leetcode-problemset/leetcode-cn/originData/minimum-array-length-after-pair-removals.json

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            "questionId": "3081",
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            "title": "Minimum Array Length After Pair Removals",
            "titleSlug": "minimum-array-length-after-pair-removals",
            "content": "<p>You are given a <strong>0-indexed</strong> <strong>sorted</strong> array of integers <code>nums</code>.</p>\n\n<p>You can perform the following operation any number of times:</p>\n\n<ul>\n\t<li>Choose <strong>two</strong> indices, <code>i</code> and <code>j</code>, where <code>i &lt; j</code>, such that <code>nums[i] &lt; nums[j]</code>.</li>\n\t<li>Then, remove the elements at indices <code>i</code> and <code>j</code> from <code>nums</code>. The remaining elements retain their original order, and the array is re-indexed.</li>\n</ul>\n\n<p>Return <em>an integer that denotes the <strong>minimum</strong> length of </em><code>nums</code><em> after performing the operation any number of times (<strong>including zero</strong>).</em></p>\n\n<p>Note that <code>nums</code> is sorted in <strong>non-decreasing</strong> order.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,3,4,9]\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> Initially, nums = [1, 3, 4, 9].\nIn the first operation, we can choose index 0 and 1 because nums[0] &lt; nums[1] &lt;=&gt; 1 &lt; 3.\nRemove indices 0 and 1, and nums becomes [4, 9].\nFor the next operation, we can choose index 0 and 1 because nums[0] &lt; nums[1] &lt;=&gt; 4 &lt; 9.\nRemove indices 0 and 1, and nums becomes an empty array [].\nHence, the minimum length achievable is 0.</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [2,3,6,9]\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> Initially, nums = [2, 3, 6, 9]. \nIn the first operation, we can choose index 0 and 2 because nums[0] &lt; nums[2] &lt;=&gt; 2 &lt; 6. \nRemove indices 0 and 2, and nums becomes [3, 9]. \nFor the next operation, we can choose index 0 and 1 because nums[0] &lt; nums[1] &lt;=&gt; 3 &lt; 9. \nRemove indices 0 and 1, and nums becomes an empty array []. \nHence, the minimum length achievable is 0.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,1,2]\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> Initially, nums = [1, 1, 2].\nIn an operation, we can choose index 0 and 2 because nums[0] &lt; nums[2] &lt;=&gt; 1 &lt; 2. \nRemove indices 0 and 2, and nums becomes [1]. \nIt is no longer possible to perform an operation on the array. \nHence, the minimum achievable length is 1. \n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>\n\t<li><code>nums</code> is sorted in <strong>non-decreasing</strong> order.</li>\n</ul>\n",
            "translatedTitle": "删除数对后的最小数组长度",
            "translatedContent": "<p>给你一个下标从 <strong>0</strong> 开始的 <strong>非递减</strong> 整数数组&nbsp;<code>nums</code>&nbsp;。</p>\n\n<p>你可以执行以下操作任意次：</p>\n\n<ul>\n\t<li>选择 <strong>两个&nbsp;</strong>下标&nbsp;<code>i</code> 和&nbsp;<code>j</code>&nbsp;，满足&nbsp;<code>i &lt; j</code>&nbsp;且&nbsp;<code>nums[i] &lt; nums[j]</code>&nbsp;。</li>\n\t<li>将 <code>nums</code>&nbsp;中下标在&nbsp;<code>i</code> 和&nbsp;<code>j</code>&nbsp;处的元素删除。剩余元素按照原来的顺序组成新的数组，下标也重新从 <strong>0</strong>&nbsp;开始编号。</li>\n</ul>\n\n<p>请你返回一个整数，表示执行以上操作任意次后（可以执行 <strong>0</strong> 次），<code>nums</code>&nbsp;数组的 <strong>最小</strong>&nbsp;数组长度。</p>\n\n<p>请注意，<code>nums</code> 数组是按&nbsp;<strong>非降序&nbsp;</strong>排序的。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<pre>\n<strong>输入：</strong>nums = [1,3,4,9]\n<strong>输出：</strong>0\n<strong>解释：</strong>一开始，nums = [1, 3, 4, 9] 。\n第一次操作，我们选择下标 0 和 1 ，满足 nums[0] &lt; nums[1] &lt;=&gt; 1 &lt; 3 。\n删除下标 0 和 1 处的元素，nums 变成 [4, 9] 。\n下一次操作，我们选择下标 0 和 1 ，满足 nums[0] &lt; nums[1] &lt;=&gt; 4 &lt; 9 。\n删除下标 0 和 1 处的元素，nums 变成空数组 [] 。\n所以，可以得到的最小数组长度为 0 。</pre>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>nums = [2,3,6,9]\n<strong>输出：</strong>0\n<strong>解释：</strong>一开始，nums = [2, 3, 6, 9] 。\n第一次操作，我们选择下标 0 和 2 ，满足 nums[0] &lt; nums[2] &lt;=&gt; 2 &lt; 6 。\n删除下标 0 和 2 处的元素，nums 变成 [3, 9] 。\n下一次操作，我们选择下标 0 和 1 ，满足 nums[0] &lt; nums[1] &lt;=&gt; 3 &lt; 9 。\n删除下标 0 和 1 处的元素，nums 变成空数组 [] 。\n所以，可以得到的最小数组长度为 0 。\n</pre>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n\n<pre>\n<strong>输入：</strong>nums = [1,1,2]\n<strong>输出：</strong>1\n<strong>解释：</strong>一开始，nums = [1, 1, 2] 。\n第一次操作，我们选择下标 0 和 2 ，满足 nums[0] &lt; nums[2] &lt;=&gt; 1 &lt; 2 。\n删除下标 0 和 2 处的元素，nums 变成 [1] 。\n无法对数组再执行操作。\n所以，可以得到的最小数组长度为 1 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>\n\t<li><code>nums</code>&nbsp;是 <strong>非递减</strong>&nbsp;数组。</li>\n</ul>\n",
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                "To minimize the length of the array, we should maximize the number of operations performed.",
                "To perform <code>k</code> operations, it is optimal to use the smallest <code>k</code> values and the largest <code>k</code> values in <code>nums</code>.",
                "What is the best way to make pairs from the smallest <code>k</code> values and the largest <code>k</code> values so it is possible to remove all the pairs?",
                "If we consider the smallest <code>k</code> values and the largest <code>k</code> values as two separate <strong>sorted 0-indexed</strong> arrays, <code>a</code> and <code>b</code>, It is optimal to pair <code>a[i]</code> and <code>b[i]</code>. So, a <code>k</code> is valid if <code>a[i] < b[i]</code> for all <code>i</code> in the range <code>[0, k - 1]</code>.",
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href=\\\"https:\\/\\/github.com\\/emirpasic\\/gods\\/tree\\/v1.18.1\\\" target=\\\"_blank\\\">https:\\/\\/godoc.org\\/github.com\\/emirpasic\\/gods@v1.18.1<\\/a> \\u7b2c\\u4e09\\u65b9\\u5e93\\u3002<\\/p>\"],\"python3\":[\"Python3\",\"<p>\\u7248\\u672c\\uff1a<code>Python 3.10<\\/code><\\/p>\\r\\n\\r\\n<p>\\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u5e38\\u7528\\u5e93\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8 \\u5bfc\\u5165\\uff0c\\u5982<a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/array.html\\\" target=\\\"_blank\\\">array<\\/a>, <a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/bisect.html\\\" target=\\\"_blank\\\">bisect<\\/a>, <a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/collections.html\\\" target=\\\"_blank\\\">collections<\\/a>\\u3002 \\u5982\\u679c\\u60a8\\u9700\\u8981\\u4f7f\\u7528\\u5176\\u4ed6\\u5e93\\u51fd\\u6570\\uff0c\\u8bf7\\u81ea\\u884c\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n<p>\\u5982\\u9700\\u4f7f\\u7528 Map\\/TreeMap 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