IIT Kh C Problems

8/9/2019 IIT Kh C Problems

1/24

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Second

Third

Fourth

Fifth

Sixth

Attempt No 1

Problem 1: Susan' GCD

The famous cryptographer Susan explained her friend David

the Euclidean

algorithm to calculate the GCD of two numbers.

Then Susan implements the GCD-algorithm :

int gcd(int a, int b){

if (b==0)

return a;

else

return gcd(b,a%b);

}

and it proposes to use the algorithm with a little integer

and another

integer that has up to 250 digits.

Your task is to help David programming an efficient code

for the

challenge of his wife Susan.

Input:

The first line of the input file contains a number

representing the

number of lines to follow. Each line consists of two

numbers A and B

(0


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10 11

Output:

2

1

Filename:

Submit

Attempt No 1

Problem 2: Susan's Primality Testing

Susan has introduced the concept of Primality into thecommon Binary

language of computers.

Computers use only 2 alphabet symbol 1 and 0 to make

words. A given word

is called "prime" if it cannot be written in the form of

the concatenation

of several copies of some shorter word.

For example the words '01', '110', and '0010' are prime,

while the words

'11', '100100', '110110', are not prime.

So, here we give a challenge to you this time, to

calculate the number of

prime words which you can form from exactly x 1s and y 0s.

Input:

The first line specifies the number of test cases t. For

each test case,


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two integers: 1


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(0.2 attr1

(0.81 attr1

(0.3)

(0.2)

)

(0.1 attr2

(0.3 attr3

(0.01)

(0.01)

)

(0.1)

)

)

A decision tree is defined recursively. It always has a

root node and a

weight(frequency here). It also, optionally, has a node-

name and two

sub-trees, which are themselves decision trees.More formally, a decision tree is defined using the

following grammar.

tree ::= (weight [feature tree tree])

weight is a real number between 0 and 1,inclusive

node-name is a string of 1 or more lower case English

letters

The part inside the square brackets, [], is optional. The

parentheses, (),

weight and name are tokens. There will be at least one

whitespace character

between any two tokens, except (possibly) after an open-bracket '('

or before a close-bracket ')'. Whitespace characters are

space (' ') and

endline ('\n').

To figure out the efficiency of a server, we start at the

root of the tree

with weight p set to 1. At each node, we multiply p by the

weight of the

node. If the node is a leaf (has no sub-trees), then we

stop, and the value

of p is the final efficiency of the entire server.Otherwise, we look at

the node-attribute associated with the node. If the server

has this

node-attribute, we move down into the first sub-tree(first

child server)

and continue recursively. If it does not have this

attribute, then we move


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down into the second sub-tree(second server) and continue

in the same way.

In the above example, there is a single server and it has 2

attributes:

attr1 and attr3. We start at the root with p equal to 1. We

multiply p by

0.2, the weight of the root and move into the first sub-

tree because the

first child-server has that attribute. There, we multiply p

by 0.81, which

makes p equal to 0.162. From there we move further down

into the first

sub-tree because the server has attribute attr1. Finally,

we multiply p

by 0.3 and end up with 0.0486 as the final efficiency.

You will be given a decision tree and a list of servers

with their

attributes. For each item, you need to return theefficiency of a server.

Input:

The first line of input contains a single integer, N, the

number of test

cases.

N test cases follow.

Each test case description will start with a line that

contains an integer

L --

the number of lines that describe a decision tree. The nextL lines will

contain

a decision tree in the format described above. The line

after that will

contain

A -- the number of servers. The next A lines will each

contain the

description of

one server in the following format.

server n attribute1 attribute2 ... attributen

Output:

For each test case, output one line containing "Case #x:"

followed by

exactly A

lines, one per server, in the same order as they appear in

the input.

Each line


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should contain the efficiency of server. Answers that are

precise to

within an

absolute or relative error of 10-6 will be considered

correct.

Limits

1 N 100

All weights will be between 0 and 1, inclusive.

All weights will consist of only digits with at most one

decimal point.

The weights will not start or end with a decimal point.

The weights will not have more than one 0 before a decimal

point.

All servers and attributes will consist of between 1 and 10

lower case

English

letters.

All server names within a test case will be distinct.All attribute names for a single server will be distinct.

Each of the L lines in a decision tree definition will have

at most 80

characters,

not including the endlines.

Small dataset

1 L 10

1 A 10

0 n 5

Large dataset1 L 100

1 A 100

0 n 100

Example:

Input:

1

7

(0.084016 pj

(0.680189 hd(0.465482)

(0.912155)

)

(0.066448)

)

8

yad 0


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ljxslm 2 hd pj

yuufr 2 hd pj

qqdtg 0

vkmqyd 1 hd

tubm 2 hd pj

ddm 2 hd pj

okwes 1 hd

Output:

Case #1:

0.00558270

0.02660079

0.02660079

0.00558270

0.00558270

0.02660079

0.02660079

0.00558270

Filename:

Submit

Attempt No 1

Problem 4: TRANSLTR At Work !!

TRANSLTR, like all great technological advancements, had

been a child of

necessity. Its three million processors would all work inparallelcounting upward at blinding speed, trying

every new permutation as they went. The hope was that even

codes within

thinkably colossal pass-

keys would not be safe from TRANSLTRs tenacity.

This multi-billion-dollar masterpiece would use

the power of parallel processing as well as some highly

classifiedadvances in clear text assessment to

guess pass-keys and break codes. It would derive its power

not only from

its staggering number of

processors but also from new advances in quantum-computing

.


8/24

The moment of truth came on a blustery Thursday morning in

October.

The first live test.

Testing strategy utilises a very simple encoding scheme.

Scheme: Assign A the code word 1, B will be 2, and so

on down to Z

being assigned 26.

So, the encoding of the word BEAN is: 25114. Does it have

a unique

decoding ?-----

Ans: Obviously No !!.......Other than BEAN, youd get

BEAAD, YAAD,

YAN, YKD and BEKD.

If you got a string of length 5000 there would be tons of

differentdecoding and with that many you would find at least two

different ones

that would make sense.

Q: How many different decoding?

A: Jillions!

Your task is to determine how many decoding there can be

for a given

string .

Input:Input will consist of multiple input sets. Each set will

consist of a

single line of at most 5000 digits representing a valid

encryption

(for example, no line will begin with a 0). There will be

no spaces

between the digits. An input line of 0 will terminate the

input and

should not be processed.

Output:For each input set, output the number of possible decoding

for the input

string. All answers will be within the range of a 64 bit

signed integer.

Example:


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Input:

25114

1111111111

3333333333

0

Output:

6

89

1

Filename:

Submit

Attempt No 1

Problem 5: Hacking NSA security

Strathmore has been caught wanting by Ernie Tankoda, as

Strathmore has

run the Digital Fortress, a junk of malicious code from

Tankoda. All

the gates are being broken one-by-one and only a few have

been left.

The Security of NSA has been defined in a unique recursive

way, such

that a gate numbered k is protected by all gates upto k-1

in followingway:

s0 = ()

sk = (s0s1.....sk-1)

Your task is to identify those gates which are yet to be

broken. The

more efficiently you can find it, more time you have to

save those

gates.

In each test case, you are given k, l, m, where k defines

the Level ofsecurity( k in the above recurrence ). l defines the

starting position

of the vulnerable gate and m defines the number of

vulnerable gates

and you have to print all the vulnerable gates in the above

range.


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Input:

The first line specifies the number of test cases t.

For each test case, two integers: 1


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Given N, the last number you wrote, compute what the next

number in

the list will be.

Input:

The first line of input contains an integer T, the number

of test

cases in the input. T lines follow, one for each test case,

each

containing a single integer N.

Output:

For each test case, output

Case #X: K

where X is the test case number, starting from 1, and K is

the next

integer in the list.

LimitsSmall dataset

1 T 50

1 N 106

Large dataset

1 T 500

1 N 1020

Examples:

Input:

1118, 181, 811

Output:

Case #1: 1018

Filename:

Submit

No 1 : 0

No 2 : 0No 3 : 0

No 4 : 0

No 5 : 0

No 6 : 0

Total Marks : 0
http://203.110.240.102/overnite/index1.php#problems


12/24

Reply Forward

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|

Ambujpandey ---------- Forwarded message ---------- From: Ambuj pandey


13/24

and it proposes to use the algorithm with a little integer

and another

integer that has up to 250 digits.

Your task is to help David programming an efficient code

for the

challenge of his wife Susan.

Input:

The first line of the input file contains a number

representing the

number of lines to follow. Each line consists of two

numbers A and B

(0


14/24

Computers use only 2 alphabet symbol 1 and 0 to make

words. A given word

is called "prime" if it cannot be written in the form of

the concatenation

of several copies of some shorter word.

For example the words '01', '110', and '0010' are prime,

while the words

'11', '100100', '110110', are not prime.

So, here we give a challenge to you this time, to

calculate the number of

prime words which you can form from exactly x 1s and y 0s.

Input:

The first line specifies the number of test cases t. For

each test case,

two integers: 1


15/24

Output:

4

Filename:

Submit

Attempt No 1

Problem 3: NSA Servers Efficiency

NSA servers have been arranged in special manners and have

been organized

in special trees, called classification trees. In this

data-structure,every server is characterised by its own clock-frequency

(in Tera flip-flops) and a node-attribute.

For any given server, we can decide its efficiency by

looking at the

frequencies of all its child nodes and using the following

decision tree.

(0.2 attr1

(0.81 attr1

(0.3)

(0.2)

)(0.1 attr2

(0.3 attr3

(0.01)

(0.01)

)

(0.1)

)

)

A decision tree is defined recursively. It always has a

root node and a

weight(frequency here). It also, optionally, has a node-name and two

sub-trees, which are themselves decision trees.

More formally, a decision tree is defined using the

following grammar.

tree ::= (weight [feature tree tree])

weight is a real number between 0 and 1,inclusive


16/24

node-name is a string of 1 or more lower case English

letters

The part inside the square brackets, [], is optional. The

parentheses, (),

weight and name are tokens. There will be at least one

whitespace character

between any two tokens, except (possibly) after an open-

bracket '('

or before a close-bracket ')'. Whitespace characters are

space (' ') and

endline ('\n').

To figure out the efficiency of a server, we start at the

root of the tree

with weight p set to 1. At each node, we multiply p by the

weight of the

node. If the node is a leaf (has no sub-trees), then we

stop, and the value

of p is the final efficiency of the entire server.Otherwise, we look at

the node-attribute associated with the node. If the server

has this

node-attribute, we move down into the first sub-tree(first

child server)

and continue recursively. If it does not have this

attribute, then we move

down into the second sub-tree(second server) and continue

in the same way.

In the above example, there is a single server and it has 2

attributes:attr1 and attr3. We start at the root with p equal to 1. We

multiply p by

0.2, the weight of the root and move into the first sub-

tree because the

first child-server has that attribute. There, we multiply p

by 0.81, which

makes p equal to 0.162. From there we move further down

into the first

sub-tree because the server has attribute attr1. Finally,

we multiply p

by 0.3 and end up with 0.0486 as the final efficiency.You will be given a decision tree and a list of servers

with their

attributes. For each item, you need to return the

efficiency of a server.

Input:


17/24

The first line of input contains a single integer, N, the

number of test

cases.

N test cases follow.

Each test case description will start with a line that

contains an integer

L --

the number of lines that describe a decision tree. The next

L lines will

contain

a decision tree in the format described above. The line

after that will

contain

A -- the number of servers. The next A lines will each

contain the

description of

one server in the following format.

server n attribute1 attribute2 ... attributen

Output:

For each test case, output one line containing "Case #x:"

followed by

exactly A

lines, one per server, in the same order as they appear in

the input.

Each line

should contain the efficiency of server. Answers that are

precise to

within anabsolute or relative error of 10-6 will be considered

correct.

Limits

1 N 100

All weights will be between 0 and 1, inclusive.

All weights will consist of only digits with at most one

decimal point.

The weights will not start or end with a decimal point.

The weights will not have more than one 0 before a decimal

point.

All servers and attributes will consist of between 1 and 10lower case

English

letters.

All server names within a test case will be distinct.

All attribute names for a single server will be distinct.

Each of the L lines in a decision tree definition will have

at most 80


18/24

characters,

not including the endlines.

Small dataset

1 L 10

1 A 10

0 n 5

Large dataset

1 L 100

1 A 100

0 n 100

Example:

Input:

1

7

(0.084016 pj(0.680189 hd

(0.465482)

(0.912155)

)

(0.066448)

)

8

yad 0

ljxslm 2 hd pj

yuufr 2 hd pj

qqdtg 0vkmqyd 1 hd

tubm 2 hd pj

ddm 2 hd pj

okwes 1 hd

Output:

Case #1:

0.00558270

0.02660079

0.02660079

0.005582700.00558270

0.02660079

0.02660079

0.00558270


19/24

Filename:

Submit

Attempt No 1

Problem 4: TRANSLTR At Work !!

TRANSLTR, like all great technological advancements, had

been a child of

necessity. Its three million processors would all work in

parallelcounting upward at blinding speed, trying

every new permutation as they went. The hope was that even

codes within

thinkably colossal pass-

keys would not be safe from TRANSLTRs tenacity.

This multi-billion-dollar masterpiece would use

the power of parallel processing as well as some highly

classified

advances in clear text assessment to

guess pass-keys and break codes. It would derive its power

not only from

its staggering number of

processors but also from new advances in quantum-computing

.

The moment of truth came on a blustery Thursday morning inOctober.

The first live test.

Testing strategy utilises a very simple encoding scheme.

Scheme: Assign A the code word 1, B will be 2, and so

on down to Z

being assigned 26.

So, the encoding of the word BEAN is: 25114. Does it have

a unique

decoding ?-----

Ans: Obviously No !!.......Other than BEAN, youd getBEAAD, YAAD,

YAN, YKD and BEKD.

If you got a string of length 5000 there would be tons of

different


20/24

decoding and with that many you would find at least two

different ones

that would make sense.

Q: How many different decoding?

A: Jillions!

Your task is to determine how many decoding there can be

for a given

string .

Input:

Input will consist of multiple input sets. Each set will

consist of a

single line of at most 5000 digits representing a valid

encryption

(for example, no line will begin with a 0). There will be

no spaces

between the digits. An input line of 0 will terminate theinput and

should not be processed.

Output:

For each input set, output the number of possible decoding

for the input

string. All answers will be within the range of a 64 bit

signed integer.

Example:

Input:

25114

1111111111

3333333333

0

Output:

6

89

1

Filename:

Submit

Attempt No 1

Problem 5: Hacking NSA security


21/24

Strathmore has been caught wanting by Ernie Tankoda, as

Strathmore has

run the Digital Fortress, a junk of malicious code from

Tankoda. All

the gates are being broken one-by-one and only a few have

been left.

The Security of NSA has been defined in a unique recursive

way, such

that a gate numbered k is protected by all gates upto k-1

in following

way:

s0 = ()

sk = (s0s1.....sk-1)

Your task is to identify those gates which are yet to be

broken. The

more efficiently you can find it, more time you have tosave those

gates.

In each test case, you are given k, l, m, where k defines

the Level of

security( k in the above recurrence ). l defines the

starting position

of the vulnerable gate and m defines the number of

vulnerable gates

and you have to print all the vulnerable gates in the above

range.

Input:

The first line specifies the number of test cases t.

For each test case, two integers: 1


22/24

Filename:

Submit

Attempt No 1

Problem 6: National SecurityAgency Selection Test

Congratulations, Mr. Becker. I hear you did a fine job

today,

Susan said.

And, National Security Agency offered David Becker a

trial post in theirAsiatic Cryptography Division.

What David did was simple, he just predicted the next

number in a

list L.

Every number in the list L satisfies the property that thelist

contains all numbers with exactly Di digits in its decimal

representation which are equal to i, for each i between 1

and 9,

inclusive in ascending order.

For example, if you consider every number with just two

'1's and

one '8', then the list would begin as : 118, 181, 811,

1018, 1081

..................

Given N, the last number you wrote, compute what the nextnumber in

the list will be.

Input:

The first line of input contains an integer T, the number

of test

cases in the input. T lines follow, one for each test case,

each

containing a single integer N.

Output:For each test case, output

Case #X: K

where X is the test case number, starting from 1, and K is

the next

integer in the list.

Limits

Small dataset


23/24

1 T 50

1 N 106

Large dataset

1 T 500

1 N 1020

Examples:

Input:

1

118, 181, 811

Output:

Case #1: 1018

Filename:

Submit

No 1 : 0

No 2 : 0

No 3 : 0

No 4 : 0

No 5 : 0

No 6 : 0

Total Marks : 0

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IIT Kh C Problems