L2 · Working engineerStacks & queues~8 min · 6 tests#47

Evaluate a Postfix (RPN) Expression

Evaluate a space-separated postfix (Reverse Polish) expression with a stack in O(n), handling + - * / and operand order. Run tests in Python.

The problem

expression is a space-separated postfix expression of integers and the operators + - * /. Return its integer value.

Operands come before their operator: "2 3 + 4 *" means (2 + 3) * 4 = 20.
/ truncates toward zero (so -7 / 2 is -3).

Examples

Example 1
Input
```
eval_postfix('2 3 + 4 *')
```
Expected output
```
20
```
Example 2
Input
```
eval_postfix('5 1 2 + 4 * + 3 -')
```
Expected output
```
14
```

+ 4 hidden tests on Submit — operand order, truncate toward zero.

Edge cases to ask about

Single number
Subtraction order
Negative division

Hints

0/3

How an interviewer scores this

0/9

1. Understand the problemRestate it, ask about edge cases and input size.
2. Write a brute-force solutionCorrect first, clever later.
3. Get the correct outputautoAll visible examples pass.
4. Analyse time complexityautoCommit to a Big-O in the Complexity Lab.
5. Analyse space complexityautoExtra memory, not the input.
6. Identify the bottleneckautoMeasure your code — where does it bend?
7. OptimiseUsually: a set or dict instead of a scan.
8. Explain why it worksSay it out loud to Solvi.
9. Test the edge casesautoSubmit passes every hidden test.

Python 3.13 · eval_postfix

def eval_postfix(expression):
    """Evaluate a space-separated postfix expression."""
    # Write your solution here
    pass

⌘/Ctrl + Enter runs the examples

Your code runs in real CPython inside your browser — nothing is sent anywhere. The first run downloads the interpreter (about 6 MB, once). Your code is saved on this device as you type.

Complexity Lab

What does this cost as n grows?

Interviewers score the analysis as much as the code. Commit to an answer first — then check it, and measure your code against the optimal one at growing input sizes.

Time complexity of the optimal solution

Space complexity (extra memory)

Pick both to reveal the answer.

Measure it

Runs the function on inputs of size 250 up to 16,000 and records the time and peak memory. Slow solutions stop early — a short curve is itself the answer.

From brute force to optimal

The progression an interviewer wants to hear, one step at a time.

Approach	Time	Space	Idea
Stack of operands	O(n)	O(n)	Operators pop two operands — the SECOND pop is the left operand.

Walkthrough of the optimal approach (try it yourself first)

Push numbers. On an operator, pop b first, then a, and push a op b — getting this order wrong breaks - and /. The final value is the only item left on the stack.

Python's // floors (-7 // 2 == -4), so use int(a / b) when truncation is required.

Complexity: O(n) time, O(n) space. Each token is processed once with O(1) stack work; the stack can hold up to n/2 operands.

Reveal the reference solution

def eval_postfix(expression):
    stack = []
    for token in expression.split():
        if token in ("+", "-", "*", "/"):
            b = stack.pop()
            a = stack.pop()
            if token == "+":
                stack.append(a + b)
            elif token == "-":
                stack.append(a - b)
            elif token == "*":
                stack.append(a * b)
            else:
                stack.append(int(a / b))
        else:
            stack.append(int(token))
    return stack[-1]

Follow-ups interviewers ask

Convert infix to postfix (shunting-yard).
Validate malformed input.

Frequently asked interview questions

Core interview concepts, complexities, and follow-ups scored by hiring teams.

What is the time complexity of Evaluate a Postfix (RPN) Expression in Python?

The optimal solution runs in O(n) time and O(n) auxiliary space. Each token is processed once with O(1) stack work; the stack can hold up to n/2 operands.

What follow-up questions do interviewers ask about Evaluate a Postfix (RPN) Expression?

Convert infix to postfix (shunting-yard). Validate malformed input.