Program to evaluate Postfix Notation in C++

Suppose we have postfix expression and we have to evaluate the value. Postfix expression is also known as Reverse polish notation. Here we have to use the stack data structure to solve the postfix expressions.

So if the expression is “21+3*”, then the answer will be 9.

Let us see the steps −

  • for each character ch in the postfix expression, do
    • if ch is an operator $\odot$ , then
      • a := pop first element from stack,
      • b := pop second element from the stack
      • res := b $\odot$ a
      • push res into the stack
    • else if ch is an operand, then
      • add ch into the stack
  • return element of stack top

Let us see the following implementation to get better understanding −


 Live Demo

using namespace std;
float scanNum(char ch){
   int value;
   value = ch;
   return float(value-'0');//return float from character
int isOperator(char ch){
   if(ch == '+'|| ch == '-'|| ch == '*'|| ch == '/' || ch == '^')
      return 1;//character is an operator
      return -1;//not an operator
   int isOperand(char ch){
      if(ch >= '0' && ch <= '9')
         return 1;//character is an operand
      return -1;//not an operand
   float operation(int a, int b, char op){
      //Perform operation
      if(op == '+')
         return b+a;
      else if(op == '-')
         return b-a;
      else if(op == '*')
         return b*a;
      else if(op == '/')
         return b/a;
      else if(op == '^')
         return pow(b,a); //find b^a
   return INT_MIN; //return negative infinity
float postfixEval(string postfix){
   int a, b;
   stack<float> stk;
   string::iterator it;
   for(it=postfix.begin(); it!=postfix.end(); it++){
      //read elements and perform postfix evaluation
      if(isOperator(*it) != -1){
         a =;
         b =;
         stk.push(operation(a, b, *it));
      }else if(isOperand(*it) > 0){
   string post = "21+3*";
   cout <<postfixEval(post);





Updated on: 20-Oct-2020

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