Evaluate Reverse Polish Notation in C++ Program

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

From the postfix expression, when some operands are found, pushed them in the stack. When some operator is found, two items are popped from stack and then the operation is performed in the correct sequence. After that, the result is also pushed in the stack for future use. After completing the whole expression, the final result is also stored in the stack top. So if the expression is “53+62/*35*+”, then the answer will be 39

Let us see the steps −

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

Example(C++)

Let us see the following implementation to get a better understanding −

 Live Demo

#include<iostream>
#include<cmath>
#include<stack>
#include<climits>
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 = "53+62/*35*+";
   cout << "The result is: "<<postfixEval(post);
}

Input

"53+62/*35*+"

Output

The result is: 39