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If we maintain DP(i, x) where i denotes the length and x denotes the last written integer (0 or 1), then it is not hard to solve in O(maxLength * max(zeroGroup, oneGroup)).
Notice that from DP(i, 0) we only have a transition to DP(j, 1) where (j - i) mod oneGroup == 0 and j > i. Similarly with DP(i,1). So we can use prefix sum to optimize our DP and solve it in O(maxLength).
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Problems like #2533 Number of Good Binary Strings appear in coding interviews because they test dynamic programming, counting techniques, and modular arithmetic. Variants of this pattern are commonly seen in FAANG-style interviews.
A one-dimensional dynamic programming array is typically used. It stores the number of ways to build binary strings of each length, enabling efficient accumulation of results while avoiding recomputation.
Yes, this problem is a classic dynamic programming counting problem. Each valid string length depends on smaller lengths, making it ideal for a bottom-up DP approach.
The optimal approach uses dynamic programming to count the number of valid strings by length. Instead of generating all binary strings, a DP array tracks how many ways each length can be formed using allowed blocks of zeros and ones.