I spent the first few minutes just re-reading the constraints because I kept second-guessing whether tokens block each other or just the destination cell.
Model the problem as a dynamic programming problem where the state is the position of the token and the set of collected coins. Since tokens move independently and only interact by blocking landings, consider each token separately and use DP to maximize coins collected without conflicts. Alternatively, treat it as a longest path problem in a DAG where nodes are positions and edges represent valid jumps, with weights equal to coins collected on landing.
Pro tip: Clarify the rules first: ask if tokens can jump over each other, if multiple tokens can occupy the same position, and if coins are removed after collection. This shows attention to detail and avoids incorrect assumptions.
Ask clarifying questions about token movement, coin collection, and interactions between tokens to ensure you understand the constraints.
Identify that each token's position and the set of collected coins define the state. Transitions are jumps of exactly 3 positions to the right, landing on empty spots or coins.
Use dynamic programming or graph search (e.g., BFS/DFS with memoization) to explore all valid sequences of moves and maximize coins.
Account for the fact that tokens cannot land on each other, so moves must be coordinated. Consider processing tokens in order or using a DP that tracks occupied positions.
Discuss time and space complexity, and suggest optimizations like greedy choices if applicable, or pruning in the search.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.