# 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 −

## Example

Live Demo

#include<bits/stdc++.h>
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
else
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 = stk.top();
stk.pop();
b = stk.top();
stk.pop();
stk.push(operation(a, b, *it));
}else if(isOperand(*it) > 0){
stk.push(scanNum(*it));
}
}
return stk.top();
}
main(){
string post = "21+3*";
cout <<postfixEval(post);
}

## Input

"21+3*"

## Output

9