Apple·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

May 2026

Summary

Apple SWE interview with a classic recursion problem that feels deceptively simple until you have to explain the complexity out loud. Pretty standard technical screen vibe.

Questions Asked (1)

Given n disks stacked on peg A by size (largest at bottom), write a program to move all disks to peg C using peg B as auxiliary, moving one disk at a time and never placing a larger disk on a smaller one. Define your move format and analyze the time complexity.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I knew it was Tower of Hanoi the second they said 'disks and pegs' so that part was fine.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem and defining the move format, then explain the recursive solution: move n-1 disks from A to B, move the largest disk from A to C, and finally move n-1 disks from B to C. After presenting the code, analyze the time complexity by deriving the recurrence T(n) = 2T(n-1) + 1, which solves to O(2^n).

Pro tip: Mention that the minimum number of moves is 2^n - 1 and that this is optimal; also note that while the recursive solution is elegant, an iterative solution exists using a stack, which can avoid recursion depth issues for large n.

1. Clarify the problem and define move format

Restate the rules: move one disk at a time, never place a larger disk on a smaller one. Define the move format, e.g., 'Move disk X from peg A to peg C' or a tuple (disk, from, to).

2. Explain the recursive strategy

Describe the three-step recursive process: move n-1 disks from source to auxiliary, move the largest disk from source to destination, then move n-1 disks from auxiliary to destination.

3. Write the code

Implement the recursive function in a language of your choice, ensuring the base case (n=1) moves the single disk directly. Use clear parameter names like source, auxiliary, destination.

4. Analyze time complexity

Derive the recurrence T(n) = 2T(n-1) + 1 with T(1)=1, and solve it to get T(n) = 2^n - 1, which is O(2^n). Mention that this is optimal because each move is necessary.

5. Discuss space complexity and trade-offs

Note that the recursion depth is O(n) due to the call stack. Mention that an iterative solution using a stack can avoid recursion limits, but the recursive solution is simpler and more readable.

Key Points to Mention

The recursive solution is based on dividing the problem into smaller subproblems.
The minimum number of moves required is exactly 2^n - 1.
Time complexity is O(2^n), which is exponential and optimal for this problem.
Space complexity is O(n) due to the recursion call stack.
The move format should be clearly defined, e.g., 'Move disk from A to C'.
An iterative solution using a stack is possible and can be more efficient for large n in terms of avoiding stack overflow.

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