You are given a binary string s of length n, where:
'1' represents an active section.'0' represents an inactive section.You can perform at most one trade to maximize the number of active sections in s. In a trade, you:
'1's that is surrounded by '0's to all '0's.'0's that is surrounded by '1's to all '1's.Additionally, you are given a 2D array queries, where queries[i] = [li, ri] represents a substring s[li...ri].
For each query, determine the maximum possible number of active sections in s after making the optimal trade on the substring s[li...ri].
Return an array answer, where answer[i] is the result for queries[i].
Note
\n\ns[li...ri] as if it is augmented with a '1' at both ends, forming t = '1' + s[li...ri] + '1'. The augmented '1's do not contribute to the final count.\n
Example 1:
\n\nInput: s = "01", queries = [[0,1]]
\n\nOutput: [1]
\n\nExplanation:
\n\nBecause there is no block of '1's surrounded by '0's, no valid trade is possible. The maximum number of active sections is 1.
Example 2:
\n\nInput: s = "0100", queries = [[0,3],[0,2],[1,3],[2,3]]
\n\nOutput: [4,3,1,1]
\n\nExplanation:
\n\nQuery [0, 3] → Substring "0100" → Augmented to "101001"
\n\tChoose "0100", convert "0100" → "0000" → "1111".
\n\tThe final string without augmentation is "1111". The maximum number of active sections is 4.
Query [0, 2] → Substring "010" → Augmented to "10101"
\n\tChoose "010", convert "010" → "000" → "111".
\n\tThe final string without augmentation is "1110". The maximum number of active sections is 3.
Query [1, 3] → Substring "100" → Augmented to "11001"
\n\tBecause there is no block of '1's surrounded by '0's, no valid trade is possible. The maximum number of active sections is 1.
Query [2, 3] → Substring "00" → Augmented to "1001"
\n\tBecause there is no block of '1's surrounded by '0's, no valid trade is possible. The maximum number of active sections is 1.
Example 3:
\n\nInput: s = "1000100", queries = [[1,5],[0,6],[0,4]]
\n\nOutput: [6,7,2]
\n\nExplanation:
\n\nQuery [1, 5] → Substring "00010" → Augmented to "1000101"
\n\tChoose "00010", convert "00010" → "00000" → "11111".
\n\tThe final string without augmentation is "1111110". The maximum number of active sections is 6.
Query [0, 6] → Substring "1000100" → Augmented to "110001001"
\n\tChoose "000100", convert "000100" → "000000" → "111111".
\n\tThe final string without augmentation is "1111111". The maximum number of active sections is 7.
Query [0, 4] → Substring "10001" → Augmented to "1100011"
\n\tBecause there is no block of '1's surrounded by '0's, no valid trade is possible. The maximum number of active sections is 2.
Example 4:
\n\nInput: s = "01010", queries = [[0,3],[1,4],[1,3]]
\n\nOutput: [4,4,2]
\n\nExplanation:
\n\nQuery [0, 3] → Substring "0101" → Augmented to "101011"
\n\tChoose "010", convert "010" → "000" → "111".
\n\tThe final string without augmentation is "11110". The maximum number of active sections is 4.
Query [1, 4] → Substring "1010" → Augmented to "110101"
\n\tChoose "010", convert "010" → "000" → "111".
\n\tThe final string without augmentation is "01111". The maximum number of active sections is 4.
Query [1, 3] → Substring "101" → Augmented to "11011"
\n\tBecause there is no block of '1's surrounded by '0's, no valid trade is possible. The maximum number of active sections is 2.
\n
Constraints:
\n\n1 <= n == s.length <= 1051 <= queries.length <= 105s[i] is either '0' or '1'.queries[i] = [li, ri]0 <= li <= ri < n给你一个长度为 n 的二进制字符串 s ，其中：
'1' 表示一个 活跃 区域。'0' 表示一个 非活跃 区域。你最多可以进行一次 操作 来最大化 s 中活跃区间的数量。在一次操作中，你可以：
'0' 包围的连续 '1' 区域转换为全 '0'。'1' 包围的连续 '0' 区域转换为全 '1'。此外，你还有一个 二维数组 queries，其中 queries[i] = [li, ri] 表示子字符串 s[li...ri]。
对于每个查询，确定在对子字符串 s[li...ri] 进行最优交换后，字符串 s 中 可能的最大 活跃区间数。
返回一个数组 answer，其中 answer[i] 是 queries[i] 的结果。
注意
\n\ns[li...ri] 处理时，将其看作是在两端都加上一个 '1' 后的字符串，形成 t = '1' + s[li...ri] + '1'。这些额外的 '1' 不会对最终的活跃区间数有贡献。\n\n
示例 1：
\n\n输入： s = \"01\", queries = [[0,1]]
\n\n输出： [1]
\n\n解释：
\n\n因为没有被 '0' 包围的 '1' 区域，所以没有有效的操作可以进行。最大活跃区间数是 1。
示例 2：
\n\n输入： s = \"0100\", queries = [[0,3],[0,2],[1,3],[2,3]]
\n\n输出： [4,3,1,1]
\n\n解释：
\n\n查询 [0, 3] → 子字符串 \"0100\" → 变为 \"101001\"
\n\t选择 \"0100\"，\"0100\" → \"0000\" → \"1111\"。
\n\t最终字符串（去掉添加的 '1'）为 \"1111\"。最大活跃区间数为 4。
查询 [0, 2] → 子字符串 \"010\" → 变为 \"10101\"
\n\t选择 \"010\"，\"010\" → \"000\" → \"111\"。
\n\t最终字符串（去掉添加的 '1'）为 \"1110\"。最大活跃区间数为 3。
查询 [1, 3] → 子字符串 \"100\" → 变为 \"11001\"
\n\t因为没有被 '0' 包围的 '1' 区域，所以没有有效的操作可以进行。最大活跃区间数为 1。
查询 [2, 3] → 子字符串 \"00\" → 变为 \"1001\"
\n\t因为没有被 '0' 包围的 '1' 区域，所以没有有效的操作可以进行。最大活跃区间数为 1。
示例 3：
\n\n输入： s = \"1000100\", queries = [[1,5],[0,6],[0,4]]
\n\n输出： [6,7,2]
\n\n解释：
\n\n查询 [1, 5] → 子字符串 \"00010\" → 变为 \"1000101\"
\n\t选择 \"00010\"，\"00010\" → \"00000\" → \"11111\"。
\n\t最终字符串（去掉添加的 '1'）为 \"1111110\"。最大活跃区间数为 6。
查询 [0, 6] → 子字符串 \"1000100\" → 变为 \"110001001\"
\n\t选择 \"000100\"，\"000100\" → \"000000\" → \"111111\"。
\n\t最终字符串（去掉添加的 '1'）为 \"1111111\"。最大活跃区间数为 7。
查询 [0, 4] → 子字符串 \"10001\" → 变为 \"1100011\"
\n\t因为没有被 '0' 包围的 '1' 区域，所以没有有效的操作可以进行。最大活跃区间数为 2。
示例 4：
\n\n输入： s = \"01010\", queries = [[0,3],[1,4],[1,3]]
\n\n输出： [4,4,2]
\n\n解释：
\n\n查询 [0, 3] → 子字符串 \"0101\" → 变为 \"101011\"
\n\t选择 \"010\"，\"010\" → \"000\" → \"111\"。
\n\t最终字符串（去掉添加的 '1'）为 \"11110\"。最大活跃区间数为 4。
查询 [1, 4] → 子字符串 \"1010\" → 变为 \"110101\"
\n\t选择 \"010\"，\"010\" → \"000\" → \"111\"。
\n\t最终字符串（去掉添加的 '1'）为 \"01111\"。最大活跃区间数为 4。
查询 [1, 3] → 子字符串 \"101\" → 变为 \"11011\"
\n\t因为没有被 '0' 包围的 '1' 区域，所以没有有效的操作可以进行。最大活跃区间数为 2。
\n\n
提示：
\n\n1 <= n == s.length <= 1051 <= queries.length <= 105s[i] 只有 '0' 或 '1'。queries[i] = [li, ri]0 <= li <= ri < nans[i] = len[i - 1] + len[i + 1], where i is a one-segment.",
"For a zero-segment, define ans[i] = 0.",
"Note that all three segments (i - 1, i, and i + 1) should be fully covered by the substring.",
"Use a segment tree to perform range maximum queries on the answer. The query to the segment tree is not straightforward since we need to ensure the zero-segments are fully covered. Handle the first and last segments separately."
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