How to Evaluate Postfix Expression: Step-by-Step Guide

To evaluate a postfix expression, use a stack to process each symbol from left to right. Push numbers onto the stack, and when an operator appears, pop the required operands, apply the operator, then push the result back. Continue until the expression ends; the stack's top is the final result.

Syntax

A postfix expression consists of operands (numbers) and operators (+, -, *, /) written without parentheses. The evaluation uses a stack with these steps:

• Operand: Push onto the stack.
• Operator: Pop the required number of operands, apply the operator, push the result back.
• End: The last value on the stack is the result.

text

operand operand operator

Example: 5 3 + means 5 + 3

Example

This example shows how to evaluate the postfix expression 6 2 3 + -, which means 6 - (2 + 3).

python

def evaluate_postfix(expression: str) -> int:
    stack = []
    operators = {'+', '-', '*', '/'}
    for token in expression.split():
        if token not in operators:
            stack.append(int(token))
        else:
            right = stack.pop()
            left = stack.pop()
            if token == '+':
                stack.append(left + right)
            elif token == '-':
                stack.append(left - right)
            elif token == '*':
                stack.append(left * right)
            elif token == '/':
                stack.append(int(left / right))  # integer division
    return stack.pop()

# Example usage
expr = "6 2 3 + -"
result = evaluate_postfix(expr)
print(result)

Output

-1

Common Pitfalls

• Not using a stack to store operands causes confusion in order of operations.
• Forgetting to pop operands in correct order leads to wrong results (left operand first, then right).
• Dividing integers without converting to int can cause float results if not intended.
• Not handling invalid expressions or empty stack errors can crash the program.

python

Wrong order example:

stack.append(right - left)  # Incorrect order

Correct order:

stack.append(left - right)  # Correct order

Quick Reference

Step	Action
Read token	If operand, push to stack
Read token	If operator, pop two operands
Apply operator	Calculate and push result
Repeat	Until expression ends
Result	Top of stack is final answer

Key Takeaways

Use a stack to store operands while scanning the postfix expression left to right.

Push numbers onto the stack and pop two operands when an operator appears.

Apply the operator to the popped operands in correct order: left then right.

The final result is the last value remaining on the stack after processing all tokens.

Handle invalid expressions and division carefully to avoid errors.