Maximize Active Section with Trade II
<p>You are given a binary string <code>s</code> of length <code>n</code>, where:</p>

<ul>
	<li><code>&#39;1&#39;</code> represents an <strong>active</strong> section.</li>
	<li><code>&#39;0&#39;</code> represents an <strong>inactive</strong> section.</li>
</ul>

<p>You can perform <strong>at most one trade</strong> to maximize the number of active sections in <code>s</code>. In a trade, you:</p>

<ul>
	<li>Convert a contiguous block of <code>&#39;1&#39;</code>s that is surrounded by <code>&#39;0&#39;</code>s to all <code>&#39;0&#39;</code>s.</li>
	<li>Afterward, convert a contiguous block of <code>&#39;0&#39;</code>s that is surrounded by <code>&#39;1&#39;</code>s to all <code>&#39;1&#39;</code>s.</li>
</ul>

<p>Additionally, you are given a <strong>2D array</strong> <code>queries</code>, where <code>queries[i] = [l<sub>i</sub>, r<sub>i</sub>]</code> represents a <span data-keyword="substring-nonempty">substring</span> <code>s[l<sub>i</sub>...r<sub>i</sub>]</code>.</p>

<p>For each query, determine the <strong>maximum</strong> possible number of active sections in <code>s</code> after making the optimal trade on the substring <code>s[l<sub>i</sub>...r<sub>i</sub>]</code>.</p>

<p>Return an array <code>answer</code>, where <code>answer[i]</code> is the result for <code>queries[i]</code>.</p>

<p><strong>Note</strong></p>

<ul>
	<li>For each query, treat <code>s[l<sub>i</sub>...r<sub>i</sub>]</code> as if it is <strong>augmented</strong> with a <code>&#39;1&#39;</code> at both ends, forming <code>t = &#39;1&#39; + s[l<sub>i</sub>...r<sub>i</sub>] + &#39;1&#39;</code>. The augmented <code>&#39;1&#39;</code>s <strong>do not</strong> contribute to the final count.</li>
	<li>The queries are independent of each other.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">s = &quot;01&quot;, queries = [[0,1]]</span></p>

<p><strong>Output:</strong> <span class="example-io">[1]</span></p>

<p><strong>Explanation:</strong></p>

<p>Because there is no block of <code>&#39;1&#39;</code>s surrounded by <code>&#39;0&#39;</code>s, no valid trade is possible. The maximum number of active sections is 1.</p>
</div>

<p><strong class="example">Example 2:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">s = &quot;0100&quot;, queries = [[0,3],[0,2],[1,3],[2,3]]</span></p>

<p><strong>Output:</strong> <span class="example-io">[4,3,1,1]</span></p>

<p><strong>Explanation:</strong></p>

<ul>
	<li>
	<p>Query <code>[0, 3]</code> &rarr; Substring <code>&quot;0100&quot;</code> &rarr; Augmented to <code>&quot;101001&quot;</code><br />
	Choose <code>&quot;0100&quot;</code>, convert <code>&quot;0100&quot;</code> &rarr; <code>&quot;0000&quot;</code> &rarr; <code>&quot;1111&quot;</code>.<br />
	The final string without augmentation is <code>&quot;1111&quot;</code>. The maximum number of active sections is 4.</p>
	</li>
	<li>
	<p>Query <code>[0, 2]</code> &rarr; Substring <code>&quot;010&quot;</code> &rarr; Augmented to <code>&quot;10101&quot;</code><br />
	Choose <code>&quot;010&quot;</code>, convert <code>&quot;010&quot;</code> &rarr; <code>&quot;000&quot;</code> &rarr; <code>&quot;111&quot;</code>.<br />
	The final string without augmentation is <code>&quot;1110&quot;</code>. The maximum number of active sections is 3.</p>
	</li>
	<li>
	<p>Query <code>[1, 3]</code> &rarr; Substring <code>&quot;100&quot;</code> &rarr; Augmented to <code>&quot;11001&quot;</code><br />
	Because there is no block of <code>&#39;1&#39;</code>s surrounded by <code>&#39;0&#39;</code>s, no valid trade is possible. The maximum number of active sections is 1.</p>
	</li>
	<li>
	<p>Query <code>[2, 3]</code> &rarr; Substring <code>&quot;00&quot;</code> &rarr; Augmented to <code>&quot;1001&quot;</code><br />
	Because there is no block of <code>&#39;1&#39;</code>s surrounded by <code>&#39;0&#39;</code>s, no valid trade is possible. The maximum number of active sections is 1.</p>
	</li>
</ul>
</div>

<p><strong class="example">Example 3:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">s = &quot;1000100&quot;, queries = [[1,5],[0,6],[0,4]]</span></p>

<p><strong>Output:</strong> <span class="example-io">[6,7,2]</span></p>

<p><strong>Explanation:</strong></p>

<ul>
	<li data-end="383" data-start="217">
	<p data-end="383" data-start="219">Query <code>[1, 5]</code> &rarr; Substring <code data-end="255" data-start="246">&quot;00010&quot;</code> &rarr; Augmented to <code data-end="282" data-start="271">&quot;1000101&quot;</code><br data-end="285" data-start="282" />
	Choose <code data-end="303" data-start="294">&quot;00010&quot;</code>, convert <code data-end="322" data-start="313">&quot;00010&quot;</code> &rarr; <code data-end="322" data-start="313">&quot;00000&quot;</code> &rarr; <code data-end="334" data-start="325">&quot;11111&quot;</code>.<br />
	The final string without augmentation is <code data-end="404" data-start="396">&quot;1111110&quot;</code>. The maximum number of active sections is 6.</p>
	</li>
	<li data-end="561" data-start="385">
	<p data-end="561" data-start="387">Query <code>[0, 6]</code> &rarr; Substring <code data-end="425" data-start="414">&quot;1000100&quot;</code> &rarr; Augmented to <code data-end="454" data-start="441">&quot;110001001&quot;</code><br data-end="457" data-start="454" />
	Choose <code data-end="477" data-start="466">&quot;000100&quot;</code>, convert <code data-end="498" data-start="487">&quot;000100&quot;</code> &rarr; <code data-end="498" data-start="487">&quot;000000&quot;</code> &rarr; <code data-end="512" data-start="501">&quot;111111&quot;</code>.<br />
	The final string without augmentation is <code data-end="404" data-start="396">&quot;1111111&quot;</code>. The maximum number of active sections is 7.</p>
	</li>
	<li data-end="741" data-start="563">
	<p data-end="741" data-start="565">Query <code>[0, 4]</code> &rarr; Substring <code data-end="601" data-start="592">&quot;10001&quot;</code> &rarr; Augmented to <code data-end="627" data-start="617">&quot;1100011&quot;</code><br data-end="630" data-start="627" />
	Because there is no block of <code>&#39;1&#39;</code>s surrounded by <code>&#39;0&#39;</code>s, no valid trade is possible. The maximum number of active sections is 2.</p>
	</li>
</ul>
</div>

<p><strong class="example">Example 4:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">s = &quot;01010&quot;, queries = [[0,3],[1,4],[1,3]]</span></p>

<p><strong>Output:</strong> <span class="example-io">[4,4,2]</span></p>

<p><strong>Explanation:</strong></p>

<ul>
	<li>
	<p>Query <code>[0, 3]</code> &rarr; Substring <code>&quot;0101&quot;</code> &rarr; Augmented to <code>&quot;101011&quot;</code><br />
	Choose <code>&quot;010&quot;</code>, convert <code>&quot;010&quot;</code> &rarr; <code>&quot;000&quot;</code> &rarr; <code>&quot;111&quot;</code>.<br />
	The final string without augmentation is <code>&quot;11110&quot;</code>. The maximum number of active sections is 4.</p>
	</li>
	<li>
	<p>Query <code>[1, 4]</code> &rarr; Substring <code>&quot;1010&quot;</code> &rarr; Augmented to <code>&quot;110101&quot;</code><br />
	Choose <code>&quot;010&quot;</code>, convert <code>&quot;010&quot;</code> &rarr; <code>&quot;000&quot;</code> &rarr; <code>&quot;111&quot;</code>.<br />
	The final string without augmentation is <code>&quot;01111&quot;</code>. The maximum number of active sections is 4.</p>
	</li>
	<li>
	<p>Query <code>[1, 3]</code> &rarr; Substring <code>&quot;101&quot;</code> &rarr; Augmented to <code>&quot;11011&quot;</code><br />
	Because there is no block of <code>&#39;1&#39;</code>s surrounded by <code>&#39;0&#39;</code>s, no valid trade is possible. The maximum number of active sections is 2.</p>
	</li>
</ul>
</div>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n == s.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= queries.length &lt;= 10<sup>5</sup></code></li>
	<li><code>s[i]</code> is either <code>&#39;0&#39;</code> or <code>&#39;1&#39;</code>.</li>
	<li><code>queries[i] = [l<sub>i</sub>, r<sub>i</sub>]</code></li>
	<li><code>0 &lt;= l<sub>i</sub> &lt;= r<sub>i</sub> &lt; n</code></li>
</ul>

[]
[]
[{"value": "cpp", "text": "C++", "defaultCode": "class Solution {\npublic:\n    vector<int> maxActiveSectionsAfterTrade(string s, vector<vector<int>>& queries) {\n        \n    }\n};"}, {"value": "java", "text": "Java", "defaultCode": "class Solution {\n    public List<Integer> maxActiveSectionsAfterTrade(String s, int[][] queries) {\n        \n    }\n}"}, {"value": "python", "text": "Python", "defaultCode": "class Solution(object):\n    def maxActiveSectionsAfterTrade(self, s, queries):\n        \"\"\"\n        :type s: str\n        :type queries: List[List[int]]\n        :rtype: List[int]\n        \"\"\"\n        "}, {"value": "python3", "text": "Python3", "defaultCode": "class Solution:\n    def maxActiveSectionsAfterTrade(self, s: str, queries: List[List[int]]) -> List[int]:\n        "}, {"value": "c", "text": "C", "defaultCode": "/**\n * Note: The returned array must be malloced, assume caller calls free().\n */\nint* maxActiveSectionsAfterTrade(char* s, int** queries, int queriesSize, int* queriesColSize, int* returnSize) {\n    \n}"}, {"value": "csharp", "text": "C#", "defaultCode": "public class Solution {\n    public IList<int> MaxActiveSectionsAfterTrade(string s, int[][] queries) {\n        \n    }\n}"}, {"value": "javascript", "text": "JavaScript", "defaultCode": "/**\n * @param {string} s\n * @param {number[][]} queries\n * @return {number[]}\n */\nvar maxActiveSectionsAfterTrade = function(s, queries) {\n    \n};"}, {"value": "typescript", "text": "TypeScript", "defaultCode": "function maxActiveSectionsAfterTrade(s: string, queries: number[][]): number[] {\n    \n};"}, {"value": "php", "text": "PHP", "defaultCode": "class Solution {\n\n    /**\n     * @param String $s\n     * @param Integer[][] $queries\n     * @return Integer[]\n     */\n    function maxActiveSectionsAfterTrade($s, $queries) {\n        \n    }\n}"}, {"value": "swift", "text": "Swift", "defaultCode": "class Solution {\n    func maxActiveSectionsAfterTrade(_ s: String, _ queries: [[Int]]) -> [Int] {\n        \n    }\n}"}, {"value": "kotlin", "text": "Kotlin", "defaultCode": "class Solution {\n    fun maxActiveSectionsAfterTrade(s: String, queries: Array<IntArray>): List<Int> {\n        \n    }\n}"}, {"value": "dart", "text": "Dart", "defaultCode": "class Solution {\n  List<int> maxActiveSectionsAfterTrade(String s, List<List<int>> queries) {\n    \n  }\n}"}, {"value": "golang", "text": "Go", "defaultCode": "func maxActiveSectionsAfterTrade(s string, queries [][]int) []int {\n    \n}"}, {"value": "ruby", "text": "Ruby", "defaultCode": "# @param {String} s\n# @param {Integer[][]} queries\n# @return {Integer[]}\ndef max_active_sections_after_trade(s, queries)\n    \nend"}, {"value": "scala", "text": "Scala", "defaultCode": "object Solution {\n    def maxActiveSectionsAfterTrade(s: String, queries: Array[Array[Int]]): List[Int] = {\n        \n    }\n}"}, {"value": "rust", "text": "Rust", "defaultCode": "impl Solution {\n    pub fn max_active_sections_after_trade(s: String, queries: Vec<Vec<i32>>) -> Vec<i32> {\n        \n    }\n}"}, {"value": "racket", "text": "Racket", "defaultCode": "(define/contract (max-active-sections-after-trade s queries)\n  (-> string? (listof (listof exact-integer?)) (listof exact-integer?))\n  )"}, {"value": "erlang", "text": "Erlang", "defaultCode": "-spec max_active_sections_after_trade(S :: unicode:unicode_binary(), Queries :: [[integer()]]) -> [integer()].\nmax_active_sections_after_trade(S, Queries) ->\n  ."}, {"value": "elixir", "text": "Elixir", "defaultCode": "defmodule Solution do\n  @spec max_active_sections_after_trade(s :: String.t, queries :: [[integer]]) :: [integer]\n  def max_active_sections_after_trade(s, queries) do\n    \n  end\nend"}]
{
  "name": "maxActiveSectionsAfterTrade",
  "params": [
    {
      "name": "s",
      "type": "string"
    },
    {
      "type": "integer[][]",
      "name": "queries"
    }
  ],
  "return": {
    "type": "list<integer>"
  }
}
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Using compile arguments: <code>--enable-preview --release 21</code></p>\r\n\r\n<p>Most standard library headers are already included automatically for your convenience.</p>\r\n<p>Includes <code>Pair</code> class from https://docs.oracle.com/javase/8/javafx/api/javafx/util/Pair.html.</p>"], "python": ["Python", "<p><code>Python 2.7.18</code>.</p>\r\n\r\n<p>Most libraries are already imported automatically for your convenience, such as <a href=\"https://docs.python.org/2/library/array.html\" target=\"_blank\">array</a>, <a href=\"https://docs.python.org/2/library/bisect.html\" target=\"_blank\">bisect</a>, <a href=\"https://docs.python.org/2/library/collections.html\" target=\"_blank\">collections</a>. 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If you need more libraries, you can import it yourself.</p>\r\n\r\n<p>For Map/TreeMap data structure, you may use <a href=\"http://www.grantjenks.com/docs/sortedcontainers/\" target=\"_blank\">sortedcontainers</a> library.</p>"], "scala": ["Scala", "<p><code>Scala 3.3.1</code>.</p>"], "kotlin": ["Kotlin", "<p><code>Kotlin 2.1.10</code>.</p>"], "rust": ["Rust", "<p><code>Rust 1.85.0</code>. Your code will be compiled with <code>opt-level</code> 2.</p>\r\n\r\n<p>Supports <a href=\"https://crates.io/crates/rand\" target=\"_blank\">rand v0.8</a> and <a href=\"https://crates.io/crates/regex\" target=\"_blank\">regex\u00a0v1</a> and <a href=\"https://crates.io/crates/itertools\" target=\"_blank\">itertools\u00a0v0.14</a> from crates.io</p>"], "php": ["PHP", "<p><code>PHP 8.2</code>.</p>\r\n<p>With bcmath module</p>"], "typescript": ["Typescript", "<p><code>TypeScript 5.7.3, Node.js 22.14.0</code>.</p>\r\n\r\n<p>Compile Options: <code>--alwaysStrict --strictBindCallApply --strictFunctionTypes --target ES2024</code></p>\r\n\r\n<p><a href=\"https://lodash.com\" target=\"_blank\">lodash.js</a> library is included by default.</p>\r\n\r\n<p>For Priority Queue / Queue data structures, you may use 6.3.2 version of <a href=\"https://github.com/datastructures-js/priority-queue/tree/v6.3.2\" target=\"_blank\">datastructures-js/priority-queue</a> and 4.2.3 version of <a href=\"https://github.com/datastructures-js/queue/tree/v4.2.3\" target=\"_blank\">datastructures-js/queue</a> and 1.0.4 version of <a href=\"https://github.com/datastructures-js/deque/tree/v1.0.4\" target=\"_blank\">datastructures-js/deque</a>.</p>"], "racket": ["Racket", "<p><a href=\"https://docs.racket-lang.org/guide/performance.html#%28tech._c%29\" target=\"_blank\">Racket CS</a> v8.15</p>\r\n\r\n<p>Using <code>#lang racket</code></p>\r\n\r\n<p>Required <code>data/gvector data/queue data/order data/heap</code> automatically for your convenience</p>"], "erlang": ["Erlang", "Erlang/OTP 26"], "elixir": ["Elixir", "Elixir 1.17 with Erlang/OTP 26"], "dart": ["Dart", "<p>Dart 3.2. You may use package <a href=\"https://pub.dev/packages/collection/versions/1.18.0\" target=\"_blank\">collection</a></p>\r\n\r\n<p>Your code will be run directly without compiling</p>"]}
['Array', 'String', 'Binary Search', 'Segment Tree']