Took me a bit to realize this isn't just a greedy scan.
Clarify the problem constraints and edge cases, then propose a greedy or dynamic programming approach. For each 'T', consider moving it right by 1 to 3 positions, ensuring it doesn't jump over another 'T', and collect any 'C's passed. Use DP to maximize total collected 'C's, or a greedy strategy if optimal.
Pro tip: Discuss the trade-offs between greedy and DP, and mention that a greedy approach might work if you always move the rightmost 'T' first, but verify with counterexamples. Also, consider that moving a 'T' may block others, so order matters.
Restate the problem: Given a string of 'T' and 'C', each 'T' can move right up to 3 positions without jumping over another 'T', collecting 'C's it passes. Goal: maximize total 'C's collected.
Consider cases with no 'T's, no 'C's, adjacent 'T's, and 'T's at the end. Note that moving a 'T' changes the positions of 'C's and may affect other 'T's moves.
Evaluate greedy vs. dynamic programming. Greedy: process 'T's from right to left, moving each as far right as possible without crossing another 'T', collecting 'C's. DP: define state based on positions of 'T's and 'C's, but may be complex due to interactions.
Test the chosen approach on small examples, such as 'TCC', 'TCT', 'TTCC', to see if greedy works or if DP is needed. Look for counterexamples where greedy fails.
If greedy works, it can be O(n) by scanning from right to left. If DP, define states and transitions, aiming for O(n) or O(n^2) time. Discuss potential optimizations.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.