Web Reference: Given an array of strings nums containing n unique binary strings each of length n, return a binary string of length n that does not appear in nums. If there are multiple answers, you may return any of them. Since we only have n strings in the array, by the Pigeonhole Principle, there must be at least one count value that doesn't appear among the strings in nums. The solution finds such a count and constructs a binary string with that many '1's. Since there are 2^n possible strings but only n strings in the input, at least one must be missing. We can systematically try building strings character by character, checking at each complete string whether it exists in the set. Store all input strings in a hash set for O (1) lookup. Use backtracking starting with a string of all zeros.
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