Reach Binary Patterns by Sorting Subsequences

# Reach Binary Patterns by Sorting Subsequences You are given a binary string `s` and an array of strings `strs`, each of the same length as `s`. Every target pattern contains only `'0'`, `'1'` and `'?'`; replace each `'?'` independently with either binary digit. You may transform `s` by repeating this operation any number of times, including zero: 1. Choose a subsequence of positions in the current string. 2. Sort the characters at those positions in nondecreasing order, with `'0'` before `'1'`. 3. Put the sorted characters back at the chosen positions in their original positional order. Other positions stay unchanged. Return a boolean array in target order. Its entry is `true` exactly when some completion of that target pattern can be reached from `s`. ### Function `vector<bool> transformStr(string s, vector<string>& strs)` ### Example 1 **Input:** `s = "0101", strs = ["?1?1", "10??", "0??1", "????"]` **Output:** `[true, false, true, true]` **Explanation:** - Complete `"?1?1"` as `"0101"` and use no operations. - Every completion of `"10??"` starts with `1`. The original leading `0` cannot become `1` through the allowed sorting operations. - Complete `"0??1"` as `"0011"`. Sorting the subsequence at indices `[1, 2]`, which contains `"10"`, produces `"01"` and reaches it. - Complete `"????"` as `"0011"` and use the same operation. ### Example 2 **Input:** `s = "000", strs = ["0?0", "?1?", "???"]` **Output:** `[true, false, true]` **Explanation:** Complete the first and third targets as `"000"`. The second target has a fixed `1`, but sorting subsequences cannot introduce a `1` when none exists. ### Constraints - `1 <= n == s.length <= 2000` - Every character of `s` is `'0'` or `'1'`. - `1 <= strs.length <= 2000` - Every string in `strs` has length `n` and contains only `'0'`, `'1'` and `'?'`. ### Clarifications - A subsequence need not be contiguous; its chosen positions keep their order. - Each target is checked independently, starting from the original `s`. - Sorting preserves the total number of zeros and ones. - Only existence is requested; do not return completed patterns or operation sequences. ### What a Strong Answer Covers - Respecting the direction in which binary values can move under sorting. - Assigning wildcards without changing the required total number of each digit. - Checking every target independently at the full combined input size.