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Infix to Postfix Expression Conversion

With a given Infix Expression, we will see how to convert Infix Expression into Postfix Expression using stack.
 

Algorithm to convert Infix expression to Postfix expression:

In this algorithm, we will use operatorStack to store operators during the conversion. The step are as follows:
  • Initialize empty operatorStack
  • While the end of input infix string
    • symbol = next input character
    • If symbol is an operand
      • add symbol to the postfix string
    • Else
      • While( operatorStack is not empty && precedence of top character of operatorStack is higher than symbol)
        • topsymbol = pop the operatorStack
        • add topsymbol to the postfix string
      • End While
      • If (operatorStack is empty || symbol is not equal to '(' )
        • push symbol into operatorStack
      • Else
        • pop the operatorStack
      • End If
    • End If
    • While the operatorStack is not empty
      • topsymbol = pop the operatorStack
      • add topsymbol to the postfix string
    • End While
 


 

Function to convert Infix expression to Postfix expression:


void infix_to_postfix(char *infix_str, char *postfix_str){
 int i = -1, j = -1;
 STACK stk;
 stk.top = -1;
 while(infix_str[++i]){
  if(infix_str[i] == ' '){
   continue;
  }
  if( ischar(infix_str[i]) ){
   postfix_str[++j] = infix_str[i];
  }
  else{
   while( !empty_stack(&stk) && precedence( top_of_stack(&stk), infix_str[i]) ){
   postfix_str[++j] = pop(&stk);
   }
   if(empty_stack(&stk) || infix_str[i] != ')'){
    push(&stk,infix_str[i]);
   }
   else{
    pop(&stk);
   }
  }
 }
 while(!empty_stack(&stk)){
  postfix_str[++j] = pop(&stk);
 }
 postfix_str[++j] = '\0';
}
 

Program to convert Infix expression to Postfix expression:


#include <stdio.h>
#include <stdlib.h>
#define STACK_SIZE 50

typedef struct{
 int top;
 char stack[STACK_SIZE];
} STACK;

void push(STACK *, char );
char pop(STACK *);
void infix_to_postfix(char *, char*);
char top_of_stack(STACK *);
int ischar(char );
int empty_stack(STACK*);
int precedence(char,char);

int main(){
 char *infix_str = "A+(B*C)/D";
 char postfix_str[100];
 infix_to_postfix(infix_str, postfix_str);
 printf("Infix Expression   : %s\n", infix_str);
 printf("Postfix Expression : %s\n", postfix_str);
 return 0;
}

// return true when op1 has higher precedence over op2
int precedence(char op1, char op2){ 
 char *sym = "/*+-";
 int i1 = -1, i2 = -1,i = -1;
 if(op1 == '(')
  return 0;
 if(op2 == '('){
  if(op1 != ')')
   return 0;
  return 1;
 }
 if(op2 == ')'){
  if(op1 != '(')
   return 1;
  return 0;
 }
 if(op1 == ')')
  exit(1);
 while(sym[++i]){
  if(op1 == sym[i])
   i1 = i;
  if(op2 == sym[i])
   i2 = i;
 }
 return i1 < i2;
}

void infix_to_postfix(char *infix_str, char *postfix_str){
 int i = -1, j = -1;
 STACK stk;
 stk.top = -1;
 while(infix_str[++i]){
  if(infix_str[i] == ' '){
   continue;
  }
  if( ischar(infix_str[i]) ){
   postfix_str[++j] = infix_str[i];
  }
  else{
   while( !empty_stack(&stk) && precedence( top_of_stack(&stk), infix_str[i]) ){
   postfix_str[++j] = pop(&stk);
   }
   if(empty_stack(&stk) || infix_str[i] != ')'){
    push(&stk,infix_str[i]);
   }
   else{
    pop(&stk);
   }
  }
 }
 while(!empty_stack(&stk)){
  postfix_str[++j] = pop(&stk);
 }
 postfix_str[++j] = '\0';
}


char top_of_stack(STACK *s){
 return s->stack[s->top];
}

int empty_stack(STACK *stk){
 return stk->top == -1;
}

int ischar(char c){
 return  ( (c >= 'a') && (c <= 'z') ) || 
   ( (c >= 'A') && (c <= 'Z') ) || 
   ( (c >= '0') && (c <= '9') );
}

void push(STACK *s, char c){
 if(s->top == STACK_SIZE-1){
  printf("Stack Overflow\n");
  exit(1);
 }
 else{
  s->stack[++s->top] = c;
 }
}

char pop(STACK *s){
 if(s->top == -1){
  printf("Stack Underflow\n");
  exit(1);
 }
 else{
  return s->stack[s->top--];
 }
}
 
Infix Expression   : A+(B*C)/D
Postfix Expression : ABC*D/+
 

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