LeetCode 150: Evaluate Reverse Polish Notation — Python Solution

Solve LeetCode 150: Evaluate Reverse Polish Notation in Python with a operand stack approach. The key is to make the state invariant explicit, so the implementation and complexity follow naturally.

This guide paraphrases the task and does not reproduce LeetCode’s prompt. Use the official page for the complete statement, examples, constraints, and submission runner.

What the problem is testing

Push numbers and, for each operator, pop the right operand then the left operand, apply the operation, and push the result.

Algorithm

1. Push numbers and, for each operator, pop the right operand then the left operand, apply the operation, and push the result.
2. Maintain this invariant: The stack contains the evaluated values of complete subexpressions in the processed token prefix.
3. Continue until every input item or reachable state has been resolved, then return the accumulated result.

Python solution

from collections import Counter, defaultdict, deque, OrderedDict
import random

class Solution:
    def evalRPN(self, tokens):
        stack = []
        for token in tokens:
            if token not in {"+", "-", "*", "/"}:
                stack.append(int(token))
                continue
            right, left = stack.pop(), stack.pop()
            if token == "+": stack.append(left + right)
            elif token == "-": stack.append(left - right)
            elif token == "*": stack.append(left * right)
            else: stack.append(int(left / right))
        return stack[-1]

Why this is correct

The proof follows the maintained state: The stack contains the evaluated values of complete subexpressions in the processed token prefix. Each iteration preserves that claim while permanently resolving at least one position, node, interval, or search state. When the loop or recursion ends, every candidate required by the problem has therefore been included or ruled out, so the returned value is correct.

Complexity

O(n) time and O(n) space. The stated auxiliary space excludes the returned output unless the output is the data structure being built.

Edge cases

Division truncates toward zero and operand order matters for subtraction and division.

Tested reference code

This implementation is included in the site’s downloadable 100-solution Python library. The complete suite compiles every solution and runs a behavioral assertion for every problem before publication.

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