Spent the first few minutes just drawing it out on the whiteboard because I wasn't sure I understood the jump constraint correctly.
Model the problem as a dynamic programming or greedy problem where each token's movement is independent except for potential collisions. Since tokens only move right and jump exactly 3 cells, their paths are determined by their starting positions modulo 3. Analyze whether the order of moving tokens can affect coin collection, considering that tokens might block each other or compete for coins.
Pro tip: Clarify with the interviewer whether tokens can occupy the same cell or if they block each other; this assumption drastically changes the solution. Also, mention that if tokens are independent, the order doesn't matter, but if they interact, a greedy approach might fail and DP or matching may be needed.
Ask about token interactions: can they occupy the same cell? Do they block each other? Are coins removed after collection? This determines if the problem is independent or coupled.
Each token moves in steps of 3, so its reachable cells are its start plus multiples of 3. Thus, tokens on different residue classes modulo 3 never interact.
If tokens do not block each other, each token's optimal path is independent, and order doesn't matter. If they block, order may matter; consider if moving one token first can free up coins for others.
For independent tokens, sum the maximum coins each can collect (e.g., using DP per residue class). For interacting tokens, model as a scheduling or matching problem, possibly using DP over positions.
Compare greedy vs DP approaches, and explain time/space complexity. Mention that if tokens are independent, the problem is linear; otherwise, it may be more complex.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.