I knew it was a DP or stack problem the second I read it, but the efficiency rating layer threw me off.
Clarify the problem by restating it and asking about constraints (e.g., string length, efficiency values, multiple types). Then propose a dynamic programming solution that tracks the maximum efficiency for each valid parentheses sequence, explaining how to handle multiple types and optimize for efficiency. Finally, discuss time and space complexity and potential optimizations.
Pro tip: Demonstrate Amazon's Leadership Principles by discussing trade-offs between different approaches (e.g., DP vs. greedy) and emphasizing customer obsession through clarifying ambiguous requirements before coding.
Ask questions to understand the input format, constraints, and what defines a valid sequence. Confirm whether the string contains only parentheses characters and if efficiency ratings are positive/negative.
Define a DP state that captures the maximum efficiency for a substring or prefix, considering the balance of parentheses and the types. For example, dp[i][j] could represent the max efficiency for substring i..j if it's valid.
For each possible split point, combine valid subsequences if they form a valid sequence. Also consider matching a pair of parentheses at the ends and adding its efficiency to the inner substring's efficiency.
Ensure the DP accounts for different types of parentheses (e.g., (), [], {}) by checking matching types when pairing. This may require additional state or careful transition conditions.
Discuss time and space complexity (likely O(n^3) for naive DP). Propose optimizations such as using a stack or reducing state space, and mention trade-offs between simplicity and efficiency.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.