Databricks·Software Engineer·Technical Phone Screen·Senior

SeniorPrefer not to say

Jun 2026Remote

Summary

Databricks software engineer interview with a meaty algorithmic question about game tree search. The whole thing was one deep technical problem and they really wanted you to think through the complexity tradeoffs carefully.

Questions Asked (1)

Given an n×n board game (like Tic-Tac-Toe) with a configurable win condition k, design an algorithm using BFS over game states to determine if the current player can force a win within at most t moves. Cover state representation, successor generation, win/draw detection, avoiding revisited states, pruning heuristics, and analyze worst-case time and space complexity in terms of n, k, t, and branching factor. Also give complexities for the standard 3×3, k=3 case.

Algorithms & Data StructuresSystem DesignTechnical Trade-offs

Author's notes

This was a lot to hold in your head at once.

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AI HintsAI Generated

Suggested Approach

Start by defining the game state representation and the BFS over states with depth limit t, then discuss successor generation, win/draw detection, and visited state tracking. Finally, analyze the worst-case time and space complexity in terms of n, k, t, and branching factor, and apply to the standard 3x3, k=3 case.

Pro tip: Emphasize that BFS is not just for shortest path but for exploring all possible game states up to depth t; also mention that alpha-beta pruning or memoization can drastically reduce the search space in practice.

1. State Representation

Represent the board as a tuple or bitmask of size n^2, with values for empty, player X, and player O. Include the current player to move.

2. Successor Generation

Generate all legal moves for the current player by placing their mark on any empty cell. Each move leads to a new state with the opponent to move.

3. Win/Draw Detection

After each move, check if the move creates a line of k consecutive marks (horizontal, vertical, diagonal). If the board is full and no win, it's a draw.

4. BFS with Depth Limit and Visited Set

Perform BFS from the initial state up to depth t. Use a queue and a visited set to avoid revisiting states. Track depth to enforce the t-move limit.

5. Complexity Analysis

Analyze worst-case time and space in terms of n, k, t, and branching factor b (up to n^2). For 3x3, k=3, compute specific bounds.

Key Points to Mention

State space size: up to 3^(n^2) possible board configurations, but reachable states are fewer.
Branching factor: at most n^2 moves per state, decreasing as board fills.
Visited set: use a hash set of state representations to avoid cycles and redundant work.
Depth limit t: BFS explores all states up to depth t, so time complexity O(b^t) in worst case, where b is branching factor.
Pruning heuristics: alpha-beta pruning, symmetry reduction, and move ordering can reduce search space.
For 3x3, k=3: maximum depth is 9, branching factor starts at 9 and decreases; total states < 3^9 = 19683, so BFS is feasible.

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