Infix, prefix and postfix notation

• A + B Infix

• + A B Prefix

• A B + Postfix

A + (B*C) A+(BC*) A(BC*)+ ABC*+

(A + B)*C (AB+)*C (AB+)C* AB+C*

Basic operations

• Five basic operations are there– Addition +– Subtraction -– Multiplication *– Division /– Exponentiation $– Now following is the order of precedence

• Exponentiation• Multiplication/Division• Addition/Subtraction

Some Rules

• When unparenthesized operators of the same precedence are scanned the order is assumed to be left to right.

• But in case of exponentiation the order is assumed to be from right to left.

• E.g. A+B+C (A+B)+C

• And A$B$C A$(B$C)

Infix Postfix

A + B AB+

A+B-C AB+C-

(A+B)*(C-D) AB+CD-*

A$B*C-D+E/F/(G+H) AB$C*D-EF/GH+/+

((A+B)*C-(D-E))$(F+G) AB+C*DE—FG+$

A-B/(C*D$E) ABCDE$*/-

Infix Prefix

A + B +AB

A+B+C -+ABC

(A+B)*(C-D) *+AB-CD

A$B*C-D+E/F/(G+H) +-*$ABCD//EF+GH

((A+B)*C-(D-E))$(F+G) $-*+ABC-DE+FG

A-B/(C*D$E) -A/B*C$DE

Infix to Prefix notation (Example)

1. A + B + A B

2. A + B - C

+ A B - C

- + A B C

3. (A + B) * (C – D)

(+ A B) * (- C D)

*(+ A B)(-C D)

*+A B – C D

4. A-B/(C*D$E)

A-B/(C*$DE)

A-B/(*C$DE)

A-/B(*C$DE)

-A/B(*C$DE)

Example (Cont…)A$B*C–D+E/F/(G+H)

A$B*C–D+E/F/(+G H)

$AB*C–D+E/F/(+GH)

*$ABC–D+/EF/(+GH)

-*$ABCD+//EF(+GH)

+-$ABCD+//EF+GH

Example (Cont…)

((A+B)*C-(D-E))$(F+G)

((+AB)*C-(-DE))$(+FG)

$(*(+AB)C-(-DE))(+FG)

$(-*(+AB)C(-DE))(+FG)

$-*+ABC-DE+FG

Evaluating a postfix Expression (Algo)

Opndstk = the empty stack/* scan the input string reading one */

While(not end of input){

symb = next input character;if(symb is an operand)

push(opndstk, symb);else{

opnd2 = pop(opndstk);opnd1 = pop(opndstk);value = result of applying symb to opnd1 and opnd2;push(opndstk, value);

}}

Evaluate :- 6 2 3 + - 3 8 2 / + * 2 $ 3 +Symb opnd1 opnd2 value Opndstk

6 6

2 6,2

3 6,2,3

+ 2 3 5 6,5

- 6 5 1 1

3 6 5 1 1,3

8 6 5 1 1,3,8

2 6 5 1 1,3,8,2

/ 8 2 4 1,3,4

+ 3 4 7 1,7

* 1 7 7 7

2 1 7 7 7,2

$ 7 2 49 49

3 7 2 49 49,3

+ 49 3 52 52

Circular Queues

1. It is a ring showing, conceptually, a circular buffer.2. This visually shows that the buffer has no real end and it can

loop around the buffer.3. However, since memory is never physically created as a ring, a

linear representation is generally used as is done below.4. A circular buffer or ring buffer is a data structure that uses a

single, fixed-size buffer as if it were connected end-to-end. 5. This structure lends itself easily to buffering data streams.

Circular Queue (Insertion)void insert(int val)

{ if((front==0 && rear==MAX-1) || (rear+1==front))

printf(" Circular Queue is Full"); else { if(rear==MAX-1)

rear=0; else

rear++; a[rear]=val; } if(front==-1) front=0;

}

55

44

33

22

11

22

11

55

44

11

55

44

33

22

4

3

2

1

0

1

0

4

3

0

4

3

2

1

Rear

Front

Front = 0

Rear = max – 1

Queue is full

Rear

Front

Rear

Front

Front != 0 &

Rear = max-1

Rear = 0

A[rear] = val

33 2

Front !=0 &

Rear != max-1

Rear ++

A[rear] = val

Inserting an element into queue (all conditions)

Since if your queue is empty means (front=-1) then make front =0 & rear = 0 (by rear++)

It will become 0 means(-1+1=0)

Circular Queue (Deletion)int deletion()

{ int k; if(front==-1)

printf("Circular Queue is Empty"); else {

k=a[front];if(front==rear) front=rear=-1;else{ if(front==MAX-1)

front=0; else

front++;}

} return k;

}

11

44

33

22

11

11

55

44

33

220

3

2

1

0

0

4

3

2

1

Rear

Front

Front = Rear

Front = Rear = -1

Rear

Front

Rear

Front

If Front != max-1 &

Front !=-1

Front ++

55 4

Deleting an element into queue (all conditions)

If (front=-1) then

Queue is empty

If Front == max -1

Then

Front = 0

void display() {

int i; if(front==-1)

printf("Circular Queue is Empty"); else {

if(rear < front) {

for(i=front;i<=MAX-1;i++) printf("%d ",a[i]);for(i=0;i<=rear;i++) printf("%d ",a[i]);

} else {

for(i=front;i<=rear;i++) printf("%d \n ",a[i]);

} }

}

Converting an Expression from Infix to Postfix

Opstk = the empty stack;While(not end of input){

symb = next input character;if(symb is an operand)

add symb to the postfix stringelse{

while(!empty(opstk) && prcd(stacktop(opstk), symb)) { topsymb = pop(opstk); add topsymb to the postfix string;}push(opstk, symb);

}}While(!empty(opstk){ topsymb = pop(opstk);

add topsymb to the postfix string;}

Example – A + B * C

Symb

1 A A

2 + A +

3 B AB +

4 * AB + *

5 C ABC + *

6 ABC* +

7 ABC*+

Example 2 (A+B) * C

symb Postfix string opstk

( (

A A (

+ A ( +

B AB ( +

) AB+

* AB+ *

C AB + C *

AB + C*

Example 3 ((A – (B + C)) * D) $ (E + F)( A (

( A ((

A A ((

- AB ((-

( AB ((-(

B ABC ((-(

+ ABC + ((-( +

C ABC + - ((-( +

) ABC + - ((-

) ABC + - D (

* ABC + - D (

D ABC + - D (*

) ABC + - D * (*

$ ABC + - D *

( ABC + - D * $

E ABC + - D * E $(

+ ABC + - D * E $(

F ABC + - D * EF $( +

) ABC + - D * EF + $

ABC + - D * EF + $