Google·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Apr 2026

Summary

Google SWE technical phone screen with a board game optimization problem. The question looked deceptively simple at first glance but the constraint interactions made it way harder than expected.

Questions Asked (1)

You have a 1D board where each cell is empty, holds a token, or holds a coin. Each turn you pick one token and move it exactly 3 cells to the right. Landing on a coin collects it (each coin collected at most once), landing on another token is illegal, landing on an empty cell does nothing. You can play as many turns as you want until no token can legally move. What's the maximum number of coins you can collect?

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

Spent the first few minutes just trying to restate the problem back correctly because the three-state cell thing plus the blocking rule felt like a lot to hold at once.

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AI HintsAI Generated

Suggested Approach

First, clarify the problem constraints and edge cases, then model the board as a sequence of tokens and coins. Recognize that tokens moving exactly 3 cells to the right means tokens only interact within the same residue class modulo 3, so the problem decomposes into three independent 1D subproblems. For each residue class, determine the maximum coins collectible by moving tokens rightward without collisions, likely via dynamic programming or greedy matching.

Pro tip: Start by asking clarifying questions about the board size, initial configuration, and whether tokens can move multiple times. This shows you think about constraints before diving into algorithms, and it helps you avoid solving the wrong problem.

1. Clarify the problem

Ask about input format, board size, number of tokens/coins, and whether tokens can move multiple times. Confirm that coins are collected only once and that landing on another token is illegal.

2. Identify independent subproblems

Observe that moving exactly 3 cells right preserves the index modulo 3. Thus, tokens and coins in different residue classes never interact, so solve each residue class independently.

3. Model as a 1D problem

For a fixed residue class, compress the positions into a 1D line where each step is 1 cell. Tokens can move right by 1, collecting coins on empty cells, but cannot land on other tokens.

4. Design an algorithm

Use dynamic programming or greedy matching: process positions left to right, track available tokens, and decide whether to move a token to collect a coin. Consider that moving a token may block others, so optimal substructure applies.

5. Analyze complexity and edge cases

Discuss time and space complexity (likely O(n) per residue class). Test edge cases: no tokens, no coins, tokens blocking each other, coins behind tokens, and multiple tokens competing for the same coin.

Key Points to Mention

Modulo 3 decomposition: tokens only interact within the same residue class modulo 3.
Greedy vs dynamic programming: moving a token to collect a coin might prevent another token from collecting a later coin, so a greedy approach may fail; DP or matching is safer.
State representation: for each residue class, track the rightmost available token or use DP over positions.
Coin collection is at most once: once collected, a coin is removed, so tokens cannot collect the same coin.
Illegal moves: landing on another token is forbidden, which imposes ordering constraints.
Complexity: aim for O(n) or O(n log n) time, where n is board length, by processing each residue class linearly.

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