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Generate Tower of Hanoi moves | Apple Coding Question

Quick Overview

This question evaluates understanding of recursion, algorithmic problem decomposition, and analysis of time complexity when generating constrained move sequences.

medium
Apple
Coding & Algorithms
Software Engineer

Generate Tower of Hanoi moves

Company: Apple

Role: Software Engineer

Category: Coding & Algorithms

Difficulty: medium

Interview Round: Technical Screen

You are given **n** disks of different sizes stacked on peg **A** (largest at bottom). You have two other pegs, **B** and **C**. You may move one disk at a time, and you may never place a larger disk on top of a smaller disk. Write a program that outputs a valid sequence of moves to transfer all disks from **A** to **C**. Define the move format (e.g., "A -> C"). Analyze the time complexity.

Quick Answer: This question evaluates understanding of recursion, algorithmic problem decomposition, and analysis of time complexity when generating constrained move sequences.

You are given n disks of different sizes stacked on peg A, with the largest disk at the bottom and the smallest at the top. You also have two other pegs, B and C. You may move only one disk at a time, and you may never place a larger disk on top of a smaller disk. Write a function that returns the minimum-length valid sequence of moves needed to transfer all disks from peg A to peg C, using peg B as the auxiliary peg. Represent each move as a string in the format "X -> Y", where X is the source peg and Y is the destination peg.

Constraints

0 <= n <= 12
The returned sequence must be a valid minimum-length solution
Peg A starts with all n disks, peg C must contain all n disks at the end

Examples

Input: (0,)

Expected Output: []

Explanation: With no disks, no moves are needed.

Input: (1,)

Expected Output: ['A -> C']

Explanation: A single disk can be moved directly from A to C.

Input: (2,)

Expected Output: ['A -> B', 'A -> C', 'B -> C']

Explanation: Move the smaller disk to B, move the larger disk to C, then move the smaller disk from B to C.

Input: (3,)

Expected Output: ['A -> C', 'A -> B', 'C -> B', 'A -> C', 'B -> A', 'B -> C', 'A -> C']

Explanation: This is the classic minimum sequence of 7 moves for 3 disks.

Hints

To move n disks, first think about what must happen to the top n-1 disks before the largest disk can move.
This problem naturally breaks into smaller subproblems with the same structure.

Last updated: Apr 28, 2026