My first instinct was greedy, just move whatever token is closest to a coin.
Model the problem as a state-space search where each state is the board configuration, and use dynamic programming or BFS to explore all possible sequences of moves. Since tokens move exactly 3 positions right and cannot overlap, the state space is manageable; compute the maximum coins collected by considering each token's choices and interactions.
Pro tip: Clarify the rules upfront: ask whether tokens can move off the board, whether coins are removed after collection, and whether tokens can move past each other. This shows attention to detail and prevents solving the wrong problem.
Ask clarifying questions about board size, token movement limits, coin collection mechanics, and whether tokens can share positions or move off the board.
Represent the board as a string and define a state as the positions of all tokens and remaining coins. A move consists of advancing one token by 3 positions if the target is empty or contains a coin.
Use dynamic programming with memoization or BFS/DFS with state hashing to explore all reachable states and compute the maximum coins collected.
Consider pruning symmetric states, using bitmasks for token positions, and handling cases where tokens block each other or no moves are possible.
Discuss time and space complexity, and walk through small examples to verify correctness and performance.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.