← Snowflake Interview Insights
Had seen this type before so I wasn't starting from scratch.
Model the game as a state-space search where each state represents the current player's turn and available moves. Use memoization (top-down DP) to avoid recomputing states, and determine if there exists a move that leads to a losing state for the opponent. If all moves lead to winning states for the opponent, the current player cannot guarantee a win.
Pro tip: Clearly define the base cases and state representation upfront; discuss how you would handle large state spaces with bitmasking or other compression techniques. Also, mention that you would test with small examples to verify the recurrence before coding.
Ask questions to understand the exact rules: what moves are allowed, what constitutes a win, and how the state can be represented (e.g., set of available numbers, board configuration). Confirm whether it's a two-player game with perfect information.
Define a function canWin(state) that returns true if the current player can force a win. The current player wins if there exists a move to a state where the opponent cannot win (i.e., canWin(nextState) is false).
Determine when the game ends: if the current player has already won, or if no moves are possible (loss). Also handle draws if applicable. These base cases terminate the recursion.
Use a hash map or array to cache results of canWin for each state. This reduces exponential time to polynomial by avoiding repeated subproblems. Discuss state encoding (e.g., bitmask) for efficiency.
Discuss time and space complexity in terms of number of states and branching factor. Mention edge cases like no moves available, immediate win, or large state space requiring iterative DP or pruning.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.