leetcode-problemset/leetcode-cn/originData/find-the-maximum-number-of-marked-indices.json

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            "questionId": "2712",
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            "categoryTitle": "Algorithms",
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            "title": "Find the Maximum Number of Marked Indices",
            "titleSlug": "find-the-maximum-number-of-marked-indices",
            "content": "<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code>.</p>\n\n<p>Initially, all of the indices are unmarked. You are allowed to make this operation any number of times:</p>\n\n<ul>\n\t<li>Pick two <strong>different unmarked</strong> indices <code>i</code> and <code>j</code> such that <code>2 * nums[i] &lt;= nums[j]</code>, then mark <code>i</code> and <code>j</code>.</li>\n</ul>\n\n<p>Return <em>the maximum possible number of marked indices in <code>nums</code> using the above operation any number of times</em>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [3,5,2,4]\n<strong>Output:</strong> 2\n<strong>Explanation: </strong>In the first operation: pick i = 2 and j = 1, the operation is allowed because 2 * nums[2] &lt;= nums[1]. Then mark index 2 and 1.\nIt can be shown that there&#39;s no other valid operation so the answer is 2.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [9,2,5,4]\n<strong>Output:</strong> 4\n<strong>Explanation: </strong>In the first operation: pick i = 3 and j = 0, the operation is allowed because 2 * nums[3] &lt;= nums[0]. Then mark index 3 and 0.\nIn the second operation: pick i = 1 and j = 2, the operation is allowed because 2 * nums[1] &lt;= nums[2]. Then mark index 1 and 2.\nSince there is no other operation, the answer is 4.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [7,6,8]\n<strong>Output:</strong> 0\n<strong>Explanation: </strong>There is no valid operation to do, so the answer is 0.\n\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</ul>\n\n<p>&nbsp;</p>\n<style type=\"text/css\">.spoilerbutton {display:block; border:dashed; padding: 0px 0px; margin:10px 0px; font-size:150%; font-weight: bold; color:#000000; background-color:cyan; outline:0; \n}\n.spoiler {overflow:hidden;}\n.spoiler > div {-webkit-transition: all 0s ease;-moz-transition: margin 0s ease;-o-transition: all 0s ease;transition: margin 0s ease;}\n.spoilerbutton[value=\"Show Message\"] + .spoiler > div {margin-top:-500%;}\n.spoilerbutton[value=\"Hide Message\"] + .spoiler {padding:5px;}\n</style>\n",
            "translatedTitle": "求出最多标记下标",
            "translatedContent": "<p>给你一个下标从 <strong>0</strong>&nbsp;开始的整数数组&nbsp;<code>nums</code>&nbsp;。</p>\n\n<p>一开始，所有下标都没有被标记。你可以执行以下操作任意次：</p>\n\n<ul>\n\t<li>选择两个 <strong>互不相同且未标记</strong>&nbsp;的下标&nbsp;<code>i</code> 和&nbsp;<code>j</code>&nbsp;，满足&nbsp;<code>2 * nums[i] &lt;= nums[j]</code>&nbsp;，标记下标&nbsp;<code>i</code> 和&nbsp;<code>j</code>&nbsp;。</li>\n</ul>\n\n<p>请你执行上述操作任意次，返回<em>&nbsp;</em><code>nums</code>&nbsp;中最多可以标记的下标数目。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<b>输入：</b>nums = [3,5,2,4]\n<b>输出：</b>2\n<strong>解释：</strong>第一次操作中，选择 i = 2 和 j = 1 ，操作可以执行的原因是 2 * nums[2] &lt;= nums[1] ，标记下标 2 和 1 。\n没有其他更多可执行的操作，所以答案为 2 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<b>输入：</b>nums = [9,2,5,4]\n<b>输出：</b>4\n<strong>解释：</strong>第一次操作中，选择 i = 3 和 j = 0 ，操作可以执行的原因是 2 * nums[3] &lt;= nums[0] ，标记下标 3 和 0 。\n第二次操作中，选择 i = 1 和 j = 2 ，操作可以执行的原因是 2 * nums[1] &lt;= nums[2] ，标记下标 1 和 2 。\n没有其他更多可执行的操作，所以答案为 4 。\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre>\n<b>输入：</b>nums = [7,6,8]\n<b>输出：</b>0\n<strong>解释：</strong>没有任何可以执行的操作，所以答案为 0 。\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</ul>\n",
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                "Think about how to check that performing k operations is possible.",
                "To perform k operations, it’s optimal to use the smallest k elements and the largest k elements and think about how to match them.",
                "It’s optimal to match the ith smallest number with the k-i + 1 largest number.",
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