The 'exactly 3 steps' constraint is the whole puzzle.
Model the problem as a maximum weight matching or dynamic programming problem where each token can move to positions i+3k and collect coins. Use DP to compute the maximum coins for each token independently, then combine using a greedy or DP approach if tokens can overlap. Clarify constraints and edge cases before coding.
Pro tip: Discuss the time and space complexity trade-offs and mention that if tokens are indistinguishable, the problem reduces to selecting disjoint positions; if distinguishable, use DP with bitmask or flow. Also, handle the case where a token cannot move (no valid positions) gracefully.
Ask about board size, number of tokens, whether tokens can occupy the same cell, and if coins are removed after collection. This determines the algorithm's complexity.
Represent each token's possible moves as a directed acyclic graph (positions i, i+3, i+6, ...). The problem becomes finding a maximum weight set of paths or matching.
If tokens don't interfere, compute max coins per token via DP: dp[i] = max coins from position i to end. Then sum over tokens.
If tokens compete for coins, use DP with state (token index, position) or reduce to maximum weight matching in a bipartite graph (tokens vs coin positions).
Discuss time/space complexity and possible optimizations like greedy if coins are sparse or using min-cost max-flow for general case.
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