Leetcode #89: Gray Code

In this guide, we solve Leetcode #89 Gray Code 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

An n-bit gray code sequence is a sequence of 2n integers where: Every integer is in the inclusive range [0, 2n - 1], The first integer is 0, An integer appears no more than once in the sequence, The binary representation of every pair of adjacent integers differs by exactly one bit, and The binary representation of the first and last integers differs by exactly one bit. Given an integer n, return any valid n-bit gray code sequence.

Quick Facts

• Difficulty: Medium
• Premium: No
• Tags: Bit Manipulation, Math, Backtracking

Intuition

We must explore combinations of choices, but many branches can be pruned early.

Backtracking enumerates valid candidates while keeping the search space under control.

Approach

Use DFS to build candidates step by step, and backtrack when constraints are violated.

Pruning keeps the exploration practical for typical constraints.

Steps:

• Define the decision tree.
• DFS through choices and backtrack.
• Prune invalid paths early.

Example

Python Solution

Complexity

The time complexity is $O(2^n)$, where $n$ is the integer given in the problem. 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.