How do you evaluate RPN?

Scan the tokens left to right. Push numbers; on an operator pop two operands, apply it, and push the result. The single value left at the end is the answer.

Why does the order of the popped operands matter?

The first value popped is the right operand and the second is the left. For subtraction and division, a - b and b - a differ, so swapping them gives wrong answers.

How should division be handled?

Problems like this usually specify truncation toward zero. Python's // floors, so use int(a / b) to match, especially for negative results.

What is the time and space complexity?

O(n) time with one pass over n tokens, and O(n) space for the stack in the worst case.

Why does postfix need no parentheses?

The position of each operator already fixes which operands it applies to. The order of evaluation is encoded in the order of the tokens.

How would you convert infix to postfix?

Use the shunting-yard algorithm: an operator stack plus precedence rules, outputting operands immediately and popping higher-precedence operators first.

Evaluate reverse Polish notation

Interview QuestionsBy Ashish JangraUpdated 25 October 2026

Push numbers; on an operator, pop two and push the result. Two details decide whether it is correct: the first value popped is the right-hand operand, which only matters for - and /; and the division truncates toward zero, which is int(a / b) and not a // b.

Stacks & queuesCoding problemMedium

Step through it

Speed

What to watch

Numbers accumulate; an operator is the only thing that shrinks the stack.
13 / 5 becomes 2, not 2.6 — integer division, truncated.
Exactly one value remains, and that is the result.

Say this out loud

"A stack. Numbers get pushed; an operator pops two operands, applies itself and pushes the result. The order matters - the first pop is the right operand - and for division I use int(a / b) rather than //, because Python floors and postfix expects truncation toward zero. At the end the stack holds exactly one value."

def evaluate(tokens): stack = [] for t in tokens: if t not in ("+", "-", "*", "/"): stack.append(int(t)) continue b = stack.pop() # FIRST pop is the right operand a = stack.pop() if t == "+": stack.append(a + b) elif t == "-": stack.append(a - b) elif t == "*": stack.append(a * b) else: stack.append(int(a / b)) # truncate toward zero if len(stack) != 1: raise ValueError("malformed: %d values left" % len(stack)) return stack[0] def evaluate_swapped(tokens): stack = [] for t in tokens: if t not in ("+", "-", "*", "/"): stack.append(int(t)); continue a = stack.pop(); b = stack.pop() # swapped on purpose stack.append({"+": a + b, "-": a - b, "*": a * b, "/": int(a / b)}[t]) return stack[0] print("3 4 - correct:", evaluate(["3","4","-"]), " swapped:", evaluate_swapped(["3","4","-"])) print("3 4 + correct:", evaluate(["3","4","+"]), " swapped:", evaluate_swapped(["3","4","+"]), " <- agrees, so + hides it") print("8 2 / correct:", evaluate(["8","2","/"]), " swapped:", evaluate_swapped(["8","2","/"]))

def evaluate(tokens): stack = [] for t in tokens: if t not in ("+", "-", "*", "/"): stack.append(int(t)) continue b = stack.pop() # FIRST pop is the right operand a = stack.pop() if t == "+": stack.append(a + b) elif t == "-": stack.append(a - b) elif t == "*": stack.append(a * b) else: stack.append(int(a / b)) # truncate toward zero if len(stack) != 1: raise ValueError("malformed: %d values left" % len(stack)) return stack[0] print("the division trap:") for a, b in ((-7, 2), (7, -2), (7, 2)): print(f" {a:>3} / {b:<3} a // b = {a // b:>3} int(a / b) = {int(a / b):>3}") print("only the negative cases differ, which is why this bug ships") print() for bad in (["1", "+"], ["1", "2", "3", "+"]): try: evaluate(bad) except (IndexError, ValueError) as e: print(f" {bad} -> {type(e).__name__}: {e}")

About the author

Ashish Jangra builds and maintains VizLearn. Every module here is written and the visualisation behind it hand-built, so the numbers in a readout come from the same code that draws the picture. Corrections are genuinely welcome and get priority over everything else — if a page states something wrong, or an animation misrepresents what the algorithm does, get in touch.

Evaluate reverse Polish notation

Step through it

What to watch

Say this out loud

Overview

Run it

Why postfix needs no parentheses

The two lines that are wrong in most first attempts

What the stack depth tells you

The follow-up: converting from infix

Edge cases to raise

Sources and next steps

How the code works

How the code works

Change one thing

Where this runs

Check yourself