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Apple·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
May 2026

Summary

Apple backend engineer interview, got the classic coin change problem. Nothing too surprising but it's one of those problems where you think you know it and then you second-guess yourself halfway through the implementation.

Questions Asked (1)

Q1

Given a list of coin denominations and a target amount, find the minimum number of coins needed to make up that amount.

Algorithms & Data Structures
Author's notes

Knew it was dynamic programming pretty fast, but I fumbled the base case setup and had to backtrack.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem constraints (e.g., unlimited coins, positive denominations, possibility of no solution). Then explain that this is a classic dynamic programming problem where you build up the minimum coins for each amount from 0 to target. Finally, discuss the time and space complexity and potential optimizations.

Pro tip: Mention that while greedy works for some coin systems (like US coins), it fails for arbitrary denominations, so DP is the safe general solution. Also, note that you can optimize space to O(target) by using a 1D array.

1. Clarify the problem

Ask about constraints: unlimited coins? positive denominations? return -1 if impossible? This shows attention to detail.

2. Choose the algorithm

Explain that dynamic programming is ideal because it avoids recomputing subproblems and handles arbitrary denominations.

3. Define the DP state and recurrence

Let dp[i] be the minimum coins to make amount i. Initialize dp[0]=0 and dp[i]=infinity for i>0. For each coin c, update dp[i] = min(dp[i], dp[i-c]+1) for i from c to target.

4. Analyze complexity and edge cases

Time O(target * number of coins), space O(target). Handle cases like target=0, no solution, and large target.

5. Discuss optimizations or alternatives

Mention BFS for unweighted graph interpretation, or if denominations are canonical, greedy might work but DP is safer.

Key Points to Mention

  • Dynamic programming approach with bottom-up tabulation
  • Time complexity O(amount * number of denominations) and space O(amount)
  • Handling of edge cases: amount=0, no solution, negative or zero denominations
  • Why greedy fails for arbitrary denominations (e.g., coins [1,3,4] and target 6)
  • Space optimization to 1D array
  • Possibility of using BFS for the same problem

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