Took me a while to even parse what the operation was doing.
First, clarify that the problem is equivalent to finding the minimum number of moves to remove all characters, where each move removes a contiguous block of identical characters. Then, propose a dynamic programming solution that considers the optimal strategy of either removing a block entirely or merging it with a matching character later to reduce total moves.
Pro tip: Demonstrate awareness of the problem's similarity to 'Strange Printer' and 'Remove Boxes', and mention that while a greedy approach might seem intuitive, it fails for cases like 'aba' where merging non-adjacent identical characters is beneficial.
Restate the problem in your own words and confirm with the interviewer that each operation removes a contiguous group of identical characters, and the goal is to minimize the number of such operations.
Recognize that the problem exhibits optimal substructure: the minimum deletions for a substring can be computed from smaller substrings. This suggests a dynamic programming approach.
Define dp[i][j] as the minimum deletions to remove substring s[i..j]. The base case is dp[i][i] = 1. For the recurrence, consider removing s[i] separately (1 + dp[i+1][j]) or merging it with a matching character s[k] (i < k <= j) to reduce operations: dp[i][j] = min(dp[i][j], dp[i+1][k-1] + dp[k][j]).
The DP has O(n^2) states and O(n) transition per state, leading to O(n^3) time and O(n^2) space. Mention that this is acceptable for typical constraints (n <= 100) and discuss potential optimizations if needed.
Walk through a few examples like 'aba' (answer 2) and 'abc' (answer 3) to validate the recurrence and ensure the logic handles merging correctly.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.