Program 3-
Write a C program that uses stack operations to convert a given infix expression into its postfix Equivalent, Implement the stack using an array.
Warm-up Exercise
Solution )
#include<stdio.h>
#include<stdlib.h> /* for exit() */
#include<ctype.h> /* for isdigit(char ) */
#include<string.h>
#define SIZE 100
/* declared here as global variable because stack[]
* is used by more than one fucntions */
char stack[SIZE];
int top = -1;
/* define push operation */
void push(char item)
{
if(top >= SIZE-1)
{
printf("\nStack Overflow.");
}
else
{
top = top+1;
stack[top] = item;
}
}
/* define pop operation */
char pop()
{
char item ;
if(top <0)
{
printf("stack under flow: invalid infix expression");
getchar();
/* underflow may occur for invalid expression */
/* where ( and ) are not matched */
exit(1);
}
else
{
item = stack[top];
top = top-1;
return(item);
}
}
/* define function that is used to determine whether any symbol is operator or not
(that is symbol is operand)
* this fucntion returns 1 if symbol is opreator else return 0 */
int is_operator(char symbol)
{
if(symbol == '^' || symbol == '*' || symbol == '/' || symbol == '+' || symbol =='-')
{
return 1;
}
else
{
return 0;
}
}
/* define fucntion that is used to assign precendence to operator.
* Here ^ denotes exponent operator.
* In this fucntion we assume that higher integer value
* means higher precendence */
int precedence(char symbol)
{
if(symbol == '^')/* exponent operator, highest precedence*/
{
return(3);
}
else if(symbol == '*' || symbol == '/')
{
return(2);
}
else if(symbol == '+' || symbol == '-') /* lowest precedence */
{
return(1);
}
else
{
return(0);
}
}
void InfixToPostfix(char infix_exp[], char postfix_exp[])
{
int i, j;
char item;
char x;
push('('); /* push '(' onto stack */
strcat(infix_exp,")"); /* add ')' to infix expression */
i=0;
j=0;
item=infix_exp[i]; /* initialize before loop*/
while(item != '\0') /* run loop till end of infix expression */
{
if(item == '(')
{
push(item);
}
else if( isdigit(item) || isalpha(item))
{
postfix_exp[j] = item; /* add operand symbol to postfix expr */
j++;
}
else if(is_operator(item) == 1) /* means symbol is operator */
{
x=pop();
while(is_operator(x) == 1 && precedence(x)>= precedence(item))
{
postfix_exp[j] = x; /* so pop all higher precendence operator and */
j++;
x = pop(); /* add them to postfix expresion */
}
push(x);
/* because just above while loop will terminate we have
oppped one extra item
for which condition fails and loop terminates, so that one*/
push(item); /* push current oprerator symbol onto stack */
}
else if(item == ')') /* if current symbol is ')' then */
{
x = pop(); /* pop and keep popping until */
while(x != '(') /* '(' encounterd */
{
postfix_exp[j] = x;
j++;
x = pop();
}
}
else
{ /* if current symbol is neither operand not '(' nor ')' and nor
operator */
printf("\nInvalid infix Expression.\n"); /* the it is illegeal symbol */
getchar();
exit(1);
}
i++;
item = infix_exp[i]; /* go to next symbol of infix expression */
} /* while loop ends here */
if(top>0)
{
printf("\nInvalid infix Expression.\n"); /* the it is illegeal symbol */
getchar();
exit(1);
}
if(top>0)
{
printf("\nInvalid infix Expression.\n"); /* the it is illegeal symbol */
getchar();
exit(1);
}
postfix_exp[j] = '\0'; /* add sentinel else puts() fucntion */
/* will print entire postfix[] array upto SIZE */
}
/* main function begins */
int main()
{
char infix[SIZE], postfix[SIZE]; /* declare infix string and postfix string */
/* why we asked the user to enter infix expression
* in parentheses ( )
* What changes are required in program to
* get rid of this restriction since it is not
* in algorithm
* */
printf("ASSUMPTION: The infix expression contains single letter variables and single digit constants only.\n");
printf("\nEnter Infix expression : ");
gets(infix);
InfixToPostfix(infix,postfix); /* call to convert */
printf("Postfix Expression: ");
puts(postfix); /* print postfix expression */
return 0;
}
