C++ Program to Evaluate a Postfix Expression

1. Introduction

• Postfix notation, also referred to as Reverse Polish Notation (RPN), is a mathematical representation where operators are positioned after their operands.
• For instance, the infix notation "A + B" is expressed as "A B +" in postfix notation.
• A significant advantage of postfix notation is its omission of the need for parentheses to establish the sequence of operations.
• This guide focuses on discussing the evaluation of a postfix expression utilizing a stack data structure in the context of C++.

2. Program Overview

To evaluate a postfix expression:

1. We'll use a stack to hold intermediate results.

2. We'll iterate over the postfix expression from left to right.

3. When an operand is encountered, it will be pushed onto the stack.

4. When an operator is encountered, the required number of operands (typically two for binary operations) will be popped from the stack, the operation will be performed, and the result will be pushed back onto the stack.

5. By the end of the iteration, the stack will contain a single value which is the result of the postfix expression.

3. Code Program

#include<iostream>
#include<stack>
using namespace std;

int evaluatePostfix(string postfix) {
    stack<int> s;
    for(int i = 0; i < postfix.length(); i++) {
        char c = postfix[i];
        if(isdigit(c)) {
            s.push(c - '0');
        } else {
            int operand2 = s.top(); s.pop();
            int operand1 = s.top(); s.pop();
            switch(c) {
                case '+': s.push(operand1 + operand2); break;
                case '-': s.push(operand1 - operand2); break;
                case '*': s.push(operand1 * operand2); break;
                case '/': s.push(operand1 / operand2); break;
                case '^': s.push(pow(operand1, operand2)); break;
            }
        }
    }
    return s.top();
}

int main() {
    string postfix;
    cout << "Enter postfix expression (single-digit operands): ";
    cin >> postfix;
    int result = evaluatePostfix(postfix);
    cout << "Evaluation result: " << result << endl;
    return 0;
}

Output:

Enter postfix expression (single-digit operands): 23+5*
Evaluation result: 25

4. Step By Step Explanation

1. We use a stack s to keep track of the operands.

2. As we iterate through the postfix expression:

- If the character is a digit, it's converted to an integer and pushed onto the stack.- If the character is an operator, we pop the required number of operands from the stack, perform the operation, and push the result back onto the stack.

3. After iterating through the entire postfix expression, the stack's top will hold the final result of the evaluation.

4. The main function captures user input and displays the evaluated result.

Note: This program assumes single-digit operands for simplicity. Enhancements can be made to handle multi-digit numbers.