Greedy problem but I spent way too long second-guessing myself on what 'overhead at a position' actually meant before it clicked.
First, clarify the definition of 'overhead' and the exact cost function, as the problem statement is ambiguous. Then, propose a dynamic programming solution that processes the string left-to-right, maintaining the minimal cost for each possible last character. Finally, discuss time and space complexity and potential optimizations.
Pro tip: Always ask clarifying questions about ambiguous terms like 'overhead' before diving into a solution; it shows you prioritize correctness over speed. Also, mention that you'd test with edge cases like all '?' or alternating patterns.
Ask the interviewer to define 'overhead' and the cost function. For example, is it the number of adjacent differing bits, or something else? Confirm input constraints and expected output.
Once clarified, formalize the cost. For instance, if overhead is the count of adjacent differing bits, then cost = sum over i of (s[i] != s[i-1]).
Use DP where dp[i][c] = minimal cost for prefix up to i ending with character c. Transition: dp[i][c] = min over prev of dp[i-1][prev] + cost(prev, c), respecting fixed characters.
Implement the DP with O(n) time and O(1) space by keeping only the previous state. Handle '?' by trying both 0 and 1.
Walk through examples, including edge cases. State time and space complexity, and mention possible greedy alternatives if applicable.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.