I recognized it as a DP problem pretty quickly but fumbled the state definition for a while.
Model the problem as a shortest path on a state graph where each state is the current position on the ring and the index of the next character to match. Use dynamic programming to compute the minimum steps to reach each state, considering both clockwise and counter-clockwise moves. Optimize by precomputing distances between positions for each character or using BFS with memoization.
Pro tip: Clarify whether the ring positions are 0-indexed and if the target string can be empty; also discuss trade-offs between precomputing distances and on-the-fly calculation, showing awareness of time-space complexity.
Confirm input format, indexing, and edge cases (e.g., empty target, characters not in ring). Ask if multiple optimal paths exist and if any tie-breaking is needed.
State: (current position, index in target). Transition: from state (i, j), move to any position k where ring[k] == target[j], with cost = min(clockwise distance, counter-clockwise distance) from i to k.
Use dynamic programming (e.g., dp[j][i] = min steps to match first j characters ending at position i) or BFS on the state graph. Precompute distances between all pairs or for each character.
Discuss time and space complexity. Optimize by grouping positions by character and using sliding window or precomputed distance matrices. Consider if O(N*M) is acceptable.
Walk through a small example (e.g., ring='abc', target='ac') to verify logic. Consider edge cases like repeated characters or target longer than ring.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.