My first instinct was brute force since the number of '!' could be small, and I think it was actually the right move to mention that O(2^k) baseline before jumping in.
First, clarify the problem and constraints, then propose a dynamic programming solution that processes the string from left to right, tracking the number of 0s and 1s seen so far to compute the cost of subsequences. Optimize by noting that the cost only depends on the counts of 0s and 1s, and use a greedy or DP approach to assign '!' characters. Finally, discuss time and space complexity and potential optimizations.
Pro tip: Demonstrate awareness of the trade-off between time and space complexity by mentioning that the DP can be optimized to O(n) time and O(1) space by keeping only the current counts, and discuss how the solution would scale for very long strings.
Restate the problem in your own words, confirm the definition of '01' and '10' subsequences, and ask about constraints (e.g., string length, cost values).
Recognize that the total cost is determined by the number of '01' and '10' subsequences, which can be computed from the counts of 0s and 1s before each character.
Define a DP state that tracks the number of 0s and 1s seen so far, and for each '!' consider both assignments, updating the cost accordingly. Use memoization or iterative DP to avoid recomputation.
Discuss how to reduce space complexity by observing that only the counts of 0s and 1s matter, and analyze the time complexity (O(n) with constant factors) and space complexity (O(1) if optimized).
Walk through a small example to verify the DP transitions, and consider edge cases such as all '!' or no '!' characters.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.