How do you solve Gray Code on LeetCode?

Gray Code (LeetCode #89) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Gray code sequences differ by one bit between adjacent numbers.

What is the brute force solution for Gray Code?

The brute force approach for Gray Code is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach generates all possible binary numbers and checks each pair to see if they differ by one bit. This is straightforward but inefficient for larger n. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Gray Code?

Gray Code uses the following concepts: Math, Backtracking, Bit Manipulation. The recommended patterns to study are: Bit Manipulation, Mathematical Sequences.

What are the interview tips for Gray Code?

Understand the properties of Gray codes before diving into code. Practice generating sequences using both brute-force and optimal methods. Be prepared to explain your thought process and the reasoning behind your chosen approach.

What are common mistakes when solving Gray Code?

Not recognizing the mathematical property of Gray codes. Overcomplicating the problem by trying to generate all permutations.

#89

Gray Code

Medium

MathBacktrackingBit ManipulationBit ManipulationMathematical Sequences

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

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Intuition

Time O(n)Space O(n)

The optimal solution uses a mathematical property of Gray codes. Each Gray code can be generated directly using the formula: G(i) = i ^ (i >> 1). This allows us to generate the sequence in linear time.

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Algorithm

3 steps

1Step 1: Initialize an empty list to store the Gray code sequence.
2Step 2: Loop from 0 to 2^n - 1 and apply the formula G(i) = i ^ (i >> 1) to generate each Gray code.
3Step 3: Append each generated Gray code to the result list.

solution.py6 lines

1# Full working Python code
2
3def grayCode(n):
4    return [i ^ (i >> 1) for i in range(2 ** n)]
5
6print(grayCode(2))

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Complexity note: The time complexity is O(n) because we generate 2^n Gray codes directly using a simple formula, and the space complexity is O(n) for storing the results.

1Gray code sequences differ by one bit between adjacent numbers.
2The optimal formula allows for efficient generation without checking pairs.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.