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Microsoft·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
Jun 2026

Summary

Microsoft SWE interview with a classic bit manipulation problem. Nothing too wild, but the Gray code question had a slick trick behind it that I almost missed entirely.

Questions Asked (1)

Q1

Given an integer n, return any valid n-bit Gray code sequence, where every adjacent pair of integers in the sequence differs by exactly one bit in binary, including the first and last elements.

Algorithms & Data Structures
Author's notes

I knew what a Gray code was vaguely but couldn't remember the formula under pressure.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem and edge cases, then explain the recursive construction of Gray code: G(n) = 0 + G(n-1) followed by 1 + reverse(G(n-1)). Discuss the formula i ^ (i >> 1) as an alternative, and analyze time and space complexity.

Pro tip: Mention that Gray codes are used in error correction and rotary encoders, and that the reflected binary code construction ensures the cyclic property. This shows practical awareness beyond the algorithm.

1. Clarify the problem

Confirm that the sequence must be cyclic (first and last differ by one bit) and that any valid sequence is acceptable. Discuss edge cases like n=0 or n=1.

2. Explain the recursive construction

Describe how to build the sequence for n bits from the sequence for n-1 bits: prefix 0 to all elements, then prefix 1 to the reversed sequence. This guarantees the Gray code property.

3. Present the iterative formula

Show that the i-th Gray code can be computed directly as i ^ (i >> 1). This is efficient and avoids recursion.

4. Analyze complexity

State that both approaches run in O(2^n) time and O(2^n) space for the output. The formula approach uses O(1) extra space per element.

5. Discuss applications and variations

Mention uses in error correction, position encoders, and combinatorial generation. Optionally, note that the sequence can be generated in different orders.

Key Points to Mention

  • Definition of Gray code: adjacent numbers differ by exactly one bit, including wrap-around.
  • Recursive construction: G(n) = 0 + G(n-1) concatenated with 1 + reverse(G(n-1)).
  • Direct formula: the i-th Gray code is i ^ (i >> 1).
  • Time and space complexity: O(2^n) time and space for output.
  • Applications: error correction, rotary encoders, and minimizing bit transitions.
  • Edge cases: n=0 returns [0], n=1 returns [0,1].

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.