My first instinct was greedy and it was wrong.
Model the problem as a dynamic programming problem where each token's movement is independent but constrained by the positions of other tokens. Define a state that captures the positions of tokens and the coins collected, then use DP to maximize coins. Alternatively, recognize that tokens moving right by 3 can be treated as a matching problem on a graph where edges represent valid moves that collect coins.
Pro tip: Clarify the constraints first (e.g., number of tokens, board size) and discuss trade-offs between greedy and DP approaches. Mention that a greedy approach might fail due to blocking, so DP is safer.
Restate the problem in your own words, identify inputs (string with '.', 'T', 'C') and outputs (max coins). Ask clarifying questions about constraints and whether tokens can move multiple times.
For DP, define state as the positions of tokens and the index of the token being considered. Since tokens move right by 3, process tokens from right to left to avoid interference. Recurrence: dp[i][pos] = max coins from token i onward given token i is at pos.
Ensure moves are valid: target cell must be empty or contain a coin, and not occupied by another token. If target has a coin, add 1 to the coin count and remove the coin from the board for subsequent tokens.
Discuss time and space complexity. If the number of tokens is small, DP over subsets may work. Otherwise, consider greedy with priority or bipartite matching. Mention that the problem can be reduced to maximum matching if each token can collect at most one coin.
Walk through a simple example, e.g., 'T.C..' or 'T.C.T.C'. Test edge cases: no coins, tokens blocking each other, multiple coins in a row.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.