My first instinct was greedy and I think that's mostly right, just match each piece to the nearest coin to its right without overlapping assignments.
Clarify the problem constraints (e.g., board size, number of pieces, coin positions) and define the goal precisely. Then propose a dynamic programming solution that processes cells from left to right, maintaining the maximum coins collectible given the last occupied cell. Discuss time and space complexity and possible optimizations.
Pro tip: Explicitly state your assumptions about the input format and constraints before diving into the solution, as this demonstrates thoroughness and prevents misunderstandings. Also, mention that you would test edge cases like no coins or pieces blocking each other.
Ask questions to understand the board representation, piece movement rules, and constraints (e.g., can pieces move any distance? Are coins only collected when landed on? Can pieces skip over coins?).
Define DP state as the maximum coins collectible up to cell i, considering the last piece placed. Derive a recurrence that either skips the current cell or places a piece to collect a coin if available.
Write pseudocode for the DP, then analyze time and space complexity. Consider optimizations like using a 1D array or greedy approach if applicable.
Walk through a small example to verify correctness, including edge cases such as no coins, multiple pieces, and pieces that cannot move.
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