Stack Application Infix and Prefix

1. Arithmetic Expression
Application of Stack

2. Example: Suppose we have an infix expression:
2+(4+3*2+1)/3.
'2' - send to the output.
'+' - push on the stack.
'(' - push on the stack.
'4' - send to the output.
'+' - push on the stack.
'3' - send to the output.
'*' - push on the stack.
'2' - send to the output.

3. Infix to Prefix Operations
Examples 1: (A * B) + C
Sol: (*AB ) + C
T + C
+ T C
+ * A B C
Example 2: (A – B / c) * ( D * E – F)
Sol.: (A – B / c) * ( D * E – F)
(A – ( B / C ) ) * ( ( D * E ) – F )
(A – ( / B C ) ) * ( ( * D E ) – F )
(A – T ) * { S – F )
(- A T) * ( - S F )
Q * P
*QP
* - A T – S F
* - A / B C - * D E F

4. Stack Operations Output
--------------------------------------
push(5); 5
push(9); 5 9
push(3); 5 9 3
push(pop() + pop()) 5 12
push(4); 5 12 4
push(2); 5 12 4 2
push(pop() * pop()) 5 12 8
push(pop() * pop()) 5 96
push(7) 5 96 7
push(pop() + pop()) 5 103
push(pop() * pop()) 515
Evaluate following postfix Expression
5 9 3 + 4 2 * * 7 + *

5. Symbol Scanned Stack
6 6
2 6,2
3 6,2,3
+ 6,5
- 1
3 1,3
8 1,3,8
2 1,3,8,2
/ 1,3,4
+ 1,7
* 7
2 7,2
49
3 49,3
+ 52

6. Examples!!!
Convert in to Prefix and Postfix Expression
1. A + B * C + D
2. (A + B) * (C + D)
3. A * B + C * D
4. A + B + C + D