Evaluate Postfix Expression Using Stack in DSA C++ - Time & Space Complexity

Time Complexity: Evaluate Postfix Expression Using Stack

O(n)

Understanding Time Complexity

We want to understand how the time to evaluate a postfix expression changes as the expression gets longer.

Specifically, how many steps does it take to process each symbol in the expression?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

int evaluatePostfix(string expr) {
    stack<int> s;
    for (char c : expr) {
        if (isdigit(c)) s.push(c - '0');
        else {
            int b = s.top(); s.pop();
            int a = s.top(); s.pop();
            if (c == '+') s.push(a + b);
            else if (c == '-') s.push(a - b);
            else if (c == '*') s.push(a * b);
            else if (c == '/') s.push(a / b);
        }
    }
    return s.top();
}
    

This code evaluates a postfix expression by scanning each character once and using a stack to store intermediate results.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Single loop over each character in the expression.
• How many times: Exactly once per character in the input string.

How Execution Grows With Input

Each character is processed once, so the total steps grow directly with the length of the expression.

Input Size (n)	Approx. Operations
10	About 10 steps
100	About 100 steps
1000	About 1000 steps

Pattern observation: Doubling the input doubles the work; growth is linear.

Final Time Complexity

Time Complexity: O(n)

This means the time to evaluate grows in direct proportion to the expression length.

Common Mistake

[X] Wrong: "Because we pop and push inside the loop, the time is more than linear, maybe quadratic."

[OK] Correct: Each character is handled once, and stack operations are fast and constant time, so total time stays linear.

Interview Connect

Understanding this linear time complexity helps you explain how stack-based evaluation is efficient and practical for expression parsing.

Self-Check

"What if the expression included multi-digit numbers separated by spaces? How would the time complexity change?"

Practice

1. What is the main data structure used to evaluate a postfix expression?

easy

A. Queue

B. Stack

C. Array

D. Linked List

Solution

1. Step 1: Understand postfix evaluation process

   Postfix expressions are evaluated by scanning from left to right and using a stack to store operands.

2. Step 2: Identify the data structure used

   Operands are pushed onto the stack, and when an operator is found, operands are popped for calculation, then the result is pushed back.

3. Final Answer:

   Stack -> Option B

4. Quick Check:

   Postfix evaluation uses Stack [OK]

Hint: Remember: postfix needs LIFO structure, so use stack [OK]

Common Mistakes:

• Using queue instead of stack
• Trying to evaluate without any data structure
• Confusing postfix with infix evaluation

2. Which of the following is the correct syntax to push an integer value '5' onto a stack named 's' in C++?

easy

A. push(s, 5);

B. s.insert(5);

C. s.add(5);

D. s.push(5);

Solution

1. Step 1: Recall C++ stack push syntax

   The standard C++ stack uses the member function push() to add elements.

2. Step 2: Match syntax with options

   Only s.push(5); uses s.push(5); which is correct syntax.

3. Final Answer:

   s.push(5); -> Option D

4. Quick Check:

   Stack push syntax = s.push(value) [OK]

Hint: Use s.push(value) to add elements to stack [OK]

Common Mistakes:

• Using non-existent methods like add() or insert()
• Calling push as a free function instead of member function
• Confusing push with pop

3. What is the output of the following C++ code that evaluates the postfix expression "231*+9-"?

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

int evaluatePostfix(string exp) {
    stack<int> s;
    for (char c : exp) {
        if (isdigit(c)) {
            s.push(c - '0');
        } else {
            int val2 = s.top(); s.pop();
            int val1 = s.top(); s.pop();
            switch(c) {
                case '+': s.push(val1 + val2); break;
                case '-': s.push(val1 - val2); break;
                case '*': s.push(val1 * val2); break;
                case '/': s.push(val1 / val2); break;
            }
        }
    }
    return s.top();
}

int main() {
    cout << evaluatePostfix("231*+9-");
    return 0;
}

medium

A. -4

B. -2

C. 4

D. 2

Solution

1. Step 1: Evaluate postfix expression "231*+9-" step-by-step

   Push 2, push 3, push 1. '*' operator: pop 1 and 3, multiply 3*1=3, push 3. '+' operator: pop 3 and 2, add 2+3=5, push 5. Push 9. '-' operator: pop 9 and 5, subtract 5-9=-4, push -4.

2. Step 2: Final value on stack is -4

   After all operations, the stack top is -4, which is the result printed.

3. Final Answer:

   -4 -> Option A

4. Quick Check:

   Postfix "231*+9-" = -4 [OK]

Hint: Evaluate stepwise: push numbers, apply operators on top two [OK]

Common Mistakes:

• Mixing operand order in subtraction
• Forgetting to convert char digits to int
• Popping operands in wrong order

4. The following code snippet is intended to evaluate a postfix expression but produces incorrect results. What is the bug?

int evaluatePostfix(string exp) {
    stack<int> s;
    for (char c : exp) {
        if (isdigit(c)) {
            s.push(c - '0');
        } else {
            int val1 = s.top(); s.pop();
            int val2 = s.top(); s.pop();
            switch(c) {
                case '+': s.push(val1 + val2); break;
                case '-': s.push(val1 - val2); break;
                case '*': s.push(val1 * val2); break;
                case '/': s.push(val1 / val2); break;
            }
        }
    }
    return s.top();
}

medium

A. Missing return statement

B. isdigit() check is incorrect

C. Operands val1 and val2 are popped in wrong order

D. Stack is not initialized properly

Solution

1. Step 1: Analyze operand popping order

   The code pops val1 first, then val2. In postfix evaluation, val2 is the top operand, val1 is below it.

2. Step 2: Correct operand order for operations

   Operations should be val1 (second popped) operator val2 (first popped). The code reverses this, causing wrong results.

3. Final Answer:

   Operands val1 and val2 are popped in wrong order -> Option C

4. Quick Check:

   Operand order matters: val2 = top, val1 = next [OK]

Hint: Pop second operand first, then first operand [OK]

Common Mistakes:

• Swapping operand order in operations
• Not popping operands before using them
• Confusing isdigit() usage

5. Given the postfix expression "56+82/-", what is the final result after evaluation using a stack?

hard

A. 7

B. 5

C. 1

D. 3

Solution

1. Step 1: Evaluate postfix "56+82/-" stepwise

   Push 5, push 6. '+' operator: pop 6 and 5, add 5+6=11, push 11. Push 8, push 2. '/' operator: pop 2 and 8, divide 8/2=4, push 4. '-' operator: pop 4 and 11, subtract 11-4=7, push 7.

2. Step 2: Final value on stack is 7

   After all operations, the stack top is 7, which is the result.

3. Final Answer:

   7 -> Option A

4. Quick Check:

   Postfix "56+82/-" = 7 [OK]

Hint: Process operators immediately on top two stack values [OK]

Common Mistakes:

• Incorrect operand order in division and subtraction
• Misreading the expression characters
• Forgetting to convert char digits to int