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Apple·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
May 2026

Summary

Apple SWE interview with a classic recursion problem. Pretty straightforward if you know your fundamentals, but they pushed on the iterative angle which I was not fully prepared for.

Questions Asked (1)

Q1

Implement Tower of Hanoi: given three pegs and N disks stacked by size on the source peg, produce the full sequence of moves to transfer all disks to the target peg following the standard rules. Then discuss recursion depth and whether you could do it iteratively.

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

The recursive solution came out fine.

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AI HintsAI Generated

Suggested Approach

Start by clearly stating the recursive solution: move N-1 disks from source to auxiliary, move the largest disk to target, then move N-1 disks from auxiliary to target. Then analyze the recursion depth (O(N)) and discuss iterative approaches, such as using a stack to simulate recursion or the binary counting method, highlighting trade-offs in clarity and performance.

Pro tip: Mention that the iterative solution can be derived from the binary representation of move numbers, which is elegant but less intuitive; showing awareness of both approaches demonstrates depth. Also, note that the recursive solution is optimal in terms of moves (2^N - 1) and that any correct solution must use exactly that many moves.

1. Clarify the problem and constraints

Restate the rules: only one disk moved at a time, no larger disk on smaller, all disks start on source and must end on target. Confirm N is given and output should be a sequence of moves.

2. Present the recursive solution

Explain the base case (N=1: move disk directly) and recursive case (move N-1 to auxiliary, move largest to target, move N-1 from auxiliary to target). Provide pseudocode or actual code.

3. Analyze recursion depth and complexity

State that recursion depth is O(N) and total moves are 2^N - 1, which is optimal. Discuss potential stack overflow for large N and tail recursion possibilities (none here).

4. Discuss iterative approaches

Describe two common iterative methods: (1) simulate recursion with an explicit stack, (2) use the binary counting method where the disk moved at step k is the position of the least significant 1-bit in k. Compare trade-offs: iterative avoids recursion overhead but is less readable.

5. Conclude with trade-offs and practical considerations

Summarize when to use recursion (clarity, small N) vs iteration (large N, memory constraints). Mention that the problem is a classic example of recursion and has no closed-form move sequence without recursion or iteration.

Key Points to Mention

  • Recursive solution: move N-1 to auxiliary, move largest, move N-1 to target.
  • Time complexity: O(2^N) moves, which is optimal; space complexity: O(N) recursion depth.
  • Iterative simulation using an explicit stack to avoid recursion depth limits.
  • Binary counting method: disk moved at step k is the position of the least significant 1-bit in k.
  • Trade-offs: recursion is simpler and more readable; iteration avoids stack overflow and may be faster for large N.
  • Edge cases: N=0 (no moves), N=1 (one move), and ensuring moves are valid.

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