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Sybill·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
Jun 2026

Summary

Interviewed for a software engineer role at Sybill and got hit with a classic shuffle problem. Seemed straightforward but the follow-up on uniformity and complexity analysis is where it gets interesting.

Questions Asked (1)

Q1

Write an in-place shuffle function in JavaScript that produces a uniformly random permutation of an array. It should run in O(n) time with O(1) extra space, handle edge cases like empty or single-element arrays, and you should be able to justify why it's unbiased.

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

I knew Fisher-Yates going in so the code itself came out fine.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the requirements and edge cases, then implement the Fisher-Yates (Knuth) shuffle iterating from the last element down to the second, swapping each with a randomly chosen index in [0, i]. Explain why this yields a uniform permutation by showing each element has an equal probability of landing in each position, and analyze time and space complexity.

Pro tip: Mention that using Math.random() is acceptable for most interviews but note its limitations (e.g., not cryptographically secure) and that for production code you might use crypto.getRandomValues for better randomness. Also, emphasize that the shuffle is in-place and modifies the input array, which is often expected but worth confirming.

1. Clarify requirements and edge cases

Confirm that the function should shuffle in-place, return the array (or undefined), and handle empty or single-element arrays gracefully. Ask if the input can be mutated or if a copy is needed.

2. Choose the algorithm

Select Fisher-Yates (Knuth) shuffle for O(n) time and O(1) space. Explain that iterating from the end and swapping with a random index in [0, i] ensures each permutation is equally likely.

3. Implement the function

Write clean JavaScript code: loop i from arr.length - 1 down to 1, generate j = Math.floor(Math.random() * (i + 1)), and swap arr[i] and arr[j]. Include a guard for arrays with length <= 1.

4. Prove unbiasedness

Explain that for each i, the probability of any remaining element being placed at position i is 1/(i+1). By induction, each of the n! permutations has probability 1/n!, so the shuffle is uniform.

5. Analyze complexity and test

State O(n) time and O(1) extra space. Walk through a small example (e.g., [1,2,3]) to verify correctness, and mention testing with edge cases like empty array and single element.

Key Points to Mention

  • Fisher-Yates (Knuth) shuffle algorithm and why it's unbiased
  • Time complexity O(n) and space complexity O(1)
  • Handling edge cases: empty array, single-element array
  • In-place modification vs returning a new array
  • Use of Math.random() and its limitations (e.g., not cryptographically secure)
  • Proof of uniformity: each element has equal probability of ending in any position

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