Leetcode #292: Nim Game

In this guide, we solve Leetcode #292 Nim Game in Python and focus on the core idea that makes the solution efficient.

You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.

Problem Statement

You are playing the following Nim Game with your friend: Initially, there is a heap of stones on the table. You and your friend will alternate taking turns, and you go first.

Quick Facts

• Difficulty: Easy
• Premium: No
• Tags: Brainteaser, Math, Game Theory

Intuition

There is a mathematical invariant or formula that directly leads to the result.

Using math avoids unnecessary loops and reduces complexity.

Approach

Derive the formula or update rule, then compute the answer directly.

Handle edge cases like overflow or zero carefully.

Steps:

• Identify the math relationship.
• Compute the result with a loop or formula.
• Handle edge cases.

Example

Python Solution

Complexity

The time complexity is $O(1)$, and the space complexity is $O(1)$. The space complexity is $O(1)$.

Edge Cases and Pitfalls

Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.

Summary

This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.