The document describes the algorithm for converting infix expressions to postfix notation using a stack. It outlines the steps for handling operands, operators, and parentheses while traversing the infix expression. The implementation is presented in C programming language with a sample code demonstrating the conversion process.

1. Infix to Postfix conversion
SOUMEN SANTRA
MCA, M.TECH, SCJP, MCP

2. ALGORITHM
Scan the Infix expression left to right
 If the character x is an operand
 Output the character into the Postfix Expression
 If the character x is a left or right parenthesis
 If the character is “(“
 Push it into the stack
 if the character is “)”
 Repeatedly pop and output all the operators/characters
until “(“ is popped from the stack.
 If the character x is a is a regular operator
 Step 1: Check the character y currently at the top of the
stack.
 Step 2: If Stack is empty or y=‘(‘ or y is an operator of
lower precedence than x, then push x into stack.
 Step 3: If y is an operator of higher or equal precedence
than x, then pop and output y and push x into the stack.
When all characters in infix expression are processed repeatedly pop the
character(s) from the stack and output them until the stack is empty.

3. Infix Expression
Postfix Expression
( a + b - c ) * d – ( e + f )
Stack
Infix to postfix conversion

4. a + b - c ) * d – ( e + f )
(
Infix Expression
Postfix Expression
Stack
Infix to postfix conversion

5. + b - c ) * d – ( e + f )
(
a
Infix Expression
Postfix Expression
Stack
Infix to postfix conversion

6. b - c ) * d – ( e + f )
(
a
+
Infix Expression
Postfix Expression
Stack
Infix to postfix conversion

7. - c ) * d – ( e + f )
(
a b
+
Infix Expression
Postfix Expression
Stack
Infix to postfix conversion

8. c ) * d – ( e + f )
(
a b +
-
Infix Expression
Postfix Expression
Stack
Infix to postfix conversion

9. ) * d – ( e + f )
(
a b + c
-
Infix Expression
Postfix Expression
Stack
Infix to postfix conversion

10. * d – ( e + f )
a b + c -
Infix Expression
Postfix Expression
Stack
Infix to postfix conversion

11. d – ( e + f )
a b + c -
*
Infix Expression
Postfix Expression
Stack
Infix to postfix conversion

12. – ( e + f )
a b + c - d
*
Infix Expression
Postfix Expression
Stack
Infix to postfix conversion

13. ( e + f )
a b + c – d *
-
Infix Expression
Postfix Expression
Stack
Infix to postfix conversion

14. e + f )
a b + c – d *
-
(
Infix Expression
Postfix Expression
Stack
Infix to postfix conversion

15. + f )
a b + c – d * e
-
(
Infix Expression
Postfix Expression
Stack
Infix to postfix conversion

16. f )
a b + c – d * e
-
(
+
Infix Expression
Postfix Expression
Stack
Infix to postfix conversion

17. )
a b + c – d * e f
-
(
+
Infix Expression
Postfix Expression
Stack
Infix to postfix conversion

18. a b + c – d * e f +
-
Infix Expression
Postfix Expression
Stack
Infix to postfix conversion

19. a b + c – d * e f + -
Infix Expression
Postfix Expression
Stack
Infix to postfix conversion

20. #include<stdio.h>
#include<stdlib.h>
#define STACKSIZE 20
typedef struct{
int top;
char items[STACKSIZE];
}STACK;
void push(STACK *, char);
char pop(STACK *);
void main()
{
int i;
char x, y, E[20] ; /* Assume that Infix Expression E contains single-digit
integers/parenthesis/operators*/
STACK s;
s.top = -1; /* Initialize the stack is */
printf("Enter the Infix Expression:");
scanf("%s",E);
for(i=0;E[i] != '0';i++){
x= E[i];
IMPLEMENTATION IN C

21. if(x<=’z’ && x>=’a’) /* Consider all lowercase letter operands from a to z */
printf(“%c”,x);
else if(x == ’(’)
push(&s ,x);
else if(x == ’)’){
y=pop(&s) ;
while(y != ‘(‘){
printf(“%c”,y);
y=pop(&s) ;
}
}
else {
if(s.top ==-1 || s.items[s.top] == ‘(‘)
push(&s ,x);
else {
y = s.items[s.top]; /* y is the top operator in the stack*/
if( y==’*’ || y==’/’){ /* precedence of y is higher/equal to x*/
printf(“%c”, pop(&s));
push(&s ,x);
}

22. else if ( y==’+’ || y==’-’)
if( x==’+’ || x==’-’) { /* precedence of y is equal to x*/
printf(“%c”, pop(&s));
push(&s ,x);
}
else /* precedence of y is less than x*/
push(&s ,x);
}
}
}
while(s.top != -1)
printf(“%c”,pop(&s));
}
void push(STACK *sptr, char ps) /*pushes ps into stack*/
{
if(sptr->top == STACKSIZE-1){
printf("Stack is fulln");
exit(1); /*exit from the function*/
}
else
sptr->items[++sptr->top]= ps;
}

23. char pop(STACK *sptr)
{
if(sptr->top == -1){
printf("Stack is emptyn");
exit(1); /*exit from the function*/
}
else
return sptr->items[sptr->top--];
}

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