Longest Balanced Binary Substring After at Most One Swap

# Longest Balanced Binary Substring After at Most One Swap You are given a binary string `s`. You may swap the characters at any two positions at most once, then choose one contiguous substring of the resulting string. A substring is balanced when it contains equally many `'0'` and `'1'` characters, in any order. Return the greatest possible length of a balanced substring. The swapped positions need not be adjacent, and either position may lie outside the substring you eventually select. You may also perform no swap. Return `0` when only the empty substring is balanced. ### Function `int longestBalanced(string s)` ### Example 1 **Input:** `s = "1100000001"` **Output:** `6` **Explanation:** Swap the characters at zero-based positions `3` and `9` to obtain `"1101000000"`. Its first six characters, `"110100"`, contain three zeros and three ones. No balanced substring can be longer because the whole string has only three ones, and a swap preserves that total. ### Example 2 **Input:** `s = "0011111100"` **Output:** `6` **Explanation:** Swap positions `2` and `8` to obtain `"0001111110"`, whose first six characters form the balanced substring `"000111"`. Each of the three length-eight windows originally contains six ones and two zeros, so one swap cannot balance it. The full length-ten string also cannot become balanced because its total counts are unequal. ### Constraints - `1 <= s.length <= 100000` - Every character of `s` is either `'0'` or `'1'`. ### Clarifications - The selected characters must be contiguous; this is not a subsequence problem. - Balanced refers only to the counts, not to a required arrangement of zeros and ones. - A swap exchanges existing characters and cannot change the string's total counts. ### What a Strong Answer Covers - Considering swaps that bring a character into the selected substring from outside it. - Handling no-swap choices and strings containing only one character value. - Returning the maximum feasible contiguous length for the full input size.