Postfix Evaluations using Stack Stack follows LIFO concept. Based on Stack operations and order of operands a mathematical expression is evaluated. When two operands pushed into Stack then the most higher order operands will be evaluated.

1. Postfix Evaluation
Using STACK
SOUMEN SANTRA
MCA, M.TECH, SCJP, MCP

2. INTRODUCTION
Scan the postfix expression left to right
 If the character x is a digit
 Push it into the stack
 if the character is an operator (+,-,*,/)
 pop two values from the stack
 Perform the operation
 Push the result of the operation into the stack
When all characters in postfix expression are processed pop the
value from the stack and output it.

3. Postfix Expression
7 5 2 3 + 8 * + 3 + *
Stack
Postfix Evaluation
   = 

4. 7
Postfix Expression
Stack
5 2 3 + 8 * + 3 + *
Postfix Evaluation
   = 

5. 7
Postfix Expression
Stack
2 3 + 8 * + 3 + *
5
Postfix Evaluation

6. 7
5
Postfix Expression
Stack
3 + 8 * + 3 + *
2
Postfix Evaluation
   = 

7. 7
5
Postfix Expression
Stack
Postfix Evaluation
+ 8 * + 3 + *
2
3
   = 

8. Postfix Expression
Stack
Postfix Evaluation
8 * + 3 + *
 +  = 
7
5
2
3

9. Postfix Expression
Stack
Postfix Evaluation
(
-
7
5
2 3
8 * + 3 + *
 + 3 = 

10. Postfix Evaluation
Postfix Expression
Stack
(
-
7
5
8 * + 3 + *
2 + 3 = 

11. d – ( e + f )
a b + c -
*
Stack
Postfix Evaluation
Postfix Expression
Stack
(
-
7
5
8 * + 3 + *
2 + 3 = 5

12. Postfix Evaluation
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
7
5
8 * + 3 + *
5    = 

13. Postfix Evaluation
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
7
5
* + 3 + *
5
8
   = 

14. e + f )
a b + c – d *
-
(
Stack
Postfix Evaluation
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
7
5
+ 3 + *
5
8
 *  = 

15. + f )
a b + c – d * e
-
(
Stack
Postfix Evaluation
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
7
5
+ 3 + *
5  * 8 = 

16. f )
a b + c – d * e
-
(
+
Stack
Postfix Evaluation
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
7
5
+ 3 + *
5 * 8 = 

17. )
a b + c – d * e f
-
(
+
Stack
Postfix Evaluation
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
7
5
+ 3 + *
5 * 8 = 40

18. Postfix Evaluation
a b + c – d * e f +
-
Stack
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
7
5
+ 3 + *
40    = 

19. a b + c – d * e f + -
Stack
Postfix Evaluation
a b + c – d * e f +
-
Stack
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
7
5
3 + *
40  +  = 

20. Postfix Evaluation
a b + c – d * e f +
-
Stack
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
7
5
3 + *
 + 40 = 

21. Postfix Evaluation
a b + c – d * e f +
-
Stack
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
7
3 + *
5 + 40 = 

22. Postfix Evaluation
a b + c – d * e f +
-
Stack
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
7
3 + *
5 + 40 = 45

23. Postfix Evaluation
a b + c – d * e f +
-
Stack
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
6
18
3 + *
a b + c – d * e f +
-
Stack
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
7
45
3 + *
   = 

24. Postfix Evaluation
a b + c – d * e f +
-
Stack
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
6
18
3 + *
a b + c – d * e f +
-
Stack
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
7
45
+ *
3
   = 

25. Postfix Evaluation
a b + c – d * e f +
-
Stack
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
6
18
3 + *
a b + c – d * e f +
-
Stack
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
7
45
*
3
 +  = 

26. Postfix Evaluation
a b + c – d * e f +
-
Stack
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
6
18
3 + *
a b + c – d * e f +
-
Stack
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
7
45
*
 + 3 = 

27. Postfix Evaluation
a b + c – d * e f +
-
Stack
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
6
18
3 + *
a b + c – d * e f +
-
Stack
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
7
*
45 + 3 = 

28. Postfix Evaluation
a b + c – d * e f +
-
Stack
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
6
18
3 + *
a b + c – d * e f +
-
Stack
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
7
*
45 + 3 = 48

29. Postfix Evaluation
a b + c – d * e f +
-
Stack
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
6
18
3 + *
a b + c – d * e f +
-
Stack
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
7
*
   = 
48

30. Postfix Evaluation
a b + c – d * e f +
-
Stack
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
6
18
3 + *
a b + c – d * e f +
-
Stack
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
7
 *  = 
48

31. Postfix Evaluation
a b + c – d * e f +
-
Stack
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
6
18
3 + *
a b + c – d * e f +
-
Stack
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
7
 * 48 = 

32. Postfix Evaluation
a b + c – d * e f +
-
Stack
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
6
18
3 + *
a b + c – d * e f +
-
Stack
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
7 * 48 = 

33. Postfix Evaluation
a b + c – d * e f +
-
Stack
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
6
18
3 + *
a b + c – d * e f +
-
Stack
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
7 * 48 = 336

34. Postfix Evaluation
a b + c – d * e f +
-
Stack
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
6
18
3 + *
a b + c – d * e f +
-
Stack
( e + f )
a b + c – d *
-
Stack
– ( e + f )
a b + c - d
*
Stack
Postfix Expression
Stack
(
-
336
   = 

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