Evaluation of Postfix Expression

Last Updated : 15 Sep, 2025

Given an array of strings arr[] representing a postfix expression, evaluate it. A postfix expression is of the form operand1 operand2 operator (e.g., "a b +"), where two operands are followed by an operator.

Note: The operators can include +, -, *, /, and ^ (where ^ denotes exponentiation, i.e., power). Division / uses floor division.

Examples:

Input: arr[] = ["2", "3", "1", "*", "+", "9", "-"]
Output: -4
Explanation: The expression in infix form is: 2 + (3 * 1) - 9. Now, evaluate step by step:
3 * 1 = 3
2 + 3 = 5
5 - 9 = -4
Final Answer: -4
Input: arr[] = ["2", "3", "^", "1", "+"]
Output: 9
Explanation: If the expression is converted into an infix expression, it will be 2 ^ 3 + 1 = 8 + 1 = 9

[Approach] Using Stack - O(n) Time and O(n) Space

The idea is to use the property of postfix notation, where two operands are always followed by an operator. We iterate through the expression from left to right, and whenever we encounter an operand, we push it onto the stack. When we encounter an operator, we pop the top two elements from the stack, apply the operator on them, and then push the result back into the stack.

Illustration:

C++

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

int floorDiv(int a, int b) {
    if (a * b < 0 && a % b != 0)
        return (a / b) - 1;
    return a / b;
}

int evaluatePostfix(vector<string>& arr) {
    stack<int> st;

    for (string token : arr) {
        
        // If it's an operand (number), push it onto the stack
        if (isdigit(token[0]) || (token.size() > 1 && token[0] == '-')) {
            st.push(stoi(token));
        } 
        
        // Otherwise, it must be an operator
        else {
            int val1 = st.top(); st.pop(); 
            int val2 = st.top(); st.pop(); 

            if (token == "+") st.push(val2 + val1);
            else if (token == "-") st.push(val2 - val1);
            else if (token == "*") st.push(val2 * val1);
            else if (token == "/") st.push(floorDiv(val2, val1));
            else if (token == "^") st.push((int)pow(val2, val1));
        }
    }
    return st.top();
}

int main() {
    vector<string> arr = {"2", "3", "1", "*", "+", "9", "-"}; 
    cout << evaluatePostfix(arr) << endl;
    return 0;
}

#include <stdio.h>
#include <stdlib.h>
#include <ctype.h>
#include <math.h>
#include <string.h>
#include <stdbool.h>
#include <limits.h>

#define MAX 100

typedef struct {
    int top;
    int arr[MAX];
} Stack;

void push(Stack *s, int val) {
    if (s->top == MAX - 1) {
        printf("Stack Overflow\n");
        return;
    }
    s->arr[++s->top] = val;
}

int pop(Stack *s) {
    if (s->top == -1) {
        printf("Stack Underflow\n");
        return INT_MIN;
    }
    return s->arr[s->top--];
}

// Check if token is an operator
bool isOperator(char *token) {
    return strcmp(token, "+") == 0 || strcmp(token, "-") == 0 
        || strcmp(token, "*") == 0 || strcmp(token, "/") == 0
        || strcmp(token, "^") == 0;
}

// Floor division for negative numbers
int floorDiv(int a, int b) {
    if (a * b < 0 && a % b != 0)
        return (a / b) - 1;
    return a / b;
}

// Evaluate postfix expression
int evaluatePostfix(char **arr, int n) {
    Stack s = { -1 };

    for (int i = 0; i < n; i++) {
        
        // If it's an operand (number), push it onto the stack
        if (isdigit(arr[i][0]) || (strlen(arr[i]) > 1 && arr[i][0] == '-')) {
            push(&s, atoi(arr[i]));
        } 
        
        // Otherwise, it must be an operator
        else if (isOperator(arr[i])) {
            int val1 = pop(&s); 
            int val2 = pop(&s); 

            if (strcmp(arr[i], "+") == 0) push(&s, val2 + val1);
            else if (strcmp(arr[i], "-") == 0) push(&s, val2 - val1);
            else if (strcmp(arr[i], "*") == 0) push(&s, val2 * val1);
            else if (strcmp(arr[i], "/") == 0) push(&s, floorDiv(val2, val1));
            else if (strcmp(arr[i], "^") == 0) push(&s, (int)pow(val2, val1));
        }
    }
    return pop(&s);
}

int main() {
    char *arr[] = {"2", "3", "1", "*", "+", "9", "-"};
    int n = sizeof(arr) / sizeof(arr[0]);
    printf("%d\n", evaluatePostfix(arr, n));
    return 0;
}

Java

import java.util.Stack;

public class GfG {
    
    static int floorDiv(int a, int b) {
        if (a * b < 0 && a % b != 0)
            return (a / b) - 1;
        return a / b;
    }
    
    public static int evaluatePostfix(String[] arr) {
        Stack<Integer> st = new Stack<>();

        for (String token : arr) {
          
            // If it's an operand (number), push it onto the stack
            if (Character.isDigit(token.charAt(0)) || 
                (token.length() > 1 && token.charAt(0) == '-')) {
                st.push(Integer.parseInt(token));
            } 
        
            // Otherwise, it must be an operator
            else {
                int val1 = st.pop();
                int val2 = st.pop();

                if (token.equals("+")) st.push(val2 + val1);
                else if (token.equals("-")) st.push(val2 - val1);
                else if (token.equals("*")) st.push(val2 * val1);
                else if (token.equals("/")) st.push(floorDiv(val2, val1));
                else if (token.equals("^")) st.push((int)Math.pow(val2, val1));
            }
        }
        return st.pop();
    }

    public static void main(String[] args) {
        String[] arr = {"2", "3", "1", "*", "+", "9", "-"};
        System.out.println(evaluatePostfix(arr));
    }
}

Python

import math

def evaluatePostfix(arr):
    st = []

    for token in arr:
        
        # If it's an operand (number), push it onto the stack
        if token[0].isdigit() or (len(token) > 1 and token[0] == '-'):
            st.append(int(token))
        
        # Otherwise, it must be an operator
        else:
            val1 = st.pop()
            val2 = st.pop()

            if token == '+':
                st.append(val2 + val1)
            elif token == '-':
                st.append(val2 - val1)
            elif token == '*':
                st.append(val2 * val1)
            elif token == '/':
                st.append(val2 // val1)
            elif token == '^':
                st.append(int(math.pow(val2, val1)))
    return st.pop()

if __name__ == '__main__':
    arr = ["2", "3", "1", "*", "+", "9", "-"]
    print(evaluatePostfix(arr))

using System;
using System.Collections.Generic;

public class GfG {
    
    static int floorDiv(int a, int b) {
        if (a * b < 0 && a % b != 0)
            return (a / b) - 1;
        return a / b;
    }
    
    public static int evaluatePostfix(string[] arr) {
        Stack<int> st = new Stack<int>();

        foreach (string token in arr) {
            
            // If it's an operand (number), push it onto the stack
            if (char.IsDigit(token[0]) || (token.Length > 1 && token[0] == '-')) {
                st.Push(int.Parse(token));
            }
            
            // Otherwise, it must be an operator
            else {
                int val1 = st.Pop();
                int val2 = st.Pop();

                if (token == "+") st.Push(val2 + val1);
                else if (token == "-") st.Push(val2 - val1);
                else if (token == "*") st.Push(val2 * val1);
                else if (token == "/") st.Push(floorDiv(val2, val1));
                else if (token == "^") st.Push((int)Math.Pow(val2, val1));
            }
        }
        return st.Pop();
    }

    public static void Main() {
        string[] arr = {"2", "3", "1", "*", "+", "9", "-"};
        Console.WriteLine(evaluatePostfix(arr));
    }
}

JavaScript

function evaluatePostfix(arr) {
    let st = [];

    for (let token of arr) {
        
        // If token is a number
        if (!isNaN(token)) {
            st.push(parseInt(token));
        } 
        
        // Otherwise, it's an operator
        else {
            let val1 = st.pop();
            let val2 = st.pop();

            if (token === '+') st.push(val2 + val1);
            else if (token === '-') st.push(val2 - val1);
            else if (token === '*') st.push(val2 * val1);
            else if (token === '/') st.push(Math.floor(val2 / val1));
            else if (token === '^') st.push(Math.pow(val2, val1));
        }
    }
    return st.pop();
}

// Driver Code
let arr = ["2", "3", "1", "*", "+", "9", "-"]; 
console.log(evaluatePostfix(arr));

Output

-4

Stack | Set 4 (Evaluation of Postfix Expression)

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Evaluation of Postfix Expression

[Approach] Using Stack - O(n) Time and O(n) Space

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