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Count binary strings formed by replacing '?' in a pattern while respecting fixed '0' and '1' characters.
Consecutive '1' segments must exactly match the lengths and order specified in the input array.
Each valid combination must satisfy both the pattern constraints and the sequential run-length requirements.
What This Tests
Dynamic programming with memoization
Multi-index state tracking across two sequences
Combinatorial counting under strict structural constraints
Recursive decomposition with overlapping subproblems
Common Patterns
Dynamic Programming
Backtracking
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