Evaluate Postfix Expression Using Stack in DSA Python

Mental Model

Use a stack to keep numbers until an operator appears, then combine the last two numbers using that operator.

Analogy: Imagine a stack of plates where you add plates with numbers. When you see a math sign, you take the top two plates, do the math, and put the result back on top.

Stack (top at right): []
Postfix expression: 2 3 + 4 *
Numbers push in order, operators combine top two numbers.

Dry Run Walkthrough

Input: Postfix expression: 2 3 + 4 *

Goal: Calculate the final result of the postfix expression using a stack

Step 1: Push 2 onto stack

Stack: [2]

Why: Numbers are pushed to stack to wait for operators

Step 2: Push 3 onto stack

Stack: [2, 3]

Why: Keep numbers until operator appears

Step 3: Operator '+' found: pop 3 and 2, add them (2+3=5), push 5

Stack: [5]

Why: Apply operator to last two numbers and push result

Step 4: Push 4 onto stack

Stack: [5, 4]

Why: Push next number to stack

Step 5: Operator '*' found: pop 4 and 5, multiply (5*4=20), push 20

Stack: [20]

Why: Apply operator to last two numbers and push result

Result:

Stack: [20]
Final result: 20

Annotated Code

DSA Python

class Stack:
    def __init__(self):
        self.items = []

    def push(self, item):
        self.items.append(item)

    def pop(self):
        if not self.is_empty():
            return self.items.pop()
        return None

    def is_empty(self):
        return len(self.items) == 0


def evaluate_postfix(expression):
    stack = Stack()
    operators = {'+', '-', '*', '/'}

    for token in expression.split():
        if token not in operators:
            stack.push(int(token))  # push number
        else:
            right = stack.pop()  # pop right operand
            left = stack.pop()   # pop left operand
            if token == '+':
                stack.push(left + right)  # add and push result
            elif token == '-':
                stack.push(left - right)  # subtract and push result
            elif token == '*':
                stack.push(left * right)  # multiply and push result
            elif token == '/':
                stack.push(int(left / right))  # divide and push result (integer division)

    return stack.pop()  # final result


# Driver code
expr = "2 3 + 4 *"
result = evaluate_postfix(expr)
print(result)

stack.push(int(token)) # push number

push number tokens onto stack to wait for operators

right = stack.pop() # pop right operand

pop right operand for operation

left = stack.pop() # pop left operand

pop left operand for operation

stack.push(left + right) # add and push result

apply operator and push result back to stack

stack.push(left - right) # subtract and push result

apply operator and push result back to stack

stack.push(left * right) # multiply and push result

apply operator and push result back to stack

stack.push(int(left / right)) # divide and push result (integer division)

apply operator and push result back to stack

return stack.pop() # final result

pop final result from stack after processing all tokens

Output

20

Complexity Analysis

Time: O(n) because we process each token in the expression once

Space: O(n) because in worst case all tokens are numbers pushed to stack

vs Alternative: Compared to evaluating infix expressions which require operator precedence handling, postfix evaluation is simpler and faster using a stack

Edge Cases

Empty expression

Returns None or error because no tokens to process

DSA Python

return stack.pop()  # final result

Single number expression like '5'

Returns the number itself as result

DSA Python

stack.push(int(token))  # push number

Division by zero in expression

Raises runtime error (ZeroDivisionError)

DSA Python

stack.push(int(left / right))  # divide and push result (integer division)

When to Use This Pattern

When you see an expression without parentheses and operators after operands, use the Evaluate Postfix Expression pattern with a stack to compute the result easily.

Common Mistakes

Mistake: Popping operands in wrong order causing wrong results
Fix: Always pop right operand first, then left operand before applying operator

Mistake: Trying to evaluate infix expression directly without converting
Fix: Use postfix expression or convert infix to postfix before evaluation

Summary

It calculates the value of a postfix expression using a stack.

Use it when you need to evaluate postfix expressions efficiently without worrying about operator precedence.

The key insight is to push numbers and apply operators immediately to the last two numbers on the stack.