The base version of this problem is pretty well known but the cost-minimization twist changed the whole approach.
First, clarify the problem: define 'wonderful' string and the cost model (e.g., cost to change a character). Then, recognize that the condition depends only on the parity of character counts. Use a bitmask to represent the parity of each character (0 for even, 1 for odd) and compute the minimum cost to reach a mask with at most one set bit.
Pro tip: Discuss the trade-off between time and space: the bitmask DP is O(n * 2^26) which is too large, but you can optimize by only considering masks that appear or using meet-in-the-middle. Also, mention that if the alphabet is small (e.g., lowercase English), the approach is feasible.
Ask the interviewer to define 'wonderful' string and the cost function. Confirm if cost is per character change and if the alphabet size is fixed (e.g., 26 lowercase letters).
Represent the parity of each character's count as a bitmask. A wonderful string has a mask with at most one bit set (0 or a power of two).
For each prefix, compute the minimum cost to reach each possible mask. Use dynamic programming where dp[mask] = min cost to achieve that parity mask.
The answer is the minimum cost among all masks with at most one bit set. If the cost is to change characters, consider the cost of flipping bits.
Discuss optimizations like using a hash map for sparse masks, or meet-in-the-middle if alphabet is large. Analyze time and space complexity.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.