the samples for exact format
Sample Input4
acmicpc
aaaaa
isyoursolutionfastenough
abbabababbaba
cpalin SubstringsInput Standard Input
Output Standard Output
ds the same forward and backward Examples
can rearrange its letters to make it a palindro
e we can rearrange the letters to make it
equence of characters of a string Some substri
is not a substring For this problem we are
e2
)1( +nn substrings of a string of length n
ow many of its substrings are dromicpalin
(T lt 100) indicating the number of test cases
ntain only lowercase letters [a - z] The lengt
mber followed by the number of substrings t
Output for Sample InpCase 1 8
Case 2 15
Case 3 24
Case 4 67
of palindromes are
e An example of a
adam which is a
ngs of acmicpc are
not considering the
Each case is a line
of each string will
at are dromicpalin
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 2020
KCan you fill an (abc) cuboid with e
cell inside the (abc) cuboid should
dimensions and for each positive integ
a (223) cuboid can be filled with fi
filled with twelve (111) cubes
To make this problem slightly more di
filled by another cube Your job is to f
the cuboid can be filled by exactly n c
InputThere will be at most 300 test cases
abc le 125 0 le m lt abc)
Each of the next m lines contains thre
(x y z) is already filled
No cell will be mentioned twice Ther
The input is terminated by a line conta
OutputFor each test case print the case num
single space before each number in the
Sample Input2 2 3 0
2 2 3 2
1 1 1
2 2 3
0 0 0 0
ill the CuboidInput Standard Input
Output Standard Output
actly n cubes The cubes may touch but cann
be covered by exactly one cube You may us
er p you can use as many (ppp) cubes as yo
e cubes four (111) cubes and one (222)
fficult m of the cells in the cuboid are already
ind out the possible values of n such that the re
ubes
ach test case begins with four integers a b c
integers x y z (1 le x le a 1 le y le b 1 le z le c)
will be at least one non-filled cell
ining four zeroes
ber and the list of possible answers in increasi
output Look at the output for sample input for
Output for Sample InpCase 1 5 12
Case 2 10
ot overlap and each
cubes of different
like For example
cube It can also be
illed and cannot be
maining cells inside
(2 le a b c le 20
that means the cell
ng order There is a
details
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 620
6
InputFirst line of input consists of an integer T (T le 100) the number of test cases Each test case starts with
an integer N (0 lt N lt10) the number of displays Next N line each contains two integers L (0 lt L lt 109)
and B (1 lt B lt 109) which are the parameters that describes the i
th display
OutputFor each case print one line ldquoCase X Srdquo where X is the case number S is either ldquoMrdquo ldquoJrdquo or
ldquoDrawrdquo based on the outcome of the game in that case
Sample Input Output for Sample Input3 1 5 2 2 3 2 2 6 1 2 2
Case 1 M
Case 2 J
Case 3 Draw
Explanation
Case 1
00000 =gt 00010 =gt 01010 =gt 01110 =gt 11110 which is 30 in decimal and divisible by 3 So J loses and
M wins However this is one possible valid game sequence But if two players play optimally J will
always lose and thus M will always win
Case 2
(00000) =gt (00010) Sum = 0 + 6 = 6
(00000) =gt (10000) =gt (10010) =gt (11010) Sum = 6 + 6 = 12
(00000) =gt (10000) =gt (10010) =gt (10020) =gt (10030) =gt (10040) =gt (10050) =gt (11050) Sum = 6
+ 30 = 36
In this way in every game sequence M is doomed to reach such a configuration where the sum will be
divisible by 3 Hence in this scenario J will win and M will lose
Case 3
(00) =gt (10) which is 2 in decimal and not divisible by 3 There is no move left So the game ends in a
draw
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 720
C G
General Broken Arrow and Lieutenant
year they fought several wars toget
happily until one day the king of G
Shadow Coder wants to become the
become king of a country at the same
other in the Great Chaos Jam (GCJ) fi
Colonel Dragoon friend of both Bro
war and comes up with a great soluti
into two disjoint sets of cities called
Shadow Coder will rule the rest of th
with these divisions To make peoples
build a sub-country of Gigaland calle
Gigaland so that peoples from set A
and B are disjoint cities might not be
set B Broken Arrow and Shadow Cod
The country of Gigaland consists of
which connects two different cities an
every city is connected to each other
le K le min(N 21)) cities 1 2 hellip K set B
Though the warriors have agreed to
Each city of set A should be incident
be incident to even number (It can
Megaland should be minimum that i
cities of Megaland may or may not be
In terms of graph theory you are give
and B = K+1 K+2 hellip N You ha
each node in A should have odd degreof S is sum of all the edge cost in S
Given N M K and description of M
Megaland
me of ThroneInput Standard Input
Output Standard Output
General Shadow Coder are two great warriors
er like ICPC NCPC etc The peoples of Gi
igaland General Rem (RIP) died Now both
new king of Gigaland As this is not possible
time they leave it to the field of war They d
ld and the winner will become the new king
en Arrow and Shadow Coder wants to avoid
n According to his proposed solution the cou
A and B Broken Arrow will rule the cities i
e cities But the people of Gigaland will get f
remain calm and happy Dragoon gave another
d Megaland that consists of some cities and
nd B can have some access to other cities Th
disjoint between Megaland and set A and bet
r both agreed with the idea of Dragoon
(numbered from 1 to N) cities and M bidirec
each road has a cost to travel Gigaland was b
ith sequence of one or more roads Set A will c
umbered cities of Gigaland and rest N ndash K citi
uild the new sub-country Megaland they ha
o odd number of roads of Megaland and each
e zero also) of roads of Megaland The cost
sum of all the road cost of Megaland should
connected to each other
a weighted graph G = (N M) two set of nod
e to find the minimum cost sub-graph S (subs
e in S and each node in B should have even de
roads of Gigaland find the minimum possible
of Gigaland Every
galand were living
Broken Arrow and
for two persons to
cided to fight each
the blood shedding
try will be divided
n the set of A and
rustrated and angry
proposal They will
onnecting roads of
ugh cities of set A
een Megaland and
ional roads each of
uilt such a way that
onsists of first K (2
s will belong to the
e some conditions
city of set B should
of road system in
be minimized The
s A = 1 2 hellip K
et of edges) where
gree in S Here cost
cost of sub-country
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 820
8
InputInput starts with a positive integer T (T le 250) denoting the number of test cases Each case starts with
three integers N (2 le N le 100) M (N-1 le M le N(N-1)2) and K (2 le K le min(N 21)) Each of the next
M lines contains three integers u v and c (1 le uv le N u ne v 0 lt c lt 10000) meaning that there is a bi-
directional road between city u and v of cost c No two roads will be same Please also note that for 90 of the test cases K is less than 20
OutputFor each test case print the test case number (starting from 1) and the minimum possible cost of
Megaland if it is possible to build the sub-country according to the conditions described above otherwise
print ldquoImpossiblerdquo (without the quotes)
Sample Input Output for Sample Input2
7 7 4
1 7 101 5 1
2 5 2
3 6 3
4 6 1
5 6 4
3 7 8
4 4 3
1 2 1
1 3 1
2 4 1
3 4 1
Case 1 7
Case 2 Impossible
Warning The judge input file is around 25 MB So use faster IO functionsExplanation
For test case 1
In Megaland degree of each node in set A = 1234 is 1 and degree nodes in set B = 5 6 7 are 2 2
and 0 respectively
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 920
D
P
Mr Anderson is in a relationship wit
Andersons phone logs and texts to fin
he decided to put a pattern locker on hi
This pattern locker comes with a 9 dot
several dots to record a pattern The
recorded before If we assume that ea
than a sequence of digits The patter
once
Here is an example of such a pattern l
Even after recording a hard to crack p
that his girlfriend might try all possi
different pattern sequences are possib
recorded in patterns
You have to help Mr Anderson in cou
ttern LockerInput Standard Input
Output Standard Output
a very suspicious and jealous girlfriend She
d out he is up to Feeling that his private spac
s phone
s arranged on a 3x3 square grid by default One
n to unlock the phone one needs to replicat
h dot is assigned a unique number then a patt
locker requires that no digit appears in the
cker and some valid and invalid recorded patte
attern Mr Anderson doesnt feel quite comfor
le sequences to break his pattern He wants t
le for a given grid size minimum and maxim
nting the number of possible such sequences
is always checking
is getting violated
has to drag through
e the same pattern
rn is nothing more
equence more than
rn
able He is worried
o know how many
m numbers of dots
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1020
10
InputThe first line of the input will give the number of test cases T (1 le T le 10000) Then T test cases follow
in separate lines Each test case consists of three numbers L M N separated by a single space in between
two numbers The first number L (1 lt L le 100) denotes the number of rows and columns in the grid The
second number M (1le
Mle
LL) denotes minimum number of dots to be included in a pattern and thethird number N (M le N le LL) denotes the maximum number of dots to be included in the pattern
OutputFor each test case you need to print the test case number X in the format ldquoCase X rdquo This will be
followed by the count of possible sequences for the given grid size minimum and maximum number of
dots in a sequence Since the count can be pretty big you need to print the value of the count modulo
10000000000007 (1 followed by 12 zeros followed by 7)
Sample Input Output for Sample Input2
3 4 9
3 1 9
Case 1 985824
Case 2 986409
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1120
EYou have pearl of 3 types
bull Type 1 pearl can be of color fr
bull Type 2 pearl can be of color fr
bull Type 3 pearl can be of color fr
You have unlimited supply of pearls
But you have 2 more additional constr
bull
The total number of Type 1 anbull The total number of Type 2 an
Given A B X Y and Z calculate ho
they have different length or there is a
InputFirst line of the input contains T (1 le
A B X Y and Z All of these 5 intege
OutputFor each test case output an integer d
huge output the result modulo 100000
Sample Input5
1 1 1 1 1
2 3 1 1 1
1 1 1 2 1
10 10 10 10 10
100 100 100 100 100
earl ChainsInput Standard Inpututput Standard Output
m 1 to X
m X+1 to X+Y
m X+Y+1 to X+Y+Z
of each type and each color You want to buil
ints
Type 3 pearls will be exactly AType 3 pearls will be exactly B
many different pearl chains are possible 2 c
position in which they have different colored p
le 100) the number of test cases Each test cas
rs are between 1 and 1017
inclusive
noting the number of possible pearl chains Si
Output for Sample Inp3
25
5
77069
329672
some pearl chain
ains are different if
arl
contains 5 integers
nce the result is too
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1220
F Two PI
O
Itrsquos a common phenomenon to mix u
that they just look at sky and can tell y
whole way they travelled ldquoFirst we
and so this one is helliprdquo and thus end u
each other and they do not always run
ends up with some ridiculous answer a
The city we are talking about is a sq
Although the city is nice square shape
rail track and it is a straight one
perpendicular to the existing one The
or not they just need location of twconnecting these two stations the line
you have to build the stations in intege
So to sum it up you will be given co-
to give any two distinct integer co-or
co-ordinates may coincide with the gi
Input
First line of input will contain an integ
be a line of four integers X1 Y1 X2
ordinates of two stations on the alread
You may assume that these two points
OutputFor each test case produce one line
integers where the first two integers
integers are the x and y co-ordinate
possible value of S and the line pa
(may not necessarily intersect the
answers you may output any of the
coordinates does not exceed9
102times F
Sample Input2
4 4 5 5
9 0 10 0
oints Revisitednput Standard Inputtput Standard Output
direction when you go to a new place Some
ou which one is north And some dumb people
ere east facing then we turned left then right
with a direction But the roads are not always
from north to south or from east to west So thi
lmost all the times
uare shaped one with vertices at (0 0) (S 0)
one the road network is already messed up
o city corporation decides to build another
do not care if the new track intersects with th
rail stations so that if a rail track is built alowould be perpendicular to the existing rail tr
r co-ordinates
rdinates of two stations on the already existing
inates within the city for building new rail tra
en co-ordinates if you want it to
er T the number of test cases (T le 15000) For
2 (0 le X1 Y1 X2 Y2 le 109) Here (X1 Y1) and
existing rail track
are different and within the city
of output This line contains the case numbe
are the x and y co-ordinate of the first statio
of the second station They should be withi
sing through them must be perpendicular
previous track within the city) Since the
but you have to make sure that absolute va
or details please go through the explanation of t
Output for Sample ICase 1 1 0 0 1
Case 2 10 0 10 2
eople are so clever
try to remember the
then again righthellip
in 90 degrees with
kind of calculation
(S S) and (0 S)
ut there is only one
rail track which is
previous rail track
ng the straight lineck The problem is
rail track you have
ck One of the new
each case there will
(X2 Y2) are the co-
r followed by four
n and the next two
the city for any
o the existing line
re can be multiple
lue of any of these
he sample cases
put
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1320
13
Explanation
First Sample
In the first sample the existing rail track goes through points (4 4) and (5 5) If you establish two new
rail stations at (1 0) and (0 1) the rail track passing through them will be perpendicular to the existingrail track Note if you output something like (5 5) and (6 4) you will get Wrong Answer since if S = 5
point (6 4) will not be within the city But for any value of S such that (4 4) and (5 5) is within the city
points (1 0) and (0 1) will also be within the city
Second Sample
In this case there are many correct answers One of them is (10 0) and (10 2) Note that unlike first
sample here the rail tracks intersect
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1420
G
Watc
Day by day number of Kangaroos is d
Now for the convenience of the spect
ldquoKangaroo appears in Screen 7rdquo an
position of Kangaroos and inform th
screen to display that animal based on
as follows
If the position x is outside the rangeOtherwise the coverage is minimum(
An example will make it clear
Suppose there are four screens coveri
Kangaroo appears at x = 10
First screen has coverage of 3 unit aro
15 ndash 10) = minimum(3 5) = 3
Second screen has coverage of 0 unit
100)
Third screen has coverage of 0 unit
minimum(10 ndash 8 10 ndash 10) = 0
Fourth screen has coverage of 1 unit a
1 11 ndash 10) = 1
ing the KangarooInput Standard Input
Output Standard Output
ecreasing just like tiger whale or lions So I de
a sanctuary where they will live peac
visitors go near them So I planted s
outside the sanctuary For this proble
the sanctuary to be a long line of 10000
The leftmost position is marked with
position with 1000000000 There ar
cameras on this line Each of the camer
(L R) which means that camera coposition L to position R inclusive Each
their associated display screens outside
can see the Kangaroos
ators we announce time to time ldquoKangaroo a
so on I have some employees who contin
system (here position is a marker) The syste
the coverage The coverage of a screen for a
of that screen (ie x lt L or x gt R) then thndash L R ndash x)
ng the range (7 15) (14 100) (8 10) and (1
nd x = 10 Because x = 10 is within (7 15) an
around x = 10 Because x = 10 does not belo
around x = 10 Because though x = 10 is
round x = 10 Because x = 10 is within (1 11)
cided to make them
fully I do not let
me display screen
you may assume
0000 unit distance
and the rightmost
at most 100000
as is described with
vers a range fromof the cameras has
where the visitors
pears in Screen 3rdquo
ously monitor the
m chooses the best
osition x is defined
coverage is zero
11) Now say one
minimum(10 ndash 7
g to the range (14
within (8 10) but
and minimum(10 ndash
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1520
15
So which one is better Obviously the first one as it has the maximum coverage
So you are given the ranges of the screens and the positions the kangaroo appears For each position of
the Kangaroo you are to tell me the maximum coverage you can have with any of the screens
Input
First line of the test file contains T (T le 3) number of test cases Hence T cases follow For each case
you are given N M in the first line N is the number of screens and M is the number of Kangaroo
appearance ( 1 le N M le 100000) In the next N lines you are given the range of screens L R ( 0 le L le R
le 1000000000 ) Next M lines contain the position of the Kangaroo- an integer x (0 le x le 1000000000)
OutputFor each case print the case number Hence print M lines ith containing the maximum coverage you can
have around irsquoth Kangaroo
Sample Input Output for Sample Input1
3 2
7 15
14 100
1 11
10
120
Case 1
3
0
Warning The judge input file is around 6 MB So use faster IO functions
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1620
HGiven an integer N find how many pa
A le N
Here gcd (A B) means the greatest c
of the bitwise xor operation on the bin
InputThe first line of the input contains a
following T lines contain an integer N
OutputFor each test case print the case nu
input) followed by a space and then th
Sample Input2
7
20000000
Explanation
Sample 1
For N=7 there are four valid pairs (3
GCD XORInput Standard Inpututput Standard Output
irs (A B) are there such that gcd (A B) = A x
mmon divisor of the numbers A and B And
ary representation of A and B
n integer T(T le 10000) denoting the number
1 le N le 30000000)
ber first in the format Case X (here X
answer for that case
Output for Sample InpCase 1 4
Case 2 34866117
2) (5 4) (6 4) and (7 6)
or B where 1 le B le
xor B is the value
of test cases The
is the serial of the
ut
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1720
INatasha always mixes up things in her
classical problem - finding shortest p
that in another class the professor t
looking but does very different things
to the Primrsquos algorithm (actually w
Pseudocode of her algorithm looks as
FiascoInput Standard Input
Output Standard Output
algorithm classes Last week Prof Chhaya Mu
th to all nodes from a specific node of a wei
aught them Primrsquos and Dijkstrarsquos algorithms
Always confused poor Natasha submitted so
should call it Natasharsquos algorithm) she did
ollows
thy gave the class a
hted graph Before
which are similar
ething very similar
rsquot test it properly
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1820
18
After submission she showed the code to a friend who is good at algorithms That friend immediately
found the flaw Natasha was really terrified and started to cry Then there came the guys the guys who
liked her They jumped at the opportunity and got hold of the dataset to be used to test the solutions Your
friend Rehan is one of those guys He really wanted to impress Natasha He asked you to change the
dataset in such a way that Natasharsquos algorithm gives the right result After the change Rehan will
somehow be able to put the modified data with the old timestamp Rehan told you that
1 The dataset has T test cases
2 Each case contains a connected weighted undirected graph with n nodes and m edges
3 Each case will contain a source node source
4 Edge weights are positive and distinct
To avoid suspicion Rehan asked you not to change which vertices the edges connect or the overall set of
edge weights You may only reorder which weights are assigned to which edges
InputThe first line of the input denotes the number of datasets T (1 le T le 15) T sets of case will follow Eachcase will start with a triplet of numbers n (2 le n le 2500) m (1 le m le 25000) and source (1 le source le
n) - the number of nodes the number of edges and the starting node respectively Each of the next m
lines will contain a triplet of numbers (u v w) meaning that there is an edge between node u and node v
with weight w (1 le w le m) Nodes are numbered from 1 to n It is guaranteed that there is no duplicate or
self-edges in the input and the graph is connected In each given graph all edge weights will be distinct
OutputFor each set of input print one set of output First line of a set should be of the format ldquoCase Xrdquo
where X is the case number Then print each edge triplet - one triplet ( u v and w) in each line separated
by a single space The edges should be printed in the order given in the input If there is more than one
solution to a dataset any one of them will do
Sample Input Output for Sample Input1
7 9 5
2 4 2
1 4 8
7 2 6
3 4 7
5 7 5
7 3 9
6 1 1
6 3 4
5 6 3
Case 1
2 4 7
1 4 9
7 2 3
3 4 8
5 7 1
7 3 4
6 1 5
6 3 6
5 6 2
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1920
J Drom
Lets first define some terms
bull A string is palindromic if it re
madam and toot
bull A string is a dromicpalin if we
dromicpalin string is mmaad becau
palindrome
bull A substring is any contiguous
a c i icp acmicpc but acpc
empty substring so that means there a
Given a string you have to figure out
InputThe first line of input is an integer T
containing a string The strings will c
be positive and not greater than 1000
OutputFor each case first output the case n
Follow the samples for exact format
Sample Input4
acmicpc
aaaaa
isyoursolutionfastenough
abbabababbaba
cpalin SubstringsInput Standard Input
Output Standard Output
ds the same forward and backward Examples
can rearrange its letters to make it a palindro
e we can rearrange the letters to make it
equence of characters of a string Some substri
is not a substring For this problem we are
e2
)1( +nn substrings of a string of length n
ow many of its substrings are dromicpalin
(T lt 100) indicating the number of test cases
ntain only lowercase letters [a - z] The lengt
mber followed by the number of substrings t
Output for Sample InpCase 1 8
Case 2 15
Case 3 24
Case 4 67
of palindromes are
e An example of a
adam which is a
ngs of acmicpc are
not considering the
Each case is a line
of each string will
at are dromicpalin
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 2020
KCan you fill an (abc) cuboid with e
cell inside the (abc) cuboid should
dimensions and for each positive integ
a (223) cuboid can be filled with fi
filled with twelve (111) cubes
To make this problem slightly more di
filled by another cube Your job is to f
the cuboid can be filled by exactly n c
InputThere will be at most 300 test cases
abc le 125 0 le m lt abc)
Each of the next m lines contains thre
(x y z) is already filled
No cell will be mentioned twice Ther
The input is terminated by a line conta
OutputFor each test case print the case num
single space before each number in the
Sample Input2 2 3 0
2 2 3 2
1 1 1
2 2 3
0 0 0 0
ill the CuboidInput Standard Input
Output Standard Output
actly n cubes The cubes may touch but cann
be covered by exactly one cube You may us
er p you can use as many (ppp) cubes as yo
e cubes four (111) cubes and one (222)
fficult m of the cells in the cuboid are already
ind out the possible values of n such that the re
ubes
ach test case begins with four integers a b c
integers x y z (1 le x le a 1 le y le b 1 le z le c)
will be at least one non-filled cell
ining four zeroes
ber and the list of possible answers in increasi
output Look at the output for sample input for
Output for Sample InpCase 1 5 12
Case 2 10
ot overlap and each
cubes of different
like For example
cube It can also be
illed and cannot be
maining cells inside
(2 le a b c le 20
that means the cell
ng order There is a
details
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 720
C G
General Broken Arrow and Lieutenant
year they fought several wars toget
happily until one day the king of G
Shadow Coder wants to become the
become king of a country at the same
other in the Great Chaos Jam (GCJ) fi
Colonel Dragoon friend of both Bro
war and comes up with a great soluti
into two disjoint sets of cities called
Shadow Coder will rule the rest of th
with these divisions To make peoples
build a sub-country of Gigaland calle
Gigaland so that peoples from set A
and B are disjoint cities might not be
set B Broken Arrow and Shadow Cod
The country of Gigaland consists of
which connects two different cities an
every city is connected to each other
le K le min(N 21)) cities 1 2 hellip K set B
Though the warriors have agreed to
Each city of set A should be incident
be incident to even number (It can
Megaland should be minimum that i
cities of Megaland may or may not be
In terms of graph theory you are give
and B = K+1 K+2 hellip N You ha
each node in A should have odd degreof S is sum of all the edge cost in S
Given N M K and description of M
Megaland
me of ThroneInput Standard Input
Output Standard Output
General Shadow Coder are two great warriors
er like ICPC NCPC etc The peoples of Gi
igaland General Rem (RIP) died Now both
new king of Gigaland As this is not possible
time they leave it to the field of war They d
ld and the winner will become the new king
en Arrow and Shadow Coder wants to avoid
n According to his proposed solution the cou
A and B Broken Arrow will rule the cities i
e cities But the people of Gigaland will get f
remain calm and happy Dragoon gave another
d Megaland that consists of some cities and
nd B can have some access to other cities Th
disjoint between Megaland and set A and bet
r both agreed with the idea of Dragoon
(numbered from 1 to N) cities and M bidirec
each road has a cost to travel Gigaland was b
ith sequence of one or more roads Set A will c
umbered cities of Gigaland and rest N ndash K citi
uild the new sub-country Megaland they ha
o odd number of roads of Megaland and each
e zero also) of roads of Megaland The cost
sum of all the road cost of Megaland should
connected to each other
a weighted graph G = (N M) two set of nod
e to find the minimum cost sub-graph S (subs
e in S and each node in B should have even de
roads of Gigaland find the minimum possible
of Gigaland Every
galand were living
Broken Arrow and
for two persons to
cided to fight each
the blood shedding
try will be divided
n the set of A and
rustrated and angry
proposal They will
onnecting roads of
ugh cities of set A
een Megaland and
ional roads each of
uilt such a way that
onsists of first K (2
s will belong to the
e some conditions
city of set B should
of road system in
be minimized The
s A = 1 2 hellip K
et of edges) where
gree in S Here cost
cost of sub-country
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 820
8
InputInput starts with a positive integer T (T le 250) denoting the number of test cases Each case starts with
three integers N (2 le N le 100) M (N-1 le M le N(N-1)2) and K (2 le K le min(N 21)) Each of the next
M lines contains three integers u v and c (1 le uv le N u ne v 0 lt c lt 10000) meaning that there is a bi-
directional road between city u and v of cost c No two roads will be same Please also note that for 90 of the test cases K is less than 20
OutputFor each test case print the test case number (starting from 1) and the minimum possible cost of
Megaland if it is possible to build the sub-country according to the conditions described above otherwise
print ldquoImpossiblerdquo (without the quotes)
Sample Input Output for Sample Input2
7 7 4
1 7 101 5 1
2 5 2
3 6 3
4 6 1
5 6 4
3 7 8
4 4 3
1 2 1
1 3 1
2 4 1
3 4 1
Case 1 7
Case 2 Impossible
Warning The judge input file is around 25 MB So use faster IO functionsExplanation
For test case 1
In Megaland degree of each node in set A = 1234 is 1 and degree nodes in set B = 5 6 7 are 2 2
and 0 respectively
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 920
D
P
Mr Anderson is in a relationship wit
Andersons phone logs and texts to fin
he decided to put a pattern locker on hi
This pattern locker comes with a 9 dot
several dots to record a pattern The
recorded before If we assume that ea
than a sequence of digits The patter
once
Here is an example of such a pattern l
Even after recording a hard to crack p
that his girlfriend might try all possi
different pattern sequences are possib
recorded in patterns
You have to help Mr Anderson in cou
ttern LockerInput Standard Input
Output Standard Output
a very suspicious and jealous girlfriend She
d out he is up to Feeling that his private spac
s phone
s arranged on a 3x3 square grid by default One
n to unlock the phone one needs to replicat
h dot is assigned a unique number then a patt
locker requires that no digit appears in the
cker and some valid and invalid recorded patte
attern Mr Anderson doesnt feel quite comfor
le sequences to break his pattern He wants t
le for a given grid size minimum and maxim
nting the number of possible such sequences
is always checking
is getting violated
has to drag through
e the same pattern
rn is nothing more
equence more than
rn
able He is worried
o know how many
m numbers of dots
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1020
10
InputThe first line of the input will give the number of test cases T (1 le T le 10000) Then T test cases follow
in separate lines Each test case consists of three numbers L M N separated by a single space in between
two numbers The first number L (1 lt L le 100) denotes the number of rows and columns in the grid The
second number M (1le
Mle
LL) denotes minimum number of dots to be included in a pattern and thethird number N (M le N le LL) denotes the maximum number of dots to be included in the pattern
OutputFor each test case you need to print the test case number X in the format ldquoCase X rdquo This will be
followed by the count of possible sequences for the given grid size minimum and maximum number of
dots in a sequence Since the count can be pretty big you need to print the value of the count modulo
10000000000007 (1 followed by 12 zeros followed by 7)
Sample Input Output for Sample Input2
3 4 9
3 1 9
Case 1 985824
Case 2 986409
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1120
EYou have pearl of 3 types
bull Type 1 pearl can be of color fr
bull Type 2 pearl can be of color fr
bull Type 3 pearl can be of color fr
You have unlimited supply of pearls
But you have 2 more additional constr
bull
The total number of Type 1 anbull The total number of Type 2 an
Given A B X Y and Z calculate ho
they have different length or there is a
InputFirst line of the input contains T (1 le
A B X Y and Z All of these 5 intege
OutputFor each test case output an integer d
huge output the result modulo 100000
Sample Input5
1 1 1 1 1
2 3 1 1 1
1 1 1 2 1
10 10 10 10 10
100 100 100 100 100
earl ChainsInput Standard Inpututput Standard Output
m 1 to X
m X+1 to X+Y
m X+Y+1 to X+Y+Z
of each type and each color You want to buil
ints
Type 3 pearls will be exactly AType 3 pearls will be exactly B
many different pearl chains are possible 2 c
position in which they have different colored p
le 100) the number of test cases Each test cas
rs are between 1 and 1017
inclusive
noting the number of possible pearl chains Si
Output for Sample Inp3
25
5
77069
329672
some pearl chain
ains are different if
arl
contains 5 integers
nce the result is too
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1220
F Two PI
O
Itrsquos a common phenomenon to mix u
that they just look at sky and can tell y
whole way they travelled ldquoFirst we
and so this one is helliprdquo and thus end u
each other and they do not always run
ends up with some ridiculous answer a
The city we are talking about is a sq
Although the city is nice square shape
rail track and it is a straight one
perpendicular to the existing one The
or not they just need location of twconnecting these two stations the line
you have to build the stations in intege
So to sum it up you will be given co-
to give any two distinct integer co-or
co-ordinates may coincide with the gi
Input
First line of input will contain an integ
be a line of four integers X1 Y1 X2
ordinates of two stations on the alread
You may assume that these two points
OutputFor each test case produce one line
integers where the first two integers
integers are the x and y co-ordinate
possible value of S and the line pa
(may not necessarily intersect the
answers you may output any of the
coordinates does not exceed9
102times F
Sample Input2
4 4 5 5
9 0 10 0
oints Revisitednput Standard Inputtput Standard Output
direction when you go to a new place Some
ou which one is north And some dumb people
ere east facing then we turned left then right
with a direction But the roads are not always
from north to south or from east to west So thi
lmost all the times
uare shaped one with vertices at (0 0) (S 0)
one the road network is already messed up
o city corporation decides to build another
do not care if the new track intersects with th
rail stations so that if a rail track is built alowould be perpendicular to the existing rail tr
r co-ordinates
rdinates of two stations on the already existing
inates within the city for building new rail tra
en co-ordinates if you want it to
er T the number of test cases (T le 15000) For
2 (0 le X1 Y1 X2 Y2 le 109) Here (X1 Y1) and
existing rail track
are different and within the city
of output This line contains the case numbe
are the x and y co-ordinate of the first statio
of the second station They should be withi
sing through them must be perpendicular
previous track within the city) Since the
but you have to make sure that absolute va
or details please go through the explanation of t
Output for Sample ICase 1 1 0 0 1
Case 2 10 0 10 2
eople are so clever
try to remember the
then again righthellip
in 90 degrees with
kind of calculation
(S S) and (0 S)
ut there is only one
rail track which is
previous rail track
ng the straight lineck The problem is
rail track you have
ck One of the new
each case there will
(X2 Y2) are the co-
r followed by four
n and the next two
the city for any
o the existing line
re can be multiple
lue of any of these
he sample cases
put
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1320
13
Explanation
First Sample
In the first sample the existing rail track goes through points (4 4) and (5 5) If you establish two new
rail stations at (1 0) and (0 1) the rail track passing through them will be perpendicular to the existingrail track Note if you output something like (5 5) and (6 4) you will get Wrong Answer since if S = 5
point (6 4) will not be within the city But for any value of S such that (4 4) and (5 5) is within the city
points (1 0) and (0 1) will also be within the city
Second Sample
In this case there are many correct answers One of them is (10 0) and (10 2) Note that unlike first
sample here the rail tracks intersect
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1420
G
Watc
Day by day number of Kangaroos is d
Now for the convenience of the spect
ldquoKangaroo appears in Screen 7rdquo an
position of Kangaroos and inform th
screen to display that animal based on
as follows
If the position x is outside the rangeOtherwise the coverage is minimum(
An example will make it clear
Suppose there are four screens coveri
Kangaroo appears at x = 10
First screen has coverage of 3 unit aro
15 ndash 10) = minimum(3 5) = 3
Second screen has coverage of 0 unit
100)
Third screen has coverage of 0 unit
minimum(10 ndash 8 10 ndash 10) = 0
Fourth screen has coverage of 1 unit a
1 11 ndash 10) = 1
ing the KangarooInput Standard Input
Output Standard Output
ecreasing just like tiger whale or lions So I de
a sanctuary where they will live peac
visitors go near them So I planted s
outside the sanctuary For this proble
the sanctuary to be a long line of 10000
The leftmost position is marked with
position with 1000000000 There ar
cameras on this line Each of the camer
(L R) which means that camera coposition L to position R inclusive Each
their associated display screens outside
can see the Kangaroos
ators we announce time to time ldquoKangaroo a
so on I have some employees who contin
system (here position is a marker) The syste
the coverage The coverage of a screen for a
of that screen (ie x lt L or x gt R) then thndash L R ndash x)
ng the range (7 15) (14 100) (8 10) and (1
nd x = 10 Because x = 10 is within (7 15) an
around x = 10 Because x = 10 does not belo
around x = 10 Because though x = 10 is
round x = 10 Because x = 10 is within (1 11)
cided to make them
fully I do not let
me display screen
you may assume
0000 unit distance
and the rightmost
at most 100000
as is described with
vers a range fromof the cameras has
where the visitors
pears in Screen 3rdquo
ously monitor the
m chooses the best
osition x is defined
coverage is zero
11) Now say one
minimum(10 ndash 7
g to the range (14
within (8 10) but
and minimum(10 ndash
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1520
15
So which one is better Obviously the first one as it has the maximum coverage
So you are given the ranges of the screens and the positions the kangaroo appears For each position of
the Kangaroo you are to tell me the maximum coverage you can have with any of the screens
Input
First line of the test file contains T (T le 3) number of test cases Hence T cases follow For each case
you are given N M in the first line N is the number of screens and M is the number of Kangaroo
appearance ( 1 le N M le 100000) In the next N lines you are given the range of screens L R ( 0 le L le R
le 1000000000 ) Next M lines contain the position of the Kangaroo- an integer x (0 le x le 1000000000)
OutputFor each case print the case number Hence print M lines ith containing the maximum coverage you can
have around irsquoth Kangaroo
Sample Input Output for Sample Input1
3 2
7 15
14 100
1 11
10
120
Case 1
3
0
Warning The judge input file is around 6 MB So use faster IO functions
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1620
HGiven an integer N find how many pa
A le N
Here gcd (A B) means the greatest c
of the bitwise xor operation on the bin
InputThe first line of the input contains a
following T lines contain an integer N
OutputFor each test case print the case nu
input) followed by a space and then th
Sample Input2
7
20000000
Explanation
Sample 1
For N=7 there are four valid pairs (3
GCD XORInput Standard Inpututput Standard Output
irs (A B) are there such that gcd (A B) = A x
mmon divisor of the numbers A and B And
ary representation of A and B
n integer T(T le 10000) denoting the number
1 le N le 30000000)
ber first in the format Case X (here X
answer for that case
Output for Sample InpCase 1 4
Case 2 34866117
2) (5 4) (6 4) and (7 6)
or B where 1 le B le
xor B is the value
of test cases The
is the serial of the
ut
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1720
INatasha always mixes up things in her
classical problem - finding shortest p
that in another class the professor t
looking but does very different things
to the Primrsquos algorithm (actually w
Pseudocode of her algorithm looks as
FiascoInput Standard Input
Output Standard Output
algorithm classes Last week Prof Chhaya Mu
th to all nodes from a specific node of a wei
aught them Primrsquos and Dijkstrarsquos algorithms
Always confused poor Natasha submitted so
should call it Natasharsquos algorithm) she did
ollows
thy gave the class a
hted graph Before
which are similar
ething very similar
rsquot test it properly
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1820
18
After submission she showed the code to a friend who is good at algorithms That friend immediately
found the flaw Natasha was really terrified and started to cry Then there came the guys the guys who
liked her They jumped at the opportunity and got hold of the dataset to be used to test the solutions Your
friend Rehan is one of those guys He really wanted to impress Natasha He asked you to change the
dataset in such a way that Natasharsquos algorithm gives the right result After the change Rehan will
somehow be able to put the modified data with the old timestamp Rehan told you that
1 The dataset has T test cases
2 Each case contains a connected weighted undirected graph with n nodes and m edges
3 Each case will contain a source node source
4 Edge weights are positive and distinct
To avoid suspicion Rehan asked you not to change which vertices the edges connect or the overall set of
edge weights You may only reorder which weights are assigned to which edges
InputThe first line of the input denotes the number of datasets T (1 le T le 15) T sets of case will follow Eachcase will start with a triplet of numbers n (2 le n le 2500) m (1 le m le 25000) and source (1 le source le
n) - the number of nodes the number of edges and the starting node respectively Each of the next m
lines will contain a triplet of numbers (u v w) meaning that there is an edge between node u and node v
with weight w (1 le w le m) Nodes are numbered from 1 to n It is guaranteed that there is no duplicate or
self-edges in the input and the graph is connected In each given graph all edge weights will be distinct
OutputFor each set of input print one set of output First line of a set should be of the format ldquoCase Xrdquo
where X is the case number Then print each edge triplet - one triplet ( u v and w) in each line separated
by a single space The edges should be printed in the order given in the input If there is more than one
solution to a dataset any one of them will do
Sample Input Output for Sample Input1
7 9 5
2 4 2
1 4 8
7 2 6
3 4 7
5 7 5
7 3 9
6 1 1
6 3 4
5 6 3
Case 1
2 4 7
1 4 9
7 2 3
3 4 8
5 7 1
7 3 4
6 1 5
6 3 6
5 6 2
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1920
J Drom
Lets first define some terms
bull A string is palindromic if it re
madam and toot
bull A string is a dromicpalin if we
dromicpalin string is mmaad becau
palindrome
bull A substring is any contiguous
a c i icp acmicpc but acpc
empty substring so that means there a
Given a string you have to figure out
InputThe first line of input is an integer T
containing a string The strings will c
be positive and not greater than 1000
OutputFor each case first output the case n
Follow the samples for exact format
Sample Input4
acmicpc
aaaaa
isyoursolutionfastenough
abbabababbaba
cpalin SubstringsInput Standard Input
Output Standard Output
ds the same forward and backward Examples
can rearrange its letters to make it a palindro
e we can rearrange the letters to make it
equence of characters of a string Some substri
is not a substring For this problem we are
e2
)1( +nn substrings of a string of length n
ow many of its substrings are dromicpalin
(T lt 100) indicating the number of test cases
ntain only lowercase letters [a - z] The lengt
mber followed by the number of substrings t
Output for Sample InpCase 1 8
Case 2 15
Case 3 24
Case 4 67
of palindromes are
e An example of a
adam which is a
ngs of acmicpc are
not considering the
Each case is a line
of each string will
at are dromicpalin
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 2020
KCan you fill an (abc) cuboid with e
cell inside the (abc) cuboid should
dimensions and for each positive integ
a (223) cuboid can be filled with fi
filled with twelve (111) cubes
To make this problem slightly more di
filled by another cube Your job is to f
the cuboid can be filled by exactly n c
InputThere will be at most 300 test cases
abc le 125 0 le m lt abc)
Each of the next m lines contains thre
(x y z) is already filled
No cell will be mentioned twice Ther
The input is terminated by a line conta
OutputFor each test case print the case num
single space before each number in the
Sample Input2 2 3 0
2 2 3 2
1 1 1
2 2 3
0 0 0 0
ill the CuboidInput Standard Input
Output Standard Output
actly n cubes The cubes may touch but cann
be covered by exactly one cube You may us
er p you can use as many (ppp) cubes as yo
e cubes four (111) cubes and one (222)
fficult m of the cells in the cuboid are already
ind out the possible values of n such that the re
ubes
ach test case begins with four integers a b c
integers x y z (1 le x le a 1 le y le b 1 le z le c)
will be at least one non-filled cell
ining four zeroes
ber and the list of possible answers in increasi
output Look at the output for sample input for
Output for Sample InpCase 1 5 12
Case 2 10
ot overlap and each
cubes of different
like For example
cube It can also be
illed and cannot be
maining cells inside
(2 le a b c le 20
that means the cell
ng order There is a
details
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 820
8
InputInput starts with a positive integer T (T le 250) denoting the number of test cases Each case starts with
three integers N (2 le N le 100) M (N-1 le M le N(N-1)2) and K (2 le K le min(N 21)) Each of the next
M lines contains three integers u v and c (1 le uv le N u ne v 0 lt c lt 10000) meaning that there is a bi-
directional road between city u and v of cost c No two roads will be same Please also note that for 90 of the test cases K is less than 20
OutputFor each test case print the test case number (starting from 1) and the minimum possible cost of
Megaland if it is possible to build the sub-country according to the conditions described above otherwise
print ldquoImpossiblerdquo (without the quotes)
Sample Input Output for Sample Input2
7 7 4
1 7 101 5 1
2 5 2
3 6 3
4 6 1
5 6 4
3 7 8
4 4 3
1 2 1
1 3 1
2 4 1
3 4 1
Case 1 7
Case 2 Impossible
Warning The judge input file is around 25 MB So use faster IO functionsExplanation
For test case 1
In Megaland degree of each node in set A = 1234 is 1 and degree nodes in set B = 5 6 7 are 2 2
and 0 respectively
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 920
D
P
Mr Anderson is in a relationship wit
Andersons phone logs and texts to fin
he decided to put a pattern locker on hi
This pattern locker comes with a 9 dot
several dots to record a pattern The
recorded before If we assume that ea
than a sequence of digits The patter
once
Here is an example of such a pattern l
Even after recording a hard to crack p
that his girlfriend might try all possi
different pattern sequences are possib
recorded in patterns
You have to help Mr Anderson in cou
ttern LockerInput Standard Input
Output Standard Output
a very suspicious and jealous girlfriend She
d out he is up to Feeling that his private spac
s phone
s arranged on a 3x3 square grid by default One
n to unlock the phone one needs to replicat
h dot is assigned a unique number then a patt
locker requires that no digit appears in the
cker and some valid and invalid recorded patte
attern Mr Anderson doesnt feel quite comfor
le sequences to break his pattern He wants t
le for a given grid size minimum and maxim
nting the number of possible such sequences
is always checking
is getting violated
has to drag through
e the same pattern
rn is nothing more
equence more than
rn
able He is worried
o know how many
m numbers of dots
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1020
10
InputThe first line of the input will give the number of test cases T (1 le T le 10000) Then T test cases follow
in separate lines Each test case consists of three numbers L M N separated by a single space in between
two numbers The first number L (1 lt L le 100) denotes the number of rows and columns in the grid The
second number M (1le
Mle
LL) denotes minimum number of dots to be included in a pattern and thethird number N (M le N le LL) denotes the maximum number of dots to be included in the pattern
OutputFor each test case you need to print the test case number X in the format ldquoCase X rdquo This will be
followed by the count of possible sequences for the given grid size minimum and maximum number of
dots in a sequence Since the count can be pretty big you need to print the value of the count modulo
10000000000007 (1 followed by 12 zeros followed by 7)
Sample Input Output for Sample Input2
3 4 9
3 1 9
Case 1 985824
Case 2 986409
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1120
EYou have pearl of 3 types
bull Type 1 pearl can be of color fr
bull Type 2 pearl can be of color fr
bull Type 3 pearl can be of color fr
You have unlimited supply of pearls
But you have 2 more additional constr
bull
The total number of Type 1 anbull The total number of Type 2 an
Given A B X Y and Z calculate ho
they have different length or there is a
InputFirst line of the input contains T (1 le
A B X Y and Z All of these 5 intege
OutputFor each test case output an integer d
huge output the result modulo 100000
Sample Input5
1 1 1 1 1
2 3 1 1 1
1 1 1 2 1
10 10 10 10 10
100 100 100 100 100
earl ChainsInput Standard Inpututput Standard Output
m 1 to X
m X+1 to X+Y
m X+Y+1 to X+Y+Z
of each type and each color You want to buil
ints
Type 3 pearls will be exactly AType 3 pearls will be exactly B
many different pearl chains are possible 2 c
position in which they have different colored p
le 100) the number of test cases Each test cas
rs are between 1 and 1017
inclusive
noting the number of possible pearl chains Si
Output for Sample Inp3
25
5
77069
329672
some pearl chain
ains are different if
arl
contains 5 integers
nce the result is too
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1220
F Two PI
O
Itrsquos a common phenomenon to mix u
that they just look at sky and can tell y
whole way they travelled ldquoFirst we
and so this one is helliprdquo and thus end u
each other and they do not always run
ends up with some ridiculous answer a
The city we are talking about is a sq
Although the city is nice square shape
rail track and it is a straight one
perpendicular to the existing one The
or not they just need location of twconnecting these two stations the line
you have to build the stations in intege
So to sum it up you will be given co-
to give any two distinct integer co-or
co-ordinates may coincide with the gi
Input
First line of input will contain an integ
be a line of four integers X1 Y1 X2
ordinates of two stations on the alread
You may assume that these two points
OutputFor each test case produce one line
integers where the first two integers
integers are the x and y co-ordinate
possible value of S and the line pa
(may not necessarily intersect the
answers you may output any of the
coordinates does not exceed9
102times F
Sample Input2
4 4 5 5
9 0 10 0
oints Revisitednput Standard Inputtput Standard Output
direction when you go to a new place Some
ou which one is north And some dumb people
ere east facing then we turned left then right
with a direction But the roads are not always
from north to south or from east to west So thi
lmost all the times
uare shaped one with vertices at (0 0) (S 0)
one the road network is already messed up
o city corporation decides to build another
do not care if the new track intersects with th
rail stations so that if a rail track is built alowould be perpendicular to the existing rail tr
r co-ordinates
rdinates of two stations on the already existing
inates within the city for building new rail tra
en co-ordinates if you want it to
er T the number of test cases (T le 15000) For
2 (0 le X1 Y1 X2 Y2 le 109) Here (X1 Y1) and
existing rail track
are different and within the city
of output This line contains the case numbe
are the x and y co-ordinate of the first statio
of the second station They should be withi
sing through them must be perpendicular
previous track within the city) Since the
but you have to make sure that absolute va
or details please go through the explanation of t
Output for Sample ICase 1 1 0 0 1
Case 2 10 0 10 2
eople are so clever
try to remember the
then again righthellip
in 90 degrees with
kind of calculation
(S S) and (0 S)
ut there is only one
rail track which is
previous rail track
ng the straight lineck The problem is
rail track you have
ck One of the new
each case there will
(X2 Y2) are the co-
r followed by four
n and the next two
the city for any
o the existing line
re can be multiple
lue of any of these
he sample cases
put
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1320
13
Explanation
First Sample
In the first sample the existing rail track goes through points (4 4) and (5 5) If you establish two new
rail stations at (1 0) and (0 1) the rail track passing through them will be perpendicular to the existingrail track Note if you output something like (5 5) and (6 4) you will get Wrong Answer since if S = 5
point (6 4) will not be within the city But for any value of S such that (4 4) and (5 5) is within the city
points (1 0) and (0 1) will also be within the city
Second Sample
In this case there are many correct answers One of them is (10 0) and (10 2) Note that unlike first
sample here the rail tracks intersect
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1420
G
Watc
Day by day number of Kangaroos is d
Now for the convenience of the spect
ldquoKangaroo appears in Screen 7rdquo an
position of Kangaroos and inform th
screen to display that animal based on
as follows
If the position x is outside the rangeOtherwise the coverage is minimum(
An example will make it clear
Suppose there are four screens coveri
Kangaroo appears at x = 10
First screen has coverage of 3 unit aro
15 ndash 10) = minimum(3 5) = 3
Second screen has coverage of 0 unit
100)
Third screen has coverage of 0 unit
minimum(10 ndash 8 10 ndash 10) = 0
Fourth screen has coverage of 1 unit a
1 11 ndash 10) = 1
ing the KangarooInput Standard Input
Output Standard Output
ecreasing just like tiger whale or lions So I de
a sanctuary where they will live peac
visitors go near them So I planted s
outside the sanctuary For this proble
the sanctuary to be a long line of 10000
The leftmost position is marked with
position with 1000000000 There ar
cameras on this line Each of the camer
(L R) which means that camera coposition L to position R inclusive Each
their associated display screens outside
can see the Kangaroos
ators we announce time to time ldquoKangaroo a
so on I have some employees who contin
system (here position is a marker) The syste
the coverage The coverage of a screen for a
of that screen (ie x lt L or x gt R) then thndash L R ndash x)
ng the range (7 15) (14 100) (8 10) and (1
nd x = 10 Because x = 10 is within (7 15) an
around x = 10 Because x = 10 does not belo
around x = 10 Because though x = 10 is
round x = 10 Because x = 10 is within (1 11)
cided to make them
fully I do not let
me display screen
you may assume
0000 unit distance
and the rightmost
at most 100000
as is described with
vers a range fromof the cameras has
where the visitors
pears in Screen 3rdquo
ously monitor the
m chooses the best
osition x is defined
coverage is zero
11) Now say one
minimum(10 ndash 7
g to the range (14
within (8 10) but
and minimum(10 ndash
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1520
15
So which one is better Obviously the first one as it has the maximum coverage
So you are given the ranges of the screens and the positions the kangaroo appears For each position of
the Kangaroo you are to tell me the maximum coverage you can have with any of the screens
Input
First line of the test file contains T (T le 3) number of test cases Hence T cases follow For each case
you are given N M in the first line N is the number of screens and M is the number of Kangaroo
appearance ( 1 le N M le 100000) In the next N lines you are given the range of screens L R ( 0 le L le R
le 1000000000 ) Next M lines contain the position of the Kangaroo- an integer x (0 le x le 1000000000)
OutputFor each case print the case number Hence print M lines ith containing the maximum coverage you can
have around irsquoth Kangaroo
Sample Input Output for Sample Input1
3 2
7 15
14 100
1 11
10
120
Case 1
3
0
Warning The judge input file is around 6 MB So use faster IO functions
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1620
HGiven an integer N find how many pa
A le N
Here gcd (A B) means the greatest c
of the bitwise xor operation on the bin
InputThe first line of the input contains a
following T lines contain an integer N
OutputFor each test case print the case nu
input) followed by a space and then th
Sample Input2
7
20000000
Explanation
Sample 1
For N=7 there are four valid pairs (3
GCD XORInput Standard Inpututput Standard Output
irs (A B) are there such that gcd (A B) = A x
mmon divisor of the numbers A and B And
ary representation of A and B
n integer T(T le 10000) denoting the number
1 le N le 30000000)
ber first in the format Case X (here X
answer for that case
Output for Sample InpCase 1 4
Case 2 34866117
2) (5 4) (6 4) and (7 6)
or B where 1 le B le
xor B is the value
of test cases The
is the serial of the
ut
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1720
INatasha always mixes up things in her
classical problem - finding shortest p
that in another class the professor t
looking but does very different things
to the Primrsquos algorithm (actually w
Pseudocode of her algorithm looks as
FiascoInput Standard Input
Output Standard Output
algorithm classes Last week Prof Chhaya Mu
th to all nodes from a specific node of a wei
aught them Primrsquos and Dijkstrarsquos algorithms
Always confused poor Natasha submitted so
should call it Natasharsquos algorithm) she did
ollows
thy gave the class a
hted graph Before
which are similar
ething very similar
rsquot test it properly
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1820
18
After submission she showed the code to a friend who is good at algorithms That friend immediately
found the flaw Natasha was really terrified and started to cry Then there came the guys the guys who
liked her They jumped at the opportunity and got hold of the dataset to be used to test the solutions Your
friend Rehan is one of those guys He really wanted to impress Natasha He asked you to change the
dataset in such a way that Natasharsquos algorithm gives the right result After the change Rehan will
somehow be able to put the modified data with the old timestamp Rehan told you that
1 The dataset has T test cases
2 Each case contains a connected weighted undirected graph with n nodes and m edges
3 Each case will contain a source node source
4 Edge weights are positive and distinct
To avoid suspicion Rehan asked you not to change which vertices the edges connect or the overall set of
edge weights You may only reorder which weights are assigned to which edges
InputThe first line of the input denotes the number of datasets T (1 le T le 15) T sets of case will follow Eachcase will start with a triplet of numbers n (2 le n le 2500) m (1 le m le 25000) and source (1 le source le
n) - the number of nodes the number of edges and the starting node respectively Each of the next m
lines will contain a triplet of numbers (u v w) meaning that there is an edge between node u and node v
with weight w (1 le w le m) Nodes are numbered from 1 to n It is guaranteed that there is no duplicate or
self-edges in the input and the graph is connected In each given graph all edge weights will be distinct
OutputFor each set of input print one set of output First line of a set should be of the format ldquoCase Xrdquo
where X is the case number Then print each edge triplet - one triplet ( u v and w) in each line separated
by a single space The edges should be printed in the order given in the input If there is more than one
solution to a dataset any one of them will do
Sample Input Output for Sample Input1
7 9 5
2 4 2
1 4 8
7 2 6
3 4 7
5 7 5
7 3 9
6 1 1
6 3 4
5 6 3
Case 1
2 4 7
1 4 9
7 2 3
3 4 8
5 7 1
7 3 4
6 1 5
6 3 6
5 6 2
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1920
J Drom
Lets first define some terms
bull A string is palindromic if it re
madam and toot
bull A string is a dromicpalin if we
dromicpalin string is mmaad becau
palindrome
bull A substring is any contiguous
a c i icp acmicpc but acpc
empty substring so that means there a
Given a string you have to figure out
InputThe first line of input is an integer T
containing a string The strings will c
be positive and not greater than 1000
OutputFor each case first output the case n
Follow the samples for exact format
Sample Input4
acmicpc
aaaaa
isyoursolutionfastenough
abbabababbaba
cpalin SubstringsInput Standard Input
Output Standard Output
ds the same forward and backward Examples
can rearrange its letters to make it a palindro
e we can rearrange the letters to make it
equence of characters of a string Some substri
is not a substring For this problem we are
e2
)1( +nn substrings of a string of length n
ow many of its substrings are dromicpalin
(T lt 100) indicating the number of test cases
ntain only lowercase letters [a - z] The lengt
mber followed by the number of substrings t
Output for Sample InpCase 1 8
Case 2 15
Case 3 24
Case 4 67
of palindromes are
e An example of a
adam which is a
ngs of acmicpc are
not considering the
Each case is a line
of each string will
at are dromicpalin
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 2020
KCan you fill an (abc) cuboid with e
cell inside the (abc) cuboid should
dimensions and for each positive integ
a (223) cuboid can be filled with fi
filled with twelve (111) cubes
To make this problem slightly more di
filled by another cube Your job is to f
the cuboid can be filled by exactly n c
InputThere will be at most 300 test cases
abc le 125 0 le m lt abc)
Each of the next m lines contains thre
(x y z) is already filled
No cell will be mentioned twice Ther
The input is terminated by a line conta
OutputFor each test case print the case num
single space before each number in the
Sample Input2 2 3 0
2 2 3 2
1 1 1
2 2 3
0 0 0 0
ill the CuboidInput Standard Input
Output Standard Output
actly n cubes The cubes may touch but cann
be covered by exactly one cube You may us
er p you can use as many (ppp) cubes as yo
e cubes four (111) cubes and one (222)
fficult m of the cells in the cuboid are already
ind out the possible values of n such that the re
ubes
ach test case begins with four integers a b c
integers x y z (1 le x le a 1 le y le b 1 le z le c)
will be at least one non-filled cell
ining four zeroes
ber and the list of possible answers in increasi
output Look at the output for sample input for
Output for Sample InpCase 1 5 12
Case 2 10
ot overlap and each
cubes of different
like For example
cube It can also be
illed and cannot be
maining cells inside
(2 le a b c le 20
that means the cell
ng order There is a
details
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 920
D
P
Mr Anderson is in a relationship wit
Andersons phone logs and texts to fin
he decided to put a pattern locker on hi
This pattern locker comes with a 9 dot
several dots to record a pattern The
recorded before If we assume that ea
than a sequence of digits The patter
once
Here is an example of such a pattern l
Even after recording a hard to crack p
that his girlfriend might try all possi
different pattern sequences are possib
recorded in patterns
You have to help Mr Anderson in cou
ttern LockerInput Standard Input
Output Standard Output
a very suspicious and jealous girlfriend She
d out he is up to Feeling that his private spac
s phone
s arranged on a 3x3 square grid by default One
n to unlock the phone one needs to replicat
h dot is assigned a unique number then a patt
locker requires that no digit appears in the
cker and some valid and invalid recorded patte
attern Mr Anderson doesnt feel quite comfor
le sequences to break his pattern He wants t
le for a given grid size minimum and maxim
nting the number of possible such sequences
is always checking
is getting violated
has to drag through
e the same pattern
rn is nothing more
equence more than
rn
able He is worried
o know how many
m numbers of dots
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1020
10
InputThe first line of the input will give the number of test cases T (1 le T le 10000) Then T test cases follow
in separate lines Each test case consists of three numbers L M N separated by a single space in between
two numbers The first number L (1 lt L le 100) denotes the number of rows and columns in the grid The
second number M (1le
Mle
LL) denotes minimum number of dots to be included in a pattern and thethird number N (M le N le LL) denotes the maximum number of dots to be included in the pattern
OutputFor each test case you need to print the test case number X in the format ldquoCase X rdquo This will be
followed by the count of possible sequences for the given grid size minimum and maximum number of
dots in a sequence Since the count can be pretty big you need to print the value of the count modulo
10000000000007 (1 followed by 12 zeros followed by 7)
Sample Input Output for Sample Input2
3 4 9
3 1 9
Case 1 985824
Case 2 986409
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1120
EYou have pearl of 3 types
bull Type 1 pearl can be of color fr
bull Type 2 pearl can be of color fr
bull Type 3 pearl can be of color fr
You have unlimited supply of pearls
But you have 2 more additional constr
bull
The total number of Type 1 anbull The total number of Type 2 an
Given A B X Y and Z calculate ho
they have different length or there is a
InputFirst line of the input contains T (1 le
A B X Y and Z All of these 5 intege
OutputFor each test case output an integer d
huge output the result modulo 100000
Sample Input5
1 1 1 1 1
2 3 1 1 1
1 1 1 2 1
10 10 10 10 10
100 100 100 100 100
earl ChainsInput Standard Inpututput Standard Output
m 1 to X
m X+1 to X+Y
m X+Y+1 to X+Y+Z
of each type and each color You want to buil
ints
Type 3 pearls will be exactly AType 3 pearls will be exactly B
many different pearl chains are possible 2 c
position in which they have different colored p
le 100) the number of test cases Each test cas
rs are between 1 and 1017
inclusive
noting the number of possible pearl chains Si
Output for Sample Inp3
25
5
77069
329672
some pearl chain
ains are different if
arl
contains 5 integers
nce the result is too
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1220
F Two PI
O
Itrsquos a common phenomenon to mix u
that they just look at sky and can tell y
whole way they travelled ldquoFirst we
and so this one is helliprdquo and thus end u
each other and they do not always run
ends up with some ridiculous answer a
The city we are talking about is a sq
Although the city is nice square shape
rail track and it is a straight one
perpendicular to the existing one The
or not they just need location of twconnecting these two stations the line
you have to build the stations in intege
So to sum it up you will be given co-
to give any two distinct integer co-or
co-ordinates may coincide with the gi
Input
First line of input will contain an integ
be a line of four integers X1 Y1 X2
ordinates of two stations on the alread
You may assume that these two points
OutputFor each test case produce one line
integers where the first two integers
integers are the x and y co-ordinate
possible value of S and the line pa
(may not necessarily intersect the
answers you may output any of the
coordinates does not exceed9
102times F
Sample Input2
4 4 5 5
9 0 10 0
oints Revisitednput Standard Inputtput Standard Output
direction when you go to a new place Some
ou which one is north And some dumb people
ere east facing then we turned left then right
with a direction But the roads are not always
from north to south or from east to west So thi
lmost all the times
uare shaped one with vertices at (0 0) (S 0)
one the road network is already messed up
o city corporation decides to build another
do not care if the new track intersects with th
rail stations so that if a rail track is built alowould be perpendicular to the existing rail tr
r co-ordinates
rdinates of two stations on the already existing
inates within the city for building new rail tra
en co-ordinates if you want it to
er T the number of test cases (T le 15000) For
2 (0 le X1 Y1 X2 Y2 le 109) Here (X1 Y1) and
existing rail track
are different and within the city
of output This line contains the case numbe
are the x and y co-ordinate of the first statio
of the second station They should be withi
sing through them must be perpendicular
previous track within the city) Since the
but you have to make sure that absolute va
or details please go through the explanation of t
Output for Sample ICase 1 1 0 0 1
Case 2 10 0 10 2
eople are so clever
try to remember the
then again righthellip
in 90 degrees with
kind of calculation
(S S) and (0 S)
ut there is only one
rail track which is
previous rail track
ng the straight lineck The problem is
rail track you have
ck One of the new
each case there will
(X2 Y2) are the co-
r followed by four
n and the next two
the city for any
o the existing line
re can be multiple
lue of any of these
he sample cases
put
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1320
13
Explanation
First Sample
In the first sample the existing rail track goes through points (4 4) and (5 5) If you establish two new
rail stations at (1 0) and (0 1) the rail track passing through them will be perpendicular to the existingrail track Note if you output something like (5 5) and (6 4) you will get Wrong Answer since if S = 5
point (6 4) will not be within the city But for any value of S such that (4 4) and (5 5) is within the city
points (1 0) and (0 1) will also be within the city
Second Sample
In this case there are many correct answers One of them is (10 0) and (10 2) Note that unlike first
sample here the rail tracks intersect
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1420
G
Watc
Day by day number of Kangaroos is d
Now for the convenience of the spect
ldquoKangaroo appears in Screen 7rdquo an
position of Kangaroos and inform th
screen to display that animal based on
as follows
If the position x is outside the rangeOtherwise the coverage is minimum(
An example will make it clear
Suppose there are four screens coveri
Kangaroo appears at x = 10
First screen has coverage of 3 unit aro
15 ndash 10) = minimum(3 5) = 3
Second screen has coverage of 0 unit
100)
Third screen has coverage of 0 unit
minimum(10 ndash 8 10 ndash 10) = 0
Fourth screen has coverage of 1 unit a
1 11 ndash 10) = 1
ing the KangarooInput Standard Input
Output Standard Output
ecreasing just like tiger whale or lions So I de
a sanctuary where they will live peac
visitors go near them So I planted s
outside the sanctuary For this proble
the sanctuary to be a long line of 10000
The leftmost position is marked with
position with 1000000000 There ar
cameras on this line Each of the camer
(L R) which means that camera coposition L to position R inclusive Each
their associated display screens outside
can see the Kangaroos
ators we announce time to time ldquoKangaroo a
so on I have some employees who contin
system (here position is a marker) The syste
the coverage The coverage of a screen for a
of that screen (ie x lt L or x gt R) then thndash L R ndash x)
ng the range (7 15) (14 100) (8 10) and (1
nd x = 10 Because x = 10 is within (7 15) an
around x = 10 Because x = 10 does not belo
around x = 10 Because though x = 10 is
round x = 10 Because x = 10 is within (1 11)
cided to make them
fully I do not let
me display screen
you may assume
0000 unit distance
and the rightmost
at most 100000
as is described with
vers a range fromof the cameras has
where the visitors
pears in Screen 3rdquo
ously monitor the
m chooses the best
osition x is defined
coverage is zero
11) Now say one
minimum(10 ndash 7
g to the range (14
within (8 10) but
and minimum(10 ndash
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1520
15
So which one is better Obviously the first one as it has the maximum coverage
So you are given the ranges of the screens and the positions the kangaroo appears For each position of
the Kangaroo you are to tell me the maximum coverage you can have with any of the screens
Input
First line of the test file contains T (T le 3) number of test cases Hence T cases follow For each case
you are given N M in the first line N is the number of screens and M is the number of Kangaroo
appearance ( 1 le N M le 100000) In the next N lines you are given the range of screens L R ( 0 le L le R
le 1000000000 ) Next M lines contain the position of the Kangaroo- an integer x (0 le x le 1000000000)
OutputFor each case print the case number Hence print M lines ith containing the maximum coverage you can
have around irsquoth Kangaroo
Sample Input Output for Sample Input1
3 2
7 15
14 100
1 11
10
120
Case 1
3
0
Warning The judge input file is around 6 MB So use faster IO functions
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1620
HGiven an integer N find how many pa
A le N
Here gcd (A B) means the greatest c
of the bitwise xor operation on the bin
InputThe first line of the input contains a
following T lines contain an integer N
OutputFor each test case print the case nu
input) followed by a space and then th
Sample Input2
7
20000000
Explanation
Sample 1
For N=7 there are four valid pairs (3
GCD XORInput Standard Inpututput Standard Output
irs (A B) are there such that gcd (A B) = A x
mmon divisor of the numbers A and B And
ary representation of A and B
n integer T(T le 10000) denoting the number
1 le N le 30000000)
ber first in the format Case X (here X
answer for that case
Output for Sample InpCase 1 4
Case 2 34866117
2) (5 4) (6 4) and (7 6)
or B where 1 le B le
xor B is the value
of test cases The
is the serial of the
ut
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1720
INatasha always mixes up things in her
classical problem - finding shortest p
that in another class the professor t
looking but does very different things
to the Primrsquos algorithm (actually w
Pseudocode of her algorithm looks as
FiascoInput Standard Input
Output Standard Output
algorithm classes Last week Prof Chhaya Mu
th to all nodes from a specific node of a wei
aught them Primrsquos and Dijkstrarsquos algorithms
Always confused poor Natasha submitted so
should call it Natasharsquos algorithm) she did
ollows
thy gave the class a
hted graph Before
which are similar
ething very similar
rsquot test it properly
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1820
18
After submission she showed the code to a friend who is good at algorithms That friend immediately
found the flaw Natasha was really terrified and started to cry Then there came the guys the guys who
liked her They jumped at the opportunity and got hold of the dataset to be used to test the solutions Your
friend Rehan is one of those guys He really wanted to impress Natasha He asked you to change the
dataset in such a way that Natasharsquos algorithm gives the right result After the change Rehan will
somehow be able to put the modified data with the old timestamp Rehan told you that
1 The dataset has T test cases
2 Each case contains a connected weighted undirected graph with n nodes and m edges
3 Each case will contain a source node source
4 Edge weights are positive and distinct
To avoid suspicion Rehan asked you not to change which vertices the edges connect or the overall set of
edge weights You may only reorder which weights are assigned to which edges
InputThe first line of the input denotes the number of datasets T (1 le T le 15) T sets of case will follow Eachcase will start with a triplet of numbers n (2 le n le 2500) m (1 le m le 25000) and source (1 le source le
n) - the number of nodes the number of edges and the starting node respectively Each of the next m
lines will contain a triplet of numbers (u v w) meaning that there is an edge between node u and node v
with weight w (1 le w le m) Nodes are numbered from 1 to n It is guaranteed that there is no duplicate or
self-edges in the input and the graph is connected In each given graph all edge weights will be distinct
OutputFor each set of input print one set of output First line of a set should be of the format ldquoCase Xrdquo
where X is the case number Then print each edge triplet - one triplet ( u v and w) in each line separated
by a single space The edges should be printed in the order given in the input If there is more than one
solution to a dataset any one of them will do
Sample Input Output for Sample Input1
7 9 5
2 4 2
1 4 8
7 2 6
3 4 7
5 7 5
7 3 9
6 1 1
6 3 4
5 6 3
Case 1
2 4 7
1 4 9
7 2 3
3 4 8
5 7 1
7 3 4
6 1 5
6 3 6
5 6 2
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1920
J Drom
Lets first define some terms
bull A string is palindromic if it re
madam and toot
bull A string is a dromicpalin if we
dromicpalin string is mmaad becau
palindrome
bull A substring is any contiguous
a c i icp acmicpc but acpc
empty substring so that means there a
Given a string you have to figure out
InputThe first line of input is an integer T
containing a string The strings will c
be positive and not greater than 1000
OutputFor each case first output the case n
Follow the samples for exact format
Sample Input4
acmicpc
aaaaa
isyoursolutionfastenough
abbabababbaba
cpalin SubstringsInput Standard Input
Output Standard Output
ds the same forward and backward Examples
can rearrange its letters to make it a palindro
e we can rearrange the letters to make it
equence of characters of a string Some substri
is not a substring For this problem we are
e2
)1( +nn substrings of a string of length n
ow many of its substrings are dromicpalin
(T lt 100) indicating the number of test cases
ntain only lowercase letters [a - z] The lengt
mber followed by the number of substrings t
Output for Sample InpCase 1 8
Case 2 15
Case 3 24
Case 4 67
of palindromes are
e An example of a
adam which is a
ngs of acmicpc are
not considering the
Each case is a line
of each string will
at are dromicpalin
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 2020
KCan you fill an (abc) cuboid with e
cell inside the (abc) cuboid should
dimensions and for each positive integ
a (223) cuboid can be filled with fi
filled with twelve (111) cubes
To make this problem slightly more di
filled by another cube Your job is to f
the cuboid can be filled by exactly n c
InputThere will be at most 300 test cases
abc le 125 0 le m lt abc)
Each of the next m lines contains thre
(x y z) is already filled
No cell will be mentioned twice Ther
The input is terminated by a line conta
OutputFor each test case print the case num
single space before each number in the
Sample Input2 2 3 0
2 2 3 2
1 1 1
2 2 3
0 0 0 0
ill the CuboidInput Standard Input
Output Standard Output
actly n cubes The cubes may touch but cann
be covered by exactly one cube You may us
er p you can use as many (ppp) cubes as yo
e cubes four (111) cubes and one (222)
fficult m of the cells in the cuboid are already
ind out the possible values of n such that the re
ubes
ach test case begins with four integers a b c
integers x y z (1 le x le a 1 le y le b 1 le z le c)
will be at least one non-filled cell
ining four zeroes
ber and the list of possible answers in increasi
output Look at the output for sample input for
Output for Sample InpCase 1 5 12
Case 2 10
ot overlap and each
cubes of different
like For example
cube It can also be
illed and cannot be
maining cells inside
(2 le a b c le 20
that means the cell
ng order There is a
details
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1020
10
InputThe first line of the input will give the number of test cases T (1 le T le 10000) Then T test cases follow
in separate lines Each test case consists of three numbers L M N separated by a single space in between
two numbers The first number L (1 lt L le 100) denotes the number of rows and columns in the grid The
second number M (1le
Mle
LL) denotes minimum number of dots to be included in a pattern and thethird number N (M le N le LL) denotes the maximum number of dots to be included in the pattern
OutputFor each test case you need to print the test case number X in the format ldquoCase X rdquo This will be
followed by the count of possible sequences for the given grid size minimum and maximum number of
dots in a sequence Since the count can be pretty big you need to print the value of the count modulo
10000000000007 (1 followed by 12 zeros followed by 7)
Sample Input Output for Sample Input2
3 4 9
3 1 9
Case 1 985824
Case 2 986409
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1120
EYou have pearl of 3 types
bull Type 1 pearl can be of color fr
bull Type 2 pearl can be of color fr
bull Type 3 pearl can be of color fr
You have unlimited supply of pearls
But you have 2 more additional constr
bull
The total number of Type 1 anbull The total number of Type 2 an
Given A B X Y and Z calculate ho
they have different length or there is a
InputFirst line of the input contains T (1 le
A B X Y and Z All of these 5 intege
OutputFor each test case output an integer d
huge output the result modulo 100000
Sample Input5
1 1 1 1 1
2 3 1 1 1
1 1 1 2 1
10 10 10 10 10
100 100 100 100 100
earl ChainsInput Standard Inpututput Standard Output
m 1 to X
m X+1 to X+Y
m X+Y+1 to X+Y+Z
of each type and each color You want to buil
ints
Type 3 pearls will be exactly AType 3 pearls will be exactly B
many different pearl chains are possible 2 c
position in which they have different colored p
le 100) the number of test cases Each test cas
rs are between 1 and 1017
inclusive
noting the number of possible pearl chains Si
Output for Sample Inp3
25
5
77069
329672
some pearl chain
ains are different if
arl
contains 5 integers
nce the result is too
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1220
F Two PI
O
Itrsquos a common phenomenon to mix u
that they just look at sky and can tell y
whole way they travelled ldquoFirst we
and so this one is helliprdquo and thus end u
each other and they do not always run
ends up with some ridiculous answer a
The city we are talking about is a sq
Although the city is nice square shape
rail track and it is a straight one
perpendicular to the existing one The
or not they just need location of twconnecting these two stations the line
you have to build the stations in intege
So to sum it up you will be given co-
to give any two distinct integer co-or
co-ordinates may coincide with the gi
Input
First line of input will contain an integ
be a line of four integers X1 Y1 X2
ordinates of two stations on the alread
You may assume that these two points
OutputFor each test case produce one line
integers where the first two integers
integers are the x and y co-ordinate
possible value of S and the line pa
(may not necessarily intersect the
answers you may output any of the
coordinates does not exceed9
102times F
Sample Input2
4 4 5 5
9 0 10 0
oints Revisitednput Standard Inputtput Standard Output
direction when you go to a new place Some
ou which one is north And some dumb people
ere east facing then we turned left then right
with a direction But the roads are not always
from north to south or from east to west So thi
lmost all the times
uare shaped one with vertices at (0 0) (S 0)
one the road network is already messed up
o city corporation decides to build another
do not care if the new track intersects with th
rail stations so that if a rail track is built alowould be perpendicular to the existing rail tr
r co-ordinates
rdinates of two stations on the already existing
inates within the city for building new rail tra
en co-ordinates if you want it to
er T the number of test cases (T le 15000) For
2 (0 le X1 Y1 X2 Y2 le 109) Here (X1 Y1) and
existing rail track
are different and within the city
of output This line contains the case numbe
are the x and y co-ordinate of the first statio
of the second station They should be withi
sing through them must be perpendicular
previous track within the city) Since the
but you have to make sure that absolute va
or details please go through the explanation of t
Output for Sample ICase 1 1 0 0 1
Case 2 10 0 10 2
eople are so clever
try to remember the
then again righthellip
in 90 degrees with
kind of calculation
(S S) and (0 S)
ut there is only one
rail track which is
previous rail track
ng the straight lineck The problem is
rail track you have
ck One of the new
each case there will
(X2 Y2) are the co-
r followed by four
n and the next two
the city for any
o the existing line
re can be multiple
lue of any of these
he sample cases
put
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1320
13
Explanation
First Sample
In the first sample the existing rail track goes through points (4 4) and (5 5) If you establish two new
rail stations at (1 0) and (0 1) the rail track passing through them will be perpendicular to the existingrail track Note if you output something like (5 5) and (6 4) you will get Wrong Answer since if S = 5
point (6 4) will not be within the city But for any value of S such that (4 4) and (5 5) is within the city
points (1 0) and (0 1) will also be within the city
Second Sample
In this case there are many correct answers One of them is (10 0) and (10 2) Note that unlike first
sample here the rail tracks intersect
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1420
G
Watc
Day by day number of Kangaroos is d
Now for the convenience of the spect
ldquoKangaroo appears in Screen 7rdquo an
position of Kangaroos and inform th
screen to display that animal based on
as follows
If the position x is outside the rangeOtherwise the coverage is minimum(
An example will make it clear
Suppose there are four screens coveri
Kangaroo appears at x = 10
First screen has coverage of 3 unit aro
15 ndash 10) = minimum(3 5) = 3
Second screen has coverage of 0 unit
100)
Third screen has coverage of 0 unit
minimum(10 ndash 8 10 ndash 10) = 0
Fourth screen has coverage of 1 unit a
1 11 ndash 10) = 1
ing the KangarooInput Standard Input
Output Standard Output
ecreasing just like tiger whale or lions So I de
a sanctuary where they will live peac
visitors go near them So I planted s
outside the sanctuary For this proble
the sanctuary to be a long line of 10000
The leftmost position is marked with
position with 1000000000 There ar
cameras on this line Each of the camer
(L R) which means that camera coposition L to position R inclusive Each
their associated display screens outside
can see the Kangaroos
ators we announce time to time ldquoKangaroo a
so on I have some employees who contin
system (here position is a marker) The syste
the coverage The coverage of a screen for a
of that screen (ie x lt L or x gt R) then thndash L R ndash x)
ng the range (7 15) (14 100) (8 10) and (1
nd x = 10 Because x = 10 is within (7 15) an
around x = 10 Because x = 10 does not belo
around x = 10 Because though x = 10 is
round x = 10 Because x = 10 is within (1 11)
cided to make them
fully I do not let
me display screen
you may assume
0000 unit distance
and the rightmost
at most 100000
as is described with
vers a range fromof the cameras has
where the visitors
pears in Screen 3rdquo
ously monitor the
m chooses the best
osition x is defined
coverage is zero
11) Now say one
minimum(10 ndash 7
g to the range (14
within (8 10) but
and minimum(10 ndash
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1520
15
So which one is better Obviously the first one as it has the maximum coverage
So you are given the ranges of the screens and the positions the kangaroo appears For each position of
the Kangaroo you are to tell me the maximum coverage you can have with any of the screens
Input
First line of the test file contains T (T le 3) number of test cases Hence T cases follow For each case
you are given N M in the first line N is the number of screens and M is the number of Kangaroo
appearance ( 1 le N M le 100000) In the next N lines you are given the range of screens L R ( 0 le L le R
le 1000000000 ) Next M lines contain the position of the Kangaroo- an integer x (0 le x le 1000000000)
OutputFor each case print the case number Hence print M lines ith containing the maximum coverage you can
have around irsquoth Kangaroo
Sample Input Output for Sample Input1
3 2
7 15
14 100
1 11
10
120
Case 1
3
0
Warning The judge input file is around 6 MB So use faster IO functions
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1620
HGiven an integer N find how many pa
A le N
Here gcd (A B) means the greatest c
of the bitwise xor operation on the bin
InputThe first line of the input contains a
following T lines contain an integer N
OutputFor each test case print the case nu
input) followed by a space and then th
Sample Input2
7
20000000
Explanation
Sample 1
For N=7 there are four valid pairs (3
GCD XORInput Standard Inpututput Standard Output
irs (A B) are there such that gcd (A B) = A x
mmon divisor of the numbers A and B And
ary representation of A and B
n integer T(T le 10000) denoting the number
1 le N le 30000000)
ber first in the format Case X (here X
answer for that case
Output for Sample InpCase 1 4
Case 2 34866117
2) (5 4) (6 4) and (7 6)
or B where 1 le B le
xor B is the value
of test cases The
is the serial of the
ut
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1720
INatasha always mixes up things in her
classical problem - finding shortest p
that in another class the professor t
looking but does very different things
to the Primrsquos algorithm (actually w
Pseudocode of her algorithm looks as
FiascoInput Standard Input
Output Standard Output
algorithm classes Last week Prof Chhaya Mu
th to all nodes from a specific node of a wei
aught them Primrsquos and Dijkstrarsquos algorithms
Always confused poor Natasha submitted so
should call it Natasharsquos algorithm) she did
ollows
thy gave the class a
hted graph Before
which are similar
ething very similar
rsquot test it properly
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1820
18
After submission she showed the code to a friend who is good at algorithms That friend immediately
found the flaw Natasha was really terrified and started to cry Then there came the guys the guys who
liked her They jumped at the opportunity and got hold of the dataset to be used to test the solutions Your
friend Rehan is one of those guys He really wanted to impress Natasha He asked you to change the
dataset in such a way that Natasharsquos algorithm gives the right result After the change Rehan will
somehow be able to put the modified data with the old timestamp Rehan told you that
1 The dataset has T test cases
2 Each case contains a connected weighted undirected graph with n nodes and m edges
3 Each case will contain a source node source
4 Edge weights are positive and distinct
To avoid suspicion Rehan asked you not to change which vertices the edges connect or the overall set of
edge weights You may only reorder which weights are assigned to which edges
InputThe first line of the input denotes the number of datasets T (1 le T le 15) T sets of case will follow Eachcase will start with a triplet of numbers n (2 le n le 2500) m (1 le m le 25000) and source (1 le source le
n) - the number of nodes the number of edges and the starting node respectively Each of the next m
lines will contain a triplet of numbers (u v w) meaning that there is an edge between node u and node v
with weight w (1 le w le m) Nodes are numbered from 1 to n It is guaranteed that there is no duplicate or
self-edges in the input and the graph is connected In each given graph all edge weights will be distinct
OutputFor each set of input print one set of output First line of a set should be of the format ldquoCase Xrdquo
where X is the case number Then print each edge triplet - one triplet ( u v and w) in each line separated
by a single space The edges should be printed in the order given in the input If there is more than one
solution to a dataset any one of them will do
Sample Input Output for Sample Input1
7 9 5
2 4 2
1 4 8
7 2 6
3 4 7
5 7 5
7 3 9
6 1 1
6 3 4
5 6 3
Case 1
2 4 7
1 4 9
7 2 3
3 4 8
5 7 1
7 3 4
6 1 5
6 3 6
5 6 2
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1920
J Drom
Lets first define some terms
bull A string is palindromic if it re
madam and toot
bull A string is a dromicpalin if we
dromicpalin string is mmaad becau
palindrome
bull A substring is any contiguous
a c i icp acmicpc but acpc
empty substring so that means there a
Given a string you have to figure out
InputThe first line of input is an integer T
containing a string The strings will c
be positive and not greater than 1000
OutputFor each case first output the case n
Follow the samples for exact format
Sample Input4
acmicpc
aaaaa
isyoursolutionfastenough
abbabababbaba
cpalin SubstringsInput Standard Input
Output Standard Output
ds the same forward and backward Examples
can rearrange its letters to make it a palindro
e we can rearrange the letters to make it
equence of characters of a string Some substri
is not a substring For this problem we are
e2
)1( +nn substrings of a string of length n
ow many of its substrings are dromicpalin
(T lt 100) indicating the number of test cases
ntain only lowercase letters [a - z] The lengt
mber followed by the number of substrings t
Output for Sample InpCase 1 8
Case 2 15
Case 3 24
Case 4 67
of palindromes are
e An example of a
adam which is a
ngs of acmicpc are
not considering the
Each case is a line
of each string will
at are dromicpalin
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 2020
KCan you fill an (abc) cuboid with e
cell inside the (abc) cuboid should
dimensions and for each positive integ
a (223) cuboid can be filled with fi
filled with twelve (111) cubes
To make this problem slightly more di
filled by another cube Your job is to f
the cuboid can be filled by exactly n c
InputThere will be at most 300 test cases
abc le 125 0 le m lt abc)
Each of the next m lines contains thre
(x y z) is already filled
No cell will be mentioned twice Ther
The input is terminated by a line conta
OutputFor each test case print the case num
single space before each number in the
Sample Input2 2 3 0
2 2 3 2
1 1 1
2 2 3
0 0 0 0
ill the CuboidInput Standard Input
Output Standard Output
actly n cubes The cubes may touch but cann
be covered by exactly one cube You may us
er p you can use as many (ppp) cubes as yo
e cubes four (111) cubes and one (222)
fficult m of the cells in the cuboid are already
ind out the possible values of n such that the re
ubes
ach test case begins with four integers a b c
integers x y z (1 le x le a 1 le y le b 1 le z le c)
will be at least one non-filled cell
ining four zeroes
ber and the list of possible answers in increasi
output Look at the output for sample input for
Output for Sample InpCase 1 5 12
Case 2 10
ot overlap and each
cubes of different
like For example
cube It can also be
illed and cannot be
maining cells inside
(2 le a b c le 20
that means the cell
ng order There is a
details
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1120
EYou have pearl of 3 types
bull Type 1 pearl can be of color fr
bull Type 2 pearl can be of color fr
bull Type 3 pearl can be of color fr
You have unlimited supply of pearls
But you have 2 more additional constr
bull
The total number of Type 1 anbull The total number of Type 2 an
Given A B X Y and Z calculate ho
they have different length or there is a
InputFirst line of the input contains T (1 le
A B X Y and Z All of these 5 intege
OutputFor each test case output an integer d
huge output the result modulo 100000
Sample Input5
1 1 1 1 1
2 3 1 1 1
1 1 1 2 1
10 10 10 10 10
100 100 100 100 100
earl ChainsInput Standard Inpututput Standard Output
m 1 to X
m X+1 to X+Y
m X+Y+1 to X+Y+Z
of each type and each color You want to buil
ints
Type 3 pearls will be exactly AType 3 pearls will be exactly B
many different pearl chains are possible 2 c
position in which they have different colored p
le 100) the number of test cases Each test cas
rs are between 1 and 1017
inclusive
noting the number of possible pearl chains Si
Output for Sample Inp3
25
5
77069
329672
some pearl chain
ains are different if
arl
contains 5 integers
nce the result is too
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1220
F Two PI
O
Itrsquos a common phenomenon to mix u
that they just look at sky and can tell y
whole way they travelled ldquoFirst we
and so this one is helliprdquo and thus end u
each other and they do not always run
ends up with some ridiculous answer a
The city we are talking about is a sq
Although the city is nice square shape
rail track and it is a straight one
perpendicular to the existing one The
or not they just need location of twconnecting these two stations the line
you have to build the stations in intege
So to sum it up you will be given co-
to give any two distinct integer co-or
co-ordinates may coincide with the gi
Input
First line of input will contain an integ
be a line of four integers X1 Y1 X2
ordinates of two stations on the alread
You may assume that these two points
OutputFor each test case produce one line
integers where the first two integers
integers are the x and y co-ordinate
possible value of S and the line pa
(may not necessarily intersect the
answers you may output any of the
coordinates does not exceed9
102times F
Sample Input2
4 4 5 5
9 0 10 0
oints Revisitednput Standard Inputtput Standard Output
direction when you go to a new place Some
ou which one is north And some dumb people
ere east facing then we turned left then right
with a direction But the roads are not always
from north to south or from east to west So thi
lmost all the times
uare shaped one with vertices at (0 0) (S 0)
one the road network is already messed up
o city corporation decides to build another
do not care if the new track intersects with th
rail stations so that if a rail track is built alowould be perpendicular to the existing rail tr
r co-ordinates
rdinates of two stations on the already existing
inates within the city for building new rail tra
en co-ordinates if you want it to
er T the number of test cases (T le 15000) For
2 (0 le X1 Y1 X2 Y2 le 109) Here (X1 Y1) and
existing rail track
are different and within the city
of output This line contains the case numbe
are the x and y co-ordinate of the first statio
of the second station They should be withi
sing through them must be perpendicular
previous track within the city) Since the
but you have to make sure that absolute va
or details please go through the explanation of t
Output for Sample ICase 1 1 0 0 1
Case 2 10 0 10 2
eople are so clever
try to remember the
then again righthellip
in 90 degrees with
kind of calculation
(S S) and (0 S)
ut there is only one
rail track which is
previous rail track
ng the straight lineck The problem is
rail track you have
ck One of the new
each case there will
(X2 Y2) are the co-
r followed by four
n and the next two
the city for any
o the existing line
re can be multiple
lue of any of these
he sample cases
put
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1320
13
Explanation
First Sample
In the first sample the existing rail track goes through points (4 4) and (5 5) If you establish two new
rail stations at (1 0) and (0 1) the rail track passing through them will be perpendicular to the existingrail track Note if you output something like (5 5) and (6 4) you will get Wrong Answer since if S = 5
point (6 4) will not be within the city But for any value of S such that (4 4) and (5 5) is within the city
points (1 0) and (0 1) will also be within the city
Second Sample
In this case there are many correct answers One of them is (10 0) and (10 2) Note that unlike first
sample here the rail tracks intersect
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1420
G
Watc
Day by day number of Kangaroos is d
Now for the convenience of the spect
ldquoKangaroo appears in Screen 7rdquo an
position of Kangaroos and inform th
screen to display that animal based on
as follows
If the position x is outside the rangeOtherwise the coverage is minimum(
An example will make it clear
Suppose there are four screens coveri
Kangaroo appears at x = 10
First screen has coverage of 3 unit aro
15 ndash 10) = minimum(3 5) = 3
Second screen has coverage of 0 unit
100)
Third screen has coverage of 0 unit
minimum(10 ndash 8 10 ndash 10) = 0
Fourth screen has coverage of 1 unit a
1 11 ndash 10) = 1
ing the KangarooInput Standard Input
Output Standard Output
ecreasing just like tiger whale or lions So I de
a sanctuary where they will live peac
visitors go near them So I planted s
outside the sanctuary For this proble
the sanctuary to be a long line of 10000
The leftmost position is marked with
position with 1000000000 There ar
cameras on this line Each of the camer
(L R) which means that camera coposition L to position R inclusive Each
their associated display screens outside
can see the Kangaroos
ators we announce time to time ldquoKangaroo a
so on I have some employees who contin
system (here position is a marker) The syste
the coverage The coverage of a screen for a
of that screen (ie x lt L or x gt R) then thndash L R ndash x)
ng the range (7 15) (14 100) (8 10) and (1
nd x = 10 Because x = 10 is within (7 15) an
around x = 10 Because x = 10 does not belo
around x = 10 Because though x = 10 is
round x = 10 Because x = 10 is within (1 11)
cided to make them
fully I do not let
me display screen
you may assume
0000 unit distance
and the rightmost
at most 100000
as is described with
vers a range fromof the cameras has
where the visitors
pears in Screen 3rdquo
ously monitor the
m chooses the best
osition x is defined
coverage is zero
11) Now say one
minimum(10 ndash 7
g to the range (14
within (8 10) but
and minimum(10 ndash
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1520
15
So which one is better Obviously the first one as it has the maximum coverage
So you are given the ranges of the screens and the positions the kangaroo appears For each position of
the Kangaroo you are to tell me the maximum coverage you can have with any of the screens
Input
First line of the test file contains T (T le 3) number of test cases Hence T cases follow For each case
you are given N M in the first line N is the number of screens and M is the number of Kangaroo
appearance ( 1 le N M le 100000) In the next N lines you are given the range of screens L R ( 0 le L le R
le 1000000000 ) Next M lines contain the position of the Kangaroo- an integer x (0 le x le 1000000000)
OutputFor each case print the case number Hence print M lines ith containing the maximum coverage you can
have around irsquoth Kangaroo
Sample Input Output for Sample Input1
3 2
7 15
14 100
1 11
10
120
Case 1
3
0
Warning The judge input file is around 6 MB So use faster IO functions
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1620
HGiven an integer N find how many pa
A le N
Here gcd (A B) means the greatest c
of the bitwise xor operation on the bin
InputThe first line of the input contains a
following T lines contain an integer N
OutputFor each test case print the case nu
input) followed by a space and then th
Sample Input2
7
20000000
Explanation
Sample 1
For N=7 there are four valid pairs (3
GCD XORInput Standard Inpututput Standard Output
irs (A B) are there such that gcd (A B) = A x
mmon divisor of the numbers A and B And
ary representation of A and B
n integer T(T le 10000) denoting the number
1 le N le 30000000)
ber first in the format Case X (here X
answer for that case
Output for Sample InpCase 1 4
Case 2 34866117
2) (5 4) (6 4) and (7 6)
or B where 1 le B le
xor B is the value
of test cases The
is the serial of the
ut
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1720
INatasha always mixes up things in her
classical problem - finding shortest p
that in another class the professor t
looking but does very different things
to the Primrsquos algorithm (actually w
Pseudocode of her algorithm looks as
FiascoInput Standard Input
Output Standard Output
algorithm classes Last week Prof Chhaya Mu
th to all nodes from a specific node of a wei
aught them Primrsquos and Dijkstrarsquos algorithms
Always confused poor Natasha submitted so
should call it Natasharsquos algorithm) she did
ollows
thy gave the class a
hted graph Before
which are similar
ething very similar
rsquot test it properly
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1820
18
After submission she showed the code to a friend who is good at algorithms That friend immediately
found the flaw Natasha was really terrified and started to cry Then there came the guys the guys who
liked her They jumped at the opportunity and got hold of the dataset to be used to test the solutions Your
friend Rehan is one of those guys He really wanted to impress Natasha He asked you to change the
dataset in such a way that Natasharsquos algorithm gives the right result After the change Rehan will
somehow be able to put the modified data with the old timestamp Rehan told you that
1 The dataset has T test cases
2 Each case contains a connected weighted undirected graph with n nodes and m edges
3 Each case will contain a source node source
4 Edge weights are positive and distinct
To avoid suspicion Rehan asked you not to change which vertices the edges connect or the overall set of
edge weights You may only reorder which weights are assigned to which edges
InputThe first line of the input denotes the number of datasets T (1 le T le 15) T sets of case will follow Eachcase will start with a triplet of numbers n (2 le n le 2500) m (1 le m le 25000) and source (1 le source le
n) - the number of nodes the number of edges and the starting node respectively Each of the next m
lines will contain a triplet of numbers (u v w) meaning that there is an edge between node u and node v
with weight w (1 le w le m) Nodes are numbered from 1 to n It is guaranteed that there is no duplicate or
self-edges in the input and the graph is connected In each given graph all edge weights will be distinct
OutputFor each set of input print one set of output First line of a set should be of the format ldquoCase Xrdquo
where X is the case number Then print each edge triplet - one triplet ( u v and w) in each line separated
by a single space The edges should be printed in the order given in the input If there is more than one
solution to a dataset any one of them will do
Sample Input Output for Sample Input1
7 9 5
2 4 2
1 4 8
7 2 6
3 4 7
5 7 5
7 3 9
6 1 1
6 3 4
5 6 3
Case 1
2 4 7
1 4 9
7 2 3
3 4 8
5 7 1
7 3 4
6 1 5
6 3 6
5 6 2
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1920
J Drom
Lets first define some terms
bull A string is palindromic if it re
madam and toot
bull A string is a dromicpalin if we
dromicpalin string is mmaad becau
palindrome
bull A substring is any contiguous
a c i icp acmicpc but acpc
empty substring so that means there a
Given a string you have to figure out
InputThe first line of input is an integer T
containing a string The strings will c
be positive and not greater than 1000
OutputFor each case first output the case n
Follow the samples for exact format
Sample Input4
acmicpc
aaaaa
isyoursolutionfastenough
abbabababbaba
cpalin SubstringsInput Standard Input
Output Standard Output
ds the same forward and backward Examples
can rearrange its letters to make it a palindro
e we can rearrange the letters to make it
equence of characters of a string Some substri
is not a substring For this problem we are
e2
)1( +nn substrings of a string of length n
ow many of its substrings are dromicpalin
(T lt 100) indicating the number of test cases
ntain only lowercase letters [a - z] The lengt
mber followed by the number of substrings t
Output for Sample InpCase 1 8
Case 2 15
Case 3 24
Case 4 67
of palindromes are
e An example of a
adam which is a
ngs of acmicpc are
not considering the
Each case is a line
of each string will
at are dromicpalin
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 2020
KCan you fill an (abc) cuboid with e
cell inside the (abc) cuboid should
dimensions and for each positive integ
a (223) cuboid can be filled with fi
filled with twelve (111) cubes
To make this problem slightly more di
filled by another cube Your job is to f
the cuboid can be filled by exactly n c
InputThere will be at most 300 test cases
abc le 125 0 le m lt abc)
Each of the next m lines contains thre
(x y z) is already filled
No cell will be mentioned twice Ther
The input is terminated by a line conta
OutputFor each test case print the case num
single space before each number in the
Sample Input2 2 3 0
2 2 3 2
1 1 1
2 2 3
0 0 0 0
ill the CuboidInput Standard Input
Output Standard Output
actly n cubes The cubes may touch but cann
be covered by exactly one cube You may us
er p you can use as many (ppp) cubes as yo
e cubes four (111) cubes and one (222)
fficult m of the cells in the cuboid are already
ind out the possible values of n such that the re
ubes
ach test case begins with four integers a b c
integers x y z (1 le x le a 1 le y le b 1 le z le c)
will be at least one non-filled cell
ining four zeroes
ber and the list of possible answers in increasi
output Look at the output for sample input for
Output for Sample InpCase 1 5 12
Case 2 10
ot overlap and each
cubes of different
like For example
cube It can also be
illed and cannot be
maining cells inside
(2 le a b c le 20
that means the cell
ng order There is a
details
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1220
F Two PI
O
Itrsquos a common phenomenon to mix u
that they just look at sky and can tell y
whole way they travelled ldquoFirst we
and so this one is helliprdquo and thus end u
each other and they do not always run
ends up with some ridiculous answer a
The city we are talking about is a sq
Although the city is nice square shape
rail track and it is a straight one
perpendicular to the existing one The
or not they just need location of twconnecting these two stations the line
you have to build the stations in intege
So to sum it up you will be given co-
to give any two distinct integer co-or
co-ordinates may coincide with the gi
Input
First line of input will contain an integ
be a line of four integers X1 Y1 X2
ordinates of two stations on the alread
You may assume that these two points
OutputFor each test case produce one line
integers where the first two integers
integers are the x and y co-ordinate
possible value of S and the line pa
(may not necessarily intersect the
answers you may output any of the
coordinates does not exceed9
102times F
Sample Input2
4 4 5 5
9 0 10 0
oints Revisitednput Standard Inputtput Standard Output
direction when you go to a new place Some
ou which one is north And some dumb people
ere east facing then we turned left then right
with a direction But the roads are not always
from north to south or from east to west So thi
lmost all the times
uare shaped one with vertices at (0 0) (S 0)
one the road network is already messed up
o city corporation decides to build another
do not care if the new track intersects with th
rail stations so that if a rail track is built alowould be perpendicular to the existing rail tr
r co-ordinates
rdinates of two stations on the already existing
inates within the city for building new rail tra
en co-ordinates if you want it to
er T the number of test cases (T le 15000) For
2 (0 le X1 Y1 X2 Y2 le 109) Here (X1 Y1) and
existing rail track
are different and within the city
of output This line contains the case numbe
are the x and y co-ordinate of the first statio
of the second station They should be withi
sing through them must be perpendicular
previous track within the city) Since the
but you have to make sure that absolute va
or details please go through the explanation of t
Output for Sample ICase 1 1 0 0 1
Case 2 10 0 10 2
eople are so clever
try to remember the
then again righthellip
in 90 degrees with
kind of calculation
(S S) and (0 S)
ut there is only one
rail track which is
previous rail track
ng the straight lineck The problem is
rail track you have
ck One of the new
each case there will
(X2 Y2) are the co-
r followed by four
n and the next two
the city for any
o the existing line
re can be multiple
lue of any of these
he sample cases
put
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1320
13
Explanation
First Sample
In the first sample the existing rail track goes through points (4 4) and (5 5) If you establish two new
rail stations at (1 0) and (0 1) the rail track passing through them will be perpendicular to the existingrail track Note if you output something like (5 5) and (6 4) you will get Wrong Answer since if S = 5
point (6 4) will not be within the city But for any value of S such that (4 4) and (5 5) is within the city
points (1 0) and (0 1) will also be within the city
Second Sample
In this case there are many correct answers One of them is (10 0) and (10 2) Note that unlike first
sample here the rail tracks intersect
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1420
G
Watc
Day by day number of Kangaroos is d
Now for the convenience of the spect
ldquoKangaroo appears in Screen 7rdquo an
position of Kangaroos and inform th
screen to display that animal based on
as follows
If the position x is outside the rangeOtherwise the coverage is minimum(
An example will make it clear
Suppose there are four screens coveri
Kangaroo appears at x = 10
First screen has coverage of 3 unit aro
15 ndash 10) = minimum(3 5) = 3
Second screen has coverage of 0 unit
100)
Third screen has coverage of 0 unit
minimum(10 ndash 8 10 ndash 10) = 0
Fourth screen has coverage of 1 unit a
1 11 ndash 10) = 1
ing the KangarooInput Standard Input
Output Standard Output
ecreasing just like tiger whale or lions So I de
a sanctuary where they will live peac
visitors go near them So I planted s
outside the sanctuary For this proble
the sanctuary to be a long line of 10000
The leftmost position is marked with
position with 1000000000 There ar
cameras on this line Each of the camer
(L R) which means that camera coposition L to position R inclusive Each
their associated display screens outside
can see the Kangaroos
ators we announce time to time ldquoKangaroo a
so on I have some employees who contin
system (here position is a marker) The syste
the coverage The coverage of a screen for a
of that screen (ie x lt L or x gt R) then thndash L R ndash x)
ng the range (7 15) (14 100) (8 10) and (1
nd x = 10 Because x = 10 is within (7 15) an
around x = 10 Because x = 10 does not belo
around x = 10 Because though x = 10 is
round x = 10 Because x = 10 is within (1 11)
cided to make them
fully I do not let
me display screen
you may assume
0000 unit distance
and the rightmost
at most 100000
as is described with
vers a range fromof the cameras has
where the visitors
pears in Screen 3rdquo
ously monitor the
m chooses the best
osition x is defined
coverage is zero
11) Now say one
minimum(10 ndash 7
g to the range (14
within (8 10) but
and minimum(10 ndash
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1520
15
So which one is better Obviously the first one as it has the maximum coverage
So you are given the ranges of the screens and the positions the kangaroo appears For each position of
the Kangaroo you are to tell me the maximum coverage you can have with any of the screens
Input
First line of the test file contains T (T le 3) number of test cases Hence T cases follow For each case
you are given N M in the first line N is the number of screens and M is the number of Kangaroo
appearance ( 1 le N M le 100000) In the next N lines you are given the range of screens L R ( 0 le L le R
le 1000000000 ) Next M lines contain the position of the Kangaroo- an integer x (0 le x le 1000000000)
OutputFor each case print the case number Hence print M lines ith containing the maximum coverage you can
have around irsquoth Kangaroo
Sample Input Output for Sample Input1
3 2
7 15
14 100
1 11
10
120
Case 1
3
0
Warning The judge input file is around 6 MB So use faster IO functions
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1620
HGiven an integer N find how many pa
A le N
Here gcd (A B) means the greatest c
of the bitwise xor operation on the bin
InputThe first line of the input contains a
following T lines contain an integer N
OutputFor each test case print the case nu
input) followed by a space and then th
Sample Input2
7
20000000
Explanation
Sample 1
For N=7 there are four valid pairs (3
GCD XORInput Standard Inpututput Standard Output
irs (A B) are there such that gcd (A B) = A x
mmon divisor of the numbers A and B And
ary representation of A and B
n integer T(T le 10000) denoting the number
1 le N le 30000000)
ber first in the format Case X (here X
answer for that case
Output for Sample InpCase 1 4
Case 2 34866117
2) (5 4) (6 4) and (7 6)
or B where 1 le B le
xor B is the value
of test cases The
is the serial of the
ut
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1720
INatasha always mixes up things in her
classical problem - finding shortest p
that in another class the professor t
looking but does very different things
to the Primrsquos algorithm (actually w
Pseudocode of her algorithm looks as
FiascoInput Standard Input
Output Standard Output
algorithm classes Last week Prof Chhaya Mu
th to all nodes from a specific node of a wei
aught them Primrsquos and Dijkstrarsquos algorithms
Always confused poor Natasha submitted so
should call it Natasharsquos algorithm) she did
ollows
thy gave the class a
hted graph Before
which are similar
ething very similar
rsquot test it properly
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1820
18
After submission she showed the code to a friend who is good at algorithms That friend immediately
found the flaw Natasha was really terrified and started to cry Then there came the guys the guys who
liked her They jumped at the opportunity and got hold of the dataset to be used to test the solutions Your
friend Rehan is one of those guys He really wanted to impress Natasha He asked you to change the
dataset in such a way that Natasharsquos algorithm gives the right result After the change Rehan will
somehow be able to put the modified data with the old timestamp Rehan told you that
1 The dataset has T test cases
2 Each case contains a connected weighted undirected graph with n nodes and m edges
3 Each case will contain a source node source
4 Edge weights are positive and distinct
To avoid suspicion Rehan asked you not to change which vertices the edges connect or the overall set of
edge weights You may only reorder which weights are assigned to which edges
InputThe first line of the input denotes the number of datasets T (1 le T le 15) T sets of case will follow Eachcase will start with a triplet of numbers n (2 le n le 2500) m (1 le m le 25000) and source (1 le source le
n) - the number of nodes the number of edges and the starting node respectively Each of the next m
lines will contain a triplet of numbers (u v w) meaning that there is an edge between node u and node v
with weight w (1 le w le m) Nodes are numbered from 1 to n It is guaranteed that there is no duplicate or
self-edges in the input and the graph is connected In each given graph all edge weights will be distinct
OutputFor each set of input print one set of output First line of a set should be of the format ldquoCase Xrdquo
where X is the case number Then print each edge triplet - one triplet ( u v and w) in each line separated
by a single space The edges should be printed in the order given in the input If there is more than one
solution to a dataset any one of them will do
Sample Input Output for Sample Input1
7 9 5
2 4 2
1 4 8
7 2 6
3 4 7
5 7 5
7 3 9
6 1 1
6 3 4
5 6 3
Case 1
2 4 7
1 4 9
7 2 3
3 4 8
5 7 1
7 3 4
6 1 5
6 3 6
5 6 2
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1920
J Drom
Lets first define some terms
bull A string is palindromic if it re
madam and toot
bull A string is a dromicpalin if we
dromicpalin string is mmaad becau
palindrome
bull A substring is any contiguous
a c i icp acmicpc but acpc
empty substring so that means there a
Given a string you have to figure out
InputThe first line of input is an integer T
containing a string The strings will c
be positive and not greater than 1000
OutputFor each case first output the case n
Follow the samples for exact format
Sample Input4
acmicpc
aaaaa
isyoursolutionfastenough
abbabababbaba
cpalin SubstringsInput Standard Input
Output Standard Output
ds the same forward and backward Examples
can rearrange its letters to make it a palindro
e we can rearrange the letters to make it
equence of characters of a string Some substri
is not a substring For this problem we are
e2
)1( +nn substrings of a string of length n
ow many of its substrings are dromicpalin
(T lt 100) indicating the number of test cases
ntain only lowercase letters [a - z] The lengt
mber followed by the number of substrings t
Output for Sample InpCase 1 8
Case 2 15
Case 3 24
Case 4 67
of palindromes are
e An example of a
adam which is a
ngs of acmicpc are
not considering the
Each case is a line
of each string will
at are dromicpalin
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 2020
KCan you fill an (abc) cuboid with e
cell inside the (abc) cuboid should
dimensions and for each positive integ
a (223) cuboid can be filled with fi
filled with twelve (111) cubes
To make this problem slightly more di
filled by another cube Your job is to f
the cuboid can be filled by exactly n c
InputThere will be at most 300 test cases
abc le 125 0 le m lt abc)
Each of the next m lines contains thre
(x y z) is already filled
No cell will be mentioned twice Ther
The input is terminated by a line conta
OutputFor each test case print the case num
single space before each number in the
Sample Input2 2 3 0
2 2 3 2
1 1 1
2 2 3
0 0 0 0
ill the CuboidInput Standard Input
Output Standard Output
actly n cubes The cubes may touch but cann
be covered by exactly one cube You may us
er p you can use as many (ppp) cubes as yo
e cubes four (111) cubes and one (222)
fficult m of the cells in the cuboid are already
ind out the possible values of n such that the re
ubes
ach test case begins with four integers a b c
integers x y z (1 le x le a 1 le y le b 1 le z le c)
will be at least one non-filled cell
ining four zeroes
ber and the list of possible answers in increasi
output Look at the output for sample input for
Output for Sample InpCase 1 5 12
Case 2 10
ot overlap and each
cubes of different
like For example
cube It can also be
illed and cannot be
maining cells inside
(2 le a b c le 20
that means the cell
ng order There is a
details
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1320
13
Explanation
First Sample
In the first sample the existing rail track goes through points (4 4) and (5 5) If you establish two new
rail stations at (1 0) and (0 1) the rail track passing through them will be perpendicular to the existingrail track Note if you output something like (5 5) and (6 4) you will get Wrong Answer since if S = 5
point (6 4) will not be within the city But for any value of S such that (4 4) and (5 5) is within the city
points (1 0) and (0 1) will also be within the city
Second Sample
In this case there are many correct answers One of them is (10 0) and (10 2) Note that unlike first
sample here the rail tracks intersect
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1420
G
Watc
Day by day number of Kangaroos is d
Now for the convenience of the spect
ldquoKangaroo appears in Screen 7rdquo an
position of Kangaroos and inform th
screen to display that animal based on
as follows
If the position x is outside the rangeOtherwise the coverage is minimum(
An example will make it clear
Suppose there are four screens coveri
Kangaroo appears at x = 10
First screen has coverage of 3 unit aro
15 ndash 10) = minimum(3 5) = 3
Second screen has coverage of 0 unit
100)
Third screen has coverage of 0 unit
minimum(10 ndash 8 10 ndash 10) = 0
Fourth screen has coverage of 1 unit a
1 11 ndash 10) = 1
ing the KangarooInput Standard Input
Output Standard Output
ecreasing just like tiger whale or lions So I de
a sanctuary where they will live peac
visitors go near them So I planted s
outside the sanctuary For this proble
the sanctuary to be a long line of 10000
The leftmost position is marked with
position with 1000000000 There ar
cameras on this line Each of the camer
(L R) which means that camera coposition L to position R inclusive Each
their associated display screens outside
can see the Kangaroos
ators we announce time to time ldquoKangaroo a
so on I have some employees who contin
system (here position is a marker) The syste
the coverage The coverage of a screen for a
of that screen (ie x lt L or x gt R) then thndash L R ndash x)
ng the range (7 15) (14 100) (8 10) and (1
nd x = 10 Because x = 10 is within (7 15) an
around x = 10 Because x = 10 does not belo
around x = 10 Because though x = 10 is
round x = 10 Because x = 10 is within (1 11)
cided to make them
fully I do not let
me display screen
you may assume
0000 unit distance
and the rightmost
at most 100000
as is described with
vers a range fromof the cameras has
where the visitors
pears in Screen 3rdquo
ously monitor the
m chooses the best
osition x is defined
coverage is zero
11) Now say one
minimum(10 ndash 7
g to the range (14
within (8 10) but
and minimum(10 ndash
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1520
15
So which one is better Obviously the first one as it has the maximum coverage
So you are given the ranges of the screens and the positions the kangaroo appears For each position of
the Kangaroo you are to tell me the maximum coverage you can have with any of the screens
Input
First line of the test file contains T (T le 3) number of test cases Hence T cases follow For each case
you are given N M in the first line N is the number of screens and M is the number of Kangaroo
appearance ( 1 le N M le 100000) In the next N lines you are given the range of screens L R ( 0 le L le R
le 1000000000 ) Next M lines contain the position of the Kangaroo- an integer x (0 le x le 1000000000)
OutputFor each case print the case number Hence print M lines ith containing the maximum coverage you can
have around irsquoth Kangaroo
Sample Input Output for Sample Input1
3 2
7 15
14 100
1 11
10
120
Case 1
3
0
Warning The judge input file is around 6 MB So use faster IO functions
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1620
HGiven an integer N find how many pa
A le N
Here gcd (A B) means the greatest c
of the bitwise xor operation on the bin
InputThe first line of the input contains a
following T lines contain an integer N
OutputFor each test case print the case nu
input) followed by a space and then th
Sample Input2
7
20000000
Explanation
Sample 1
For N=7 there are four valid pairs (3
GCD XORInput Standard Inpututput Standard Output
irs (A B) are there such that gcd (A B) = A x
mmon divisor of the numbers A and B And
ary representation of A and B
n integer T(T le 10000) denoting the number
1 le N le 30000000)
ber first in the format Case X (here X
answer for that case
Output for Sample InpCase 1 4
Case 2 34866117
2) (5 4) (6 4) and (7 6)
or B where 1 le B le
xor B is the value
of test cases The
is the serial of the
ut
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1720
INatasha always mixes up things in her
classical problem - finding shortest p
that in another class the professor t
looking but does very different things
to the Primrsquos algorithm (actually w
Pseudocode of her algorithm looks as
FiascoInput Standard Input
Output Standard Output
algorithm classes Last week Prof Chhaya Mu
th to all nodes from a specific node of a wei
aught them Primrsquos and Dijkstrarsquos algorithms
Always confused poor Natasha submitted so
should call it Natasharsquos algorithm) she did
ollows
thy gave the class a
hted graph Before
which are similar
ething very similar
rsquot test it properly
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1820
18
After submission she showed the code to a friend who is good at algorithms That friend immediately
found the flaw Natasha was really terrified and started to cry Then there came the guys the guys who
liked her They jumped at the opportunity and got hold of the dataset to be used to test the solutions Your
friend Rehan is one of those guys He really wanted to impress Natasha He asked you to change the
dataset in such a way that Natasharsquos algorithm gives the right result After the change Rehan will
somehow be able to put the modified data with the old timestamp Rehan told you that
1 The dataset has T test cases
2 Each case contains a connected weighted undirected graph with n nodes and m edges
3 Each case will contain a source node source
4 Edge weights are positive and distinct
To avoid suspicion Rehan asked you not to change which vertices the edges connect or the overall set of
edge weights You may only reorder which weights are assigned to which edges
InputThe first line of the input denotes the number of datasets T (1 le T le 15) T sets of case will follow Eachcase will start with a triplet of numbers n (2 le n le 2500) m (1 le m le 25000) and source (1 le source le
n) - the number of nodes the number of edges and the starting node respectively Each of the next m
lines will contain a triplet of numbers (u v w) meaning that there is an edge between node u and node v
with weight w (1 le w le m) Nodes are numbered from 1 to n It is guaranteed that there is no duplicate or
self-edges in the input and the graph is connected In each given graph all edge weights will be distinct
OutputFor each set of input print one set of output First line of a set should be of the format ldquoCase Xrdquo
where X is the case number Then print each edge triplet - one triplet ( u v and w) in each line separated
by a single space The edges should be printed in the order given in the input If there is more than one
solution to a dataset any one of them will do
Sample Input Output for Sample Input1
7 9 5
2 4 2
1 4 8
7 2 6
3 4 7
5 7 5
7 3 9
6 1 1
6 3 4
5 6 3
Case 1
2 4 7
1 4 9
7 2 3
3 4 8
5 7 1
7 3 4
6 1 5
6 3 6
5 6 2
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1920
J Drom
Lets first define some terms
bull A string is palindromic if it re
madam and toot
bull A string is a dromicpalin if we
dromicpalin string is mmaad becau
palindrome
bull A substring is any contiguous
a c i icp acmicpc but acpc
empty substring so that means there a
Given a string you have to figure out
InputThe first line of input is an integer T
containing a string The strings will c
be positive and not greater than 1000
OutputFor each case first output the case n
Follow the samples for exact format
Sample Input4
acmicpc
aaaaa
isyoursolutionfastenough
abbabababbaba
cpalin SubstringsInput Standard Input
Output Standard Output
ds the same forward and backward Examples
can rearrange its letters to make it a palindro
e we can rearrange the letters to make it
equence of characters of a string Some substri
is not a substring For this problem we are
e2
)1( +nn substrings of a string of length n
ow many of its substrings are dromicpalin
(T lt 100) indicating the number of test cases
ntain only lowercase letters [a - z] The lengt
mber followed by the number of substrings t
Output for Sample InpCase 1 8
Case 2 15
Case 3 24
Case 4 67
of palindromes are
e An example of a
adam which is a
ngs of acmicpc are
not considering the
Each case is a line
of each string will
at are dromicpalin
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 2020
KCan you fill an (abc) cuboid with e
cell inside the (abc) cuboid should
dimensions and for each positive integ
a (223) cuboid can be filled with fi
filled with twelve (111) cubes
To make this problem slightly more di
filled by another cube Your job is to f
the cuboid can be filled by exactly n c
InputThere will be at most 300 test cases
abc le 125 0 le m lt abc)
Each of the next m lines contains thre
(x y z) is already filled
No cell will be mentioned twice Ther
The input is terminated by a line conta
OutputFor each test case print the case num
single space before each number in the
Sample Input2 2 3 0
2 2 3 2
1 1 1
2 2 3
0 0 0 0
ill the CuboidInput Standard Input
Output Standard Output
actly n cubes The cubes may touch but cann
be covered by exactly one cube You may us
er p you can use as many (ppp) cubes as yo
e cubes four (111) cubes and one (222)
fficult m of the cells in the cuboid are already
ind out the possible values of n such that the re
ubes
ach test case begins with four integers a b c
integers x y z (1 le x le a 1 le y le b 1 le z le c)
will be at least one non-filled cell
ining four zeroes
ber and the list of possible answers in increasi
output Look at the output for sample input for
Output for Sample InpCase 1 5 12
Case 2 10
ot overlap and each
cubes of different
like For example
cube It can also be
illed and cannot be
maining cells inside
(2 le a b c le 20
that means the cell
ng order There is a
details
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1420
G
Watc
Day by day number of Kangaroos is d
Now for the convenience of the spect
ldquoKangaroo appears in Screen 7rdquo an
position of Kangaroos and inform th
screen to display that animal based on
as follows
If the position x is outside the rangeOtherwise the coverage is minimum(
An example will make it clear
Suppose there are four screens coveri
Kangaroo appears at x = 10
First screen has coverage of 3 unit aro
15 ndash 10) = minimum(3 5) = 3
Second screen has coverage of 0 unit
100)
Third screen has coverage of 0 unit
minimum(10 ndash 8 10 ndash 10) = 0
Fourth screen has coverage of 1 unit a
1 11 ndash 10) = 1
ing the KangarooInput Standard Input
Output Standard Output
ecreasing just like tiger whale or lions So I de
a sanctuary where they will live peac
visitors go near them So I planted s
outside the sanctuary For this proble
the sanctuary to be a long line of 10000
The leftmost position is marked with
position with 1000000000 There ar
cameras on this line Each of the camer
(L R) which means that camera coposition L to position R inclusive Each
their associated display screens outside
can see the Kangaroos
ators we announce time to time ldquoKangaroo a
so on I have some employees who contin
system (here position is a marker) The syste
the coverage The coverage of a screen for a
of that screen (ie x lt L or x gt R) then thndash L R ndash x)
ng the range (7 15) (14 100) (8 10) and (1
nd x = 10 Because x = 10 is within (7 15) an
around x = 10 Because x = 10 does not belo
around x = 10 Because though x = 10 is
round x = 10 Because x = 10 is within (1 11)
cided to make them
fully I do not let
me display screen
you may assume
0000 unit distance
and the rightmost
at most 100000
as is described with
vers a range fromof the cameras has
where the visitors
pears in Screen 3rdquo
ously monitor the
m chooses the best
osition x is defined
coverage is zero
11) Now say one
minimum(10 ndash 7
g to the range (14
within (8 10) but
and minimum(10 ndash
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1520
15
So which one is better Obviously the first one as it has the maximum coverage
So you are given the ranges of the screens and the positions the kangaroo appears For each position of
the Kangaroo you are to tell me the maximum coverage you can have with any of the screens
Input
First line of the test file contains T (T le 3) number of test cases Hence T cases follow For each case
you are given N M in the first line N is the number of screens and M is the number of Kangaroo
appearance ( 1 le N M le 100000) In the next N lines you are given the range of screens L R ( 0 le L le R
le 1000000000 ) Next M lines contain the position of the Kangaroo- an integer x (0 le x le 1000000000)
OutputFor each case print the case number Hence print M lines ith containing the maximum coverage you can
have around irsquoth Kangaroo
Sample Input Output for Sample Input1
3 2
7 15
14 100
1 11
10
120
Case 1
3
0
Warning The judge input file is around 6 MB So use faster IO functions
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1620
HGiven an integer N find how many pa
A le N
Here gcd (A B) means the greatest c
of the bitwise xor operation on the bin
InputThe first line of the input contains a
following T lines contain an integer N
OutputFor each test case print the case nu
input) followed by a space and then th
Sample Input2
7
20000000
Explanation
Sample 1
For N=7 there are four valid pairs (3
GCD XORInput Standard Inpututput Standard Output
irs (A B) are there such that gcd (A B) = A x
mmon divisor of the numbers A and B And
ary representation of A and B
n integer T(T le 10000) denoting the number
1 le N le 30000000)
ber first in the format Case X (here X
answer for that case
Output for Sample InpCase 1 4
Case 2 34866117
2) (5 4) (6 4) and (7 6)
or B where 1 le B le
xor B is the value
of test cases The
is the serial of the
ut
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1720
INatasha always mixes up things in her
classical problem - finding shortest p
that in another class the professor t
looking but does very different things
to the Primrsquos algorithm (actually w
Pseudocode of her algorithm looks as
FiascoInput Standard Input
Output Standard Output
algorithm classes Last week Prof Chhaya Mu
th to all nodes from a specific node of a wei
aught them Primrsquos and Dijkstrarsquos algorithms
Always confused poor Natasha submitted so
should call it Natasharsquos algorithm) she did
ollows
thy gave the class a
hted graph Before
which are similar
ething very similar
rsquot test it properly
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1820
18
After submission she showed the code to a friend who is good at algorithms That friend immediately
found the flaw Natasha was really terrified and started to cry Then there came the guys the guys who
liked her They jumped at the opportunity and got hold of the dataset to be used to test the solutions Your
friend Rehan is one of those guys He really wanted to impress Natasha He asked you to change the
dataset in such a way that Natasharsquos algorithm gives the right result After the change Rehan will
somehow be able to put the modified data with the old timestamp Rehan told you that
1 The dataset has T test cases
2 Each case contains a connected weighted undirected graph with n nodes and m edges
3 Each case will contain a source node source
4 Edge weights are positive and distinct
To avoid suspicion Rehan asked you not to change which vertices the edges connect or the overall set of
edge weights You may only reorder which weights are assigned to which edges
InputThe first line of the input denotes the number of datasets T (1 le T le 15) T sets of case will follow Eachcase will start with a triplet of numbers n (2 le n le 2500) m (1 le m le 25000) and source (1 le source le
n) - the number of nodes the number of edges and the starting node respectively Each of the next m
lines will contain a triplet of numbers (u v w) meaning that there is an edge between node u and node v
with weight w (1 le w le m) Nodes are numbered from 1 to n It is guaranteed that there is no duplicate or
self-edges in the input and the graph is connected In each given graph all edge weights will be distinct
OutputFor each set of input print one set of output First line of a set should be of the format ldquoCase Xrdquo
where X is the case number Then print each edge triplet - one triplet ( u v and w) in each line separated
by a single space The edges should be printed in the order given in the input If there is more than one
solution to a dataset any one of them will do
Sample Input Output for Sample Input1
7 9 5
2 4 2
1 4 8
7 2 6
3 4 7
5 7 5
7 3 9
6 1 1
6 3 4
5 6 3
Case 1
2 4 7
1 4 9
7 2 3
3 4 8
5 7 1
7 3 4
6 1 5
6 3 6
5 6 2
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1920
J Drom
Lets first define some terms
bull A string is palindromic if it re
madam and toot
bull A string is a dromicpalin if we
dromicpalin string is mmaad becau
palindrome
bull A substring is any contiguous
a c i icp acmicpc but acpc
empty substring so that means there a
Given a string you have to figure out
InputThe first line of input is an integer T
containing a string The strings will c
be positive and not greater than 1000
OutputFor each case first output the case n
Follow the samples for exact format
Sample Input4
acmicpc
aaaaa
isyoursolutionfastenough
abbabababbaba
cpalin SubstringsInput Standard Input
Output Standard Output
ds the same forward and backward Examples
can rearrange its letters to make it a palindro
e we can rearrange the letters to make it
equence of characters of a string Some substri
is not a substring For this problem we are
e2
)1( +nn substrings of a string of length n
ow many of its substrings are dromicpalin
(T lt 100) indicating the number of test cases
ntain only lowercase letters [a - z] The lengt
mber followed by the number of substrings t
Output for Sample InpCase 1 8
Case 2 15
Case 3 24
Case 4 67
of palindromes are
e An example of a
adam which is a
ngs of acmicpc are
not considering the
Each case is a line
of each string will
at are dromicpalin
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 2020
KCan you fill an (abc) cuboid with e
cell inside the (abc) cuboid should
dimensions and for each positive integ
a (223) cuboid can be filled with fi
filled with twelve (111) cubes
To make this problem slightly more di
filled by another cube Your job is to f
the cuboid can be filled by exactly n c
InputThere will be at most 300 test cases
abc le 125 0 le m lt abc)
Each of the next m lines contains thre
(x y z) is already filled
No cell will be mentioned twice Ther
The input is terminated by a line conta
OutputFor each test case print the case num
single space before each number in the
Sample Input2 2 3 0
2 2 3 2
1 1 1
2 2 3
0 0 0 0
ill the CuboidInput Standard Input
Output Standard Output
actly n cubes The cubes may touch but cann
be covered by exactly one cube You may us
er p you can use as many (ppp) cubes as yo
e cubes four (111) cubes and one (222)
fficult m of the cells in the cuboid are already
ind out the possible values of n such that the re
ubes
ach test case begins with four integers a b c
integers x y z (1 le x le a 1 le y le b 1 le z le c)
will be at least one non-filled cell
ining four zeroes
ber and the list of possible answers in increasi
output Look at the output for sample input for
Output for Sample InpCase 1 5 12
Case 2 10
ot overlap and each
cubes of different
like For example
cube It can also be
illed and cannot be
maining cells inside
(2 le a b c le 20
that means the cell
ng order There is a
details
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1520
15
So which one is better Obviously the first one as it has the maximum coverage
So you are given the ranges of the screens and the positions the kangaroo appears For each position of
the Kangaroo you are to tell me the maximum coverage you can have with any of the screens
Input
First line of the test file contains T (T le 3) number of test cases Hence T cases follow For each case
you are given N M in the first line N is the number of screens and M is the number of Kangaroo
appearance ( 1 le N M le 100000) In the next N lines you are given the range of screens L R ( 0 le L le R
le 1000000000 ) Next M lines contain the position of the Kangaroo- an integer x (0 le x le 1000000000)
OutputFor each case print the case number Hence print M lines ith containing the maximum coverage you can
have around irsquoth Kangaroo
Sample Input Output for Sample Input1
3 2
7 15
14 100
1 11
10
120
Case 1
3
0
Warning The judge input file is around 6 MB So use faster IO functions
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1620
HGiven an integer N find how many pa
A le N
Here gcd (A B) means the greatest c
of the bitwise xor operation on the bin
InputThe first line of the input contains a
following T lines contain an integer N
OutputFor each test case print the case nu
input) followed by a space and then th
Sample Input2
7
20000000
Explanation
Sample 1
For N=7 there are four valid pairs (3
GCD XORInput Standard Inpututput Standard Output
irs (A B) are there such that gcd (A B) = A x
mmon divisor of the numbers A and B And
ary representation of A and B
n integer T(T le 10000) denoting the number
1 le N le 30000000)
ber first in the format Case X (here X
answer for that case
Output for Sample InpCase 1 4
Case 2 34866117
2) (5 4) (6 4) and (7 6)
or B where 1 le B le
xor B is the value
of test cases The
is the serial of the
ut
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1720
INatasha always mixes up things in her
classical problem - finding shortest p
that in another class the professor t
looking but does very different things
to the Primrsquos algorithm (actually w
Pseudocode of her algorithm looks as
FiascoInput Standard Input
Output Standard Output
algorithm classes Last week Prof Chhaya Mu
th to all nodes from a specific node of a wei
aught them Primrsquos and Dijkstrarsquos algorithms
Always confused poor Natasha submitted so
should call it Natasharsquos algorithm) she did
ollows
thy gave the class a
hted graph Before
which are similar
ething very similar
rsquot test it properly
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1820
18
After submission she showed the code to a friend who is good at algorithms That friend immediately
found the flaw Natasha was really terrified and started to cry Then there came the guys the guys who
liked her They jumped at the opportunity and got hold of the dataset to be used to test the solutions Your
friend Rehan is one of those guys He really wanted to impress Natasha He asked you to change the
dataset in such a way that Natasharsquos algorithm gives the right result After the change Rehan will
somehow be able to put the modified data with the old timestamp Rehan told you that
1 The dataset has T test cases
2 Each case contains a connected weighted undirected graph with n nodes and m edges
3 Each case will contain a source node source
4 Edge weights are positive and distinct
To avoid suspicion Rehan asked you not to change which vertices the edges connect or the overall set of
edge weights You may only reorder which weights are assigned to which edges
InputThe first line of the input denotes the number of datasets T (1 le T le 15) T sets of case will follow Eachcase will start with a triplet of numbers n (2 le n le 2500) m (1 le m le 25000) and source (1 le source le
n) - the number of nodes the number of edges and the starting node respectively Each of the next m
lines will contain a triplet of numbers (u v w) meaning that there is an edge between node u and node v
with weight w (1 le w le m) Nodes are numbered from 1 to n It is guaranteed that there is no duplicate or
self-edges in the input and the graph is connected In each given graph all edge weights will be distinct
OutputFor each set of input print one set of output First line of a set should be of the format ldquoCase Xrdquo
where X is the case number Then print each edge triplet - one triplet ( u v and w) in each line separated
by a single space The edges should be printed in the order given in the input If there is more than one
solution to a dataset any one of them will do
Sample Input Output for Sample Input1
7 9 5
2 4 2
1 4 8
7 2 6
3 4 7
5 7 5
7 3 9
6 1 1
6 3 4
5 6 3
Case 1
2 4 7
1 4 9
7 2 3
3 4 8
5 7 1
7 3 4
6 1 5
6 3 6
5 6 2
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1920
J Drom
Lets first define some terms
bull A string is palindromic if it re
madam and toot
bull A string is a dromicpalin if we
dromicpalin string is mmaad becau
palindrome
bull A substring is any contiguous
a c i icp acmicpc but acpc
empty substring so that means there a
Given a string you have to figure out
InputThe first line of input is an integer T
containing a string The strings will c
be positive and not greater than 1000
OutputFor each case first output the case n
Follow the samples for exact format
Sample Input4
acmicpc
aaaaa
isyoursolutionfastenough
abbabababbaba
cpalin SubstringsInput Standard Input
Output Standard Output
ds the same forward and backward Examples
can rearrange its letters to make it a palindro
e we can rearrange the letters to make it
equence of characters of a string Some substri
is not a substring For this problem we are
e2
)1( +nn substrings of a string of length n
ow many of its substrings are dromicpalin
(T lt 100) indicating the number of test cases
ntain only lowercase letters [a - z] The lengt
mber followed by the number of substrings t
Output for Sample InpCase 1 8
Case 2 15
Case 3 24
Case 4 67
of palindromes are
e An example of a
adam which is a
ngs of acmicpc are
not considering the
Each case is a line
of each string will
at are dromicpalin
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 2020
KCan you fill an (abc) cuboid with e
cell inside the (abc) cuboid should
dimensions and for each positive integ
a (223) cuboid can be filled with fi
filled with twelve (111) cubes
To make this problem slightly more di
filled by another cube Your job is to f
the cuboid can be filled by exactly n c
InputThere will be at most 300 test cases
abc le 125 0 le m lt abc)
Each of the next m lines contains thre
(x y z) is already filled
No cell will be mentioned twice Ther
The input is terminated by a line conta
OutputFor each test case print the case num
single space before each number in the
Sample Input2 2 3 0
2 2 3 2
1 1 1
2 2 3
0 0 0 0
ill the CuboidInput Standard Input
Output Standard Output
actly n cubes The cubes may touch but cann
be covered by exactly one cube You may us
er p you can use as many (ppp) cubes as yo
e cubes four (111) cubes and one (222)
fficult m of the cells in the cuboid are already
ind out the possible values of n such that the re
ubes
ach test case begins with four integers a b c
integers x y z (1 le x le a 1 le y le b 1 le z le c)
will be at least one non-filled cell
ining four zeroes
ber and the list of possible answers in increasi
output Look at the output for sample input for
Output for Sample InpCase 1 5 12
Case 2 10
ot overlap and each
cubes of different
like For example
cube It can also be
illed and cannot be
maining cells inside
(2 le a b c le 20
that means the cell
ng order There is a
details
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1620
HGiven an integer N find how many pa
A le N
Here gcd (A B) means the greatest c
of the bitwise xor operation on the bin
InputThe first line of the input contains a
following T lines contain an integer N
OutputFor each test case print the case nu
input) followed by a space and then th
Sample Input2
7
20000000
Explanation
Sample 1
For N=7 there are four valid pairs (3
GCD XORInput Standard Inpututput Standard Output
irs (A B) are there such that gcd (A B) = A x
mmon divisor of the numbers A and B And
ary representation of A and B
n integer T(T le 10000) denoting the number
1 le N le 30000000)
ber first in the format Case X (here X
answer for that case
Output for Sample InpCase 1 4
Case 2 34866117
2) (5 4) (6 4) and (7 6)
or B where 1 le B le
xor B is the value
of test cases The
is the serial of the
ut
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1720
INatasha always mixes up things in her
classical problem - finding shortest p
that in another class the professor t
looking but does very different things
to the Primrsquos algorithm (actually w
Pseudocode of her algorithm looks as
FiascoInput Standard Input
Output Standard Output
algorithm classes Last week Prof Chhaya Mu
th to all nodes from a specific node of a wei
aught them Primrsquos and Dijkstrarsquos algorithms
Always confused poor Natasha submitted so
should call it Natasharsquos algorithm) she did
ollows
thy gave the class a
hted graph Before
which are similar
ething very similar
rsquot test it properly
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1820
18
After submission she showed the code to a friend who is good at algorithms That friend immediately
found the flaw Natasha was really terrified and started to cry Then there came the guys the guys who
liked her They jumped at the opportunity and got hold of the dataset to be used to test the solutions Your
friend Rehan is one of those guys He really wanted to impress Natasha He asked you to change the
dataset in such a way that Natasharsquos algorithm gives the right result After the change Rehan will
somehow be able to put the modified data with the old timestamp Rehan told you that
1 The dataset has T test cases
2 Each case contains a connected weighted undirected graph with n nodes and m edges
3 Each case will contain a source node source
4 Edge weights are positive and distinct
To avoid suspicion Rehan asked you not to change which vertices the edges connect or the overall set of
edge weights You may only reorder which weights are assigned to which edges
InputThe first line of the input denotes the number of datasets T (1 le T le 15) T sets of case will follow Eachcase will start with a triplet of numbers n (2 le n le 2500) m (1 le m le 25000) and source (1 le source le
n) - the number of nodes the number of edges and the starting node respectively Each of the next m
lines will contain a triplet of numbers (u v w) meaning that there is an edge between node u and node v
with weight w (1 le w le m) Nodes are numbered from 1 to n It is guaranteed that there is no duplicate or
self-edges in the input and the graph is connected In each given graph all edge weights will be distinct
OutputFor each set of input print one set of output First line of a set should be of the format ldquoCase Xrdquo
where X is the case number Then print each edge triplet - one triplet ( u v and w) in each line separated
by a single space The edges should be printed in the order given in the input If there is more than one
solution to a dataset any one of them will do
Sample Input Output for Sample Input1
7 9 5
2 4 2
1 4 8
7 2 6
3 4 7
5 7 5
7 3 9
6 1 1
6 3 4
5 6 3
Case 1
2 4 7
1 4 9
7 2 3
3 4 8
5 7 1
7 3 4
6 1 5
6 3 6
5 6 2
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1920
J Drom
Lets first define some terms
bull A string is palindromic if it re
madam and toot
bull A string is a dromicpalin if we
dromicpalin string is mmaad becau
palindrome
bull A substring is any contiguous
a c i icp acmicpc but acpc
empty substring so that means there a
Given a string you have to figure out
InputThe first line of input is an integer T
containing a string The strings will c
be positive and not greater than 1000
OutputFor each case first output the case n
Follow the samples for exact format
Sample Input4
acmicpc
aaaaa
isyoursolutionfastenough
abbabababbaba
cpalin SubstringsInput Standard Input
Output Standard Output
ds the same forward and backward Examples
can rearrange its letters to make it a palindro
e we can rearrange the letters to make it
equence of characters of a string Some substri
is not a substring For this problem we are
e2
)1( +nn substrings of a string of length n
ow many of its substrings are dromicpalin
(T lt 100) indicating the number of test cases
ntain only lowercase letters [a - z] The lengt
mber followed by the number of substrings t
Output for Sample InpCase 1 8
Case 2 15
Case 3 24
Case 4 67
of palindromes are
e An example of a
adam which is a
ngs of acmicpc are
not considering the
Each case is a line
of each string will
at are dromicpalin
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 2020
KCan you fill an (abc) cuboid with e
cell inside the (abc) cuboid should
dimensions and for each positive integ
a (223) cuboid can be filled with fi
filled with twelve (111) cubes
To make this problem slightly more di
filled by another cube Your job is to f
the cuboid can be filled by exactly n c
InputThere will be at most 300 test cases
abc le 125 0 le m lt abc)
Each of the next m lines contains thre
(x y z) is already filled
No cell will be mentioned twice Ther
The input is terminated by a line conta
OutputFor each test case print the case num
single space before each number in the
Sample Input2 2 3 0
2 2 3 2
1 1 1
2 2 3
0 0 0 0
ill the CuboidInput Standard Input
Output Standard Output
actly n cubes The cubes may touch but cann
be covered by exactly one cube You may us
er p you can use as many (ppp) cubes as yo
e cubes four (111) cubes and one (222)
fficult m of the cells in the cuboid are already
ind out the possible values of n such that the re
ubes
ach test case begins with four integers a b c
integers x y z (1 le x le a 1 le y le b 1 le z le c)
will be at least one non-filled cell
ining four zeroes
ber and the list of possible answers in increasi
output Look at the output for sample input for
Output for Sample InpCase 1 5 12
Case 2 10
ot overlap and each
cubes of different
like For example
cube It can also be
illed and cannot be
maining cells inside
(2 le a b c le 20
that means the cell
ng order There is a
details
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1720
INatasha always mixes up things in her
classical problem - finding shortest p
that in another class the professor t
looking but does very different things
to the Primrsquos algorithm (actually w
Pseudocode of her algorithm looks as
FiascoInput Standard Input
Output Standard Output
algorithm classes Last week Prof Chhaya Mu
th to all nodes from a specific node of a wei
aught them Primrsquos and Dijkstrarsquos algorithms
Always confused poor Natasha submitted so
should call it Natasharsquos algorithm) she did
ollows
thy gave the class a
hted graph Before
which are similar
ething very similar
rsquot test it properly
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1820
18
After submission she showed the code to a friend who is good at algorithms That friend immediately
found the flaw Natasha was really terrified and started to cry Then there came the guys the guys who
liked her They jumped at the opportunity and got hold of the dataset to be used to test the solutions Your
friend Rehan is one of those guys He really wanted to impress Natasha He asked you to change the
dataset in such a way that Natasharsquos algorithm gives the right result After the change Rehan will
somehow be able to put the modified data with the old timestamp Rehan told you that
1 The dataset has T test cases
2 Each case contains a connected weighted undirected graph with n nodes and m edges
3 Each case will contain a source node source
4 Edge weights are positive and distinct
To avoid suspicion Rehan asked you not to change which vertices the edges connect or the overall set of
edge weights You may only reorder which weights are assigned to which edges
InputThe first line of the input denotes the number of datasets T (1 le T le 15) T sets of case will follow Eachcase will start with a triplet of numbers n (2 le n le 2500) m (1 le m le 25000) and source (1 le source le
n) - the number of nodes the number of edges and the starting node respectively Each of the next m
lines will contain a triplet of numbers (u v w) meaning that there is an edge between node u and node v
with weight w (1 le w le m) Nodes are numbered from 1 to n It is guaranteed that there is no duplicate or
self-edges in the input and the graph is connected In each given graph all edge weights will be distinct
OutputFor each set of input print one set of output First line of a set should be of the format ldquoCase Xrdquo
where X is the case number Then print each edge triplet - one triplet ( u v and w) in each line separated
by a single space The edges should be printed in the order given in the input If there is more than one
solution to a dataset any one of them will do
Sample Input Output for Sample Input1
7 9 5
2 4 2
1 4 8
7 2 6
3 4 7
5 7 5
7 3 9
6 1 1
6 3 4
5 6 3
Case 1
2 4 7
1 4 9
7 2 3
3 4 8
5 7 1
7 3 4
6 1 5
6 3 6
5 6 2
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1920
J Drom
Lets first define some terms
bull A string is palindromic if it re
madam and toot
bull A string is a dromicpalin if we
dromicpalin string is mmaad becau
palindrome
bull A substring is any contiguous
a c i icp acmicpc but acpc
empty substring so that means there a
Given a string you have to figure out
InputThe first line of input is an integer T
containing a string The strings will c
be positive and not greater than 1000
OutputFor each case first output the case n
Follow the samples for exact format
Sample Input4
acmicpc
aaaaa
isyoursolutionfastenough
abbabababbaba
cpalin SubstringsInput Standard Input
Output Standard Output
ds the same forward and backward Examples
can rearrange its letters to make it a palindro
e we can rearrange the letters to make it
equence of characters of a string Some substri
is not a substring For this problem we are
e2
)1( +nn substrings of a string of length n
ow many of its substrings are dromicpalin
(T lt 100) indicating the number of test cases
ntain only lowercase letters [a - z] The lengt
mber followed by the number of substrings t
Output for Sample InpCase 1 8
Case 2 15
Case 3 24
Case 4 67
of palindromes are
e An example of a
adam which is a
ngs of acmicpc are
not considering the
Each case is a line
of each string will
at are dromicpalin
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 2020
KCan you fill an (abc) cuboid with e
cell inside the (abc) cuboid should
dimensions and for each positive integ
a (223) cuboid can be filled with fi
filled with twelve (111) cubes
To make this problem slightly more di
filled by another cube Your job is to f
the cuboid can be filled by exactly n c
InputThere will be at most 300 test cases
abc le 125 0 le m lt abc)
Each of the next m lines contains thre
(x y z) is already filled
No cell will be mentioned twice Ther
The input is terminated by a line conta
OutputFor each test case print the case num
single space before each number in the
Sample Input2 2 3 0
2 2 3 2
1 1 1
2 2 3
0 0 0 0
ill the CuboidInput Standard Input
Output Standard Output
actly n cubes The cubes may touch but cann
be covered by exactly one cube You may us
er p you can use as many (ppp) cubes as yo
e cubes four (111) cubes and one (222)
fficult m of the cells in the cuboid are already
ind out the possible values of n such that the re
ubes
ach test case begins with four integers a b c
integers x y z (1 le x le a 1 le y le b 1 le z le c)
will be at least one non-filled cell
ining four zeroes
ber and the list of possible answers in increasi
output Look at the output for sample input for
Output for Sample InpCase 1 5 12
Case 2 10
ot overlap and each
cubes of different
like For example
cube It can also be
illed and cannot be
maining cells inside
(2 le a b c le 20
that means the cell
ng order There is a
details
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1820
18
After submission she showed the code to a friend who is good at algorithms That friend immediately
found the flaw Natasha was really terrified and started to cry Then there came the guys the guys who
liked her They jumped at the opportunity and got hold of the dataset to be used to test the solutions Your
friend Rehan is one of those guys He really wanted to impress Natasha He asked you to change the
dataset in such a way that Natasharsquos algorithm gives the right result After the change Rehan will
somehow be able to put the modified data with the old timestamp Rehan told you that
1 The dataset has T test cases
2 Each case contains a connected weighted undirected graph with n nodes and m edges
3 Each case will contain a source node source
4 Edge weights are positive and distinct
To avoid suspicion Rehan asked you not to change which vertices the edges connect or the overall set of
edge weights You may only reorder which weights are assigned to which edges
InputThe first line of the input denotes the number of datasets T (1 le T le 15) T sets of case will follow Eachcase will start with a triplet of numbers n (2 le n le 2500) m (1 le m le 25000) and source (1 le source le
n) - the number of nodes the number of edges and the starting node respectively Each of the next m
lines will contain a triplet of numbers (u v w) meaning that there is an edge between node u and node v
with weight w (1 le w le m) Nodes are numbered from 1 to n It is guaranteed that there is no duplicate or
self-edges in the input and the graph is connected In each given graph all edge weights will be distinct
OutputFor each set of input print one set of output First line of a set should be of the format ldquoCase Xrdquo
where X is the case number Then print each edge triplet - one triplet ( u v and w) in each line separated
by a single space The edges should be printed in the order given in the input If there is more than one
solution to a dataset any one of them will do
Sample Input Output for Sample Input1
7 9 5
2 4 2
1 4 8
7 2 6
3 4 7
5 7 5
7 3 9
6 1 1
6 3 4
5 6 3
Case 1
2 4 7
1 4 9
7 2 3
3 4 8
5 7 1
7 3 4
6 1 5
6 3 6
5 6 2
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1920
J Drom
Lets first define some terms
bull A string is palindromic if it re
madam and toot
bull A string is a dromicpalin if we
dromicpalin string is mmaad becau
palindrome
bull A substring is any contiguous
a c i icp acmicpc but acpc
empty substring so that means there a
Given a string you have to figure out
InputThe first line of input is an integer T
containing a string The strings will c
be positive and not greater than 1000
OutputFor each case first output the case n
Follow the samples for exact format
Sample Input4
acmicpc
aaaaa
isyoursolutionfastenough
abbabababbaba
cpalin SubstringsInput Standard Input
Output Standard Output
ds the same forward and backward Examples
can rearrange its letters to make it a palindro
e we can rearrange the letters to make it
equence of characters of a string Some substri
is not a substring For this problem we are
e2
)1( +nn substrings of a string of length n
ow many of its substrings are dromicpalin
(T lt 100) indicating the number of test cases
ntain only lowercase letters [a - z] The lengt
mber followed by the number of substrings t
Output for Sample InpCase 1 8
Case 2 15
Case 3 24
Case 4 67
of palindromes are
e An example of a
adam which is a
ngs of acmicpc are
not considering the
Each case is a line
of each string will
at are dromicpalin
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 2020
KCan you fill an (abc) cuboid with e
cell inside the (abc) cuboid should
dimensions and for each positive integ
a (223) cuboid can be filled with fi
filled with twelve (111) cubes
To make this problem slightly more di
filled by another cube Your job is to f
the cuboid can be filled by exactly n c
InputThere will be at most 300 test cases
abc le 125 0 le m lt abc)
Each of the next m lines contains thre
(x y z) is already filled
No cell will be mentioned twice Ther
The input is terminated by a line conta
OutputFor each test case print the case num
single space before each number in the
Sample Input2 2 3 0
2 2 3 2
1 1 1
2 2 3
0 0 0 0
ill the CuboidInput Standard Input
Output Standard Output
actly n cubes The cubes may touch but cann
be covered by exactly one cube You may us
er p you can use as many (ppp) cubes as yo
e cubes four (111) cubes and one (222)
fficult m of the cells in the cuboid are already
ind out the possible values of n such that the re
ubes
ach test case begins with four integers a b c
integers x y z (1 le x le a 1 le y le b 1 le z le c)
will be at least one non-filled cell
ining four zeroes
ber and the list of possible answers in increasi
output Look at the output for sample input for
Output for Sample InpCase 1 5 12
Case 2 10
ot overlap and each
cubes of different
like For example
cube It can also be
illed and cannot be
maining cells inside
(2 le a b c le 20
that means the cell
ng order There is a
details
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 1920
J Drom
Lets first define some terms
bull A string is palindromic if it re
madam and toot
bull A string is a dromicpalin if we
dromicpalin string is mmaad becau
palindrome
bull A substring is any contiguous
a c i icp acmicpc but acpc
empty substring so that means there a
Given a string you have to figure out
InputThe first line of input is an integer T
containing a string The strings will c
be positive and not greater than 1000
OutputFor each case first output the case n
Follow the samples for exact format
Sample Input4
acmicpc
aaaaa
isyoursolutionfastenough
abbabababbaba
cpalin SubstringsInput Standard Input
Output Standard Output
ds the same forward and backward Examples
can rearrange its letters to make it a palindro
e we can rearrange the letters to make it
equence of characters of a string Some substri
is not a substring For this problem we are
e2
)1( +nn substrings of a string of length n
ow many of its substrings are dromicpalin
(T lt 100) indicating the number of test cases
ntain only lowercase letters [a - z] The lengt
mber followed by the number of substrings t
Output for Sample InpCase 1 8
Case 2 15
Case 3 24
Case 4 67
of palindromes are
e An example of a
adam which is a
ngs of acmicpc are
not considering the
Each case is a line
of each string will
at are dromicpalin
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 2020
KCan you fill an (abc) cuboid with e
cell inside the (abc) cuboid should
dimensions and for each positive integ
a (223) cuboid can be filled with fi
filled with twelve (111) cubes
To make this problem slightly more di
filled by another cube Your job is to f
the cuboid can be filled by exactly n c
InputThere will be at most 300 test cases
abc le 125 0 le m lt abc)
Each of the next m lines contains thre
(x y z) is already filled
No cell will be mentioned twice Ther
The input is terminated by a line conta
OutputFor each test case print the case num
single space before each number in the
Sample Input2 2 3 0
2 2 3 2
1 1 1
2 2 3
0 0 0 0
ill the CuboidInput Standard Input
Output Standard Output
actly n cubes The cubes may touch but cann
be covered by exactly one cube You may us
er p you can use as many (ppp) cubes as yo
e cubes four (111) cubes and one (222)
fficult m of the cells in the cuboid are already
ind out the possible values of n such that the re
ubes
ach test case begins with four integers a b c
integers x y z (1 le x le a 1 le y le b 1 le z le c)
will be at least one non-filled cell
ining four zeroes
ber and the list of possible answers in increasi
output Look at the output for sample input for
Output for Sample InpCase 1 5 12
Case 2 10
ot overlap and each
cubes of different
like For example
cube It can also be
illed and cannot be
maining cells inside
(2 le a b c le 20
that means the cell
ng order There is a
details
t
7232019 Problem Set 2013 Acm Icpc
httpslidepdfcomreaderfullproblem-set-2013-acm-icpc 2020
KCan you fill an (abc) cuboid with e
cell inside the (abc) cuboid should
dimensions and for each positive integ
a (223) cuboid can be filled with fi
filled with twelve (111) cubes
To make this problem slightly more di
filled by another cube Your job is to f
the cuboid can be filled by exactly n c
InputThere will be at most 300 test cases
abc le 125 0 le m lt abc)
Each of the next m lines contains thre
(x y z) is already filled
No cell will be mentioned twice Ther
The input is terminated by a line conta
OutputFor each test case print the case num
single space before each number in the
Sample Input2 2 3 0
2 2 3 2
1 1 1
2 2 3
0 0 0 0
ill the CuboidInput Standard Input
Output Standard Output
actly n cubes The cubes may touch but cann
be covered by exactly one cube You may us
er p you can use as many (ppp) cubes as yo
e cubes four (111) cubes and one (222)
fficult m of the cells in the cuboid are already
ind out the possible values of n such that the re
ubes
ach test case begins with four integers a b c
integers x y z (1 le x le a 1 le y le b 1 le z le c)
will be at least one non-filled cell
ining four zeroes
ber and the list of possible answers in increasi
output Look at the output for sample input for
Output for Sample InpCase 1 5 12
Case 2 10
ot overlap and each
cubes of different
like For example
cube It can also be
illed and cannot be
maining cells inside
(2 le a b c le 20
that means the cell
ng order There is a
details
t