leetcode-problemset/leetcode-cn/originData/sorting-three-groups.json

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            "title": "Sorting Three Groups",
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            "content": "<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code> of length <code>n</code>.<br />\n<br />\nThe numbers from <code>0</code> to <code>n - 1</code> are divided into three groups numbered from <code>1</code> to <code>3</code>, where number <code>i</code> belongs to group <code>nums[i]</code>. Notice that some groups may be <strong>empty</strong>.<br />\n<br />\nYou are allowed to perform this operation any number of times:</p>\n\n<ul>\n\t<li>Pick number <code>x</code> and change its group. More formally, change <code>nums[x]</code> to any number from <code>1</code> to <code>3</code>.</li>\n</ul>\n\n<p>A new array <code>res</code> is constructed using the following procedure:</p>\n\n<ol>\n\t<li>Sort the numbers in each group independently.</li>\n\t<li>Append the elements of groups <code>1</code>, <code>2</code>, and <code>3</code> to <code>res</code> <strong>in this order</strong>.</li>\n</ol>\n\n<p>Array <code>nums</code> is called a <strong>beautiful array</strong> if the constructed array <code>res</code> is sorted in <strong>non-decreasing</strong> order.</p>\n\n<p>Return <em>the <strong>minimum</strong> number of operations to make </em><code>nums</code><em> a <strong>beautiful array</strong></em>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [2,1,3,2,1]\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> It&#39;s optimal to perform three operations:\n1. change nums[0] to 1.\n2. change nums[2] to 1.\n3. change nums[3] to 1.\nAfter performing the operations and sorting the numbers in each group, group 1 becomes equal to [0,1,2,3,4] and group 2 and group 3 become empty. Hence, res is equal to [0,1,2,3,4] which is sorted in non-decreasing order.\nIt can be proven that there is no valid sequence of less than three operations.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,3,2,1,3,3]\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> It&#39;s optimal to perform two operations:\n1. change nums[1] to 1.\n2. change nums[2] to 1.\nAfter performing the operations and sorting the numbers in each group, group 1 becomes equal to [0,1,2,3], group 2 becomes empty, and group 3 becomes equal to [4,5]. Hence, res is equal to [0,1,2,3,4,5] which is sorted in non-decreasing order.\nIt can be proven that there is no valid sequence of less than two operations.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [2,2,2,2,3,3]\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> It&#39;s optimal to not perform operations.\nAfter sorting the numbers in each group, group 1 becomes empty, group 2 becomes equal to [0,1,2,3] and group 3 becomes equal to [4,5]. Hence, res is equal to [0,1,2,3,4,5] which is sorted in non-decreasing order.\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;= 100</code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 3</code></li>\n</ul>\n",
            "translatedTitle": "将三个组排序",
            "translatedContent": "<p>给你一个下标从 <strong>0</strong>&nbsp;开始长度为 <code>n</code>&nbsp;的整数数组&nbsp;<code>nums</code>&nbsp;。<br />\n<br />\n从&nbsp;<code>0</code>&nbsp;到&nbsp;<code>n - 1</code>&nbsp;的数字被分为编号从&nbsp;<code>1</code>&nbsp;到&nbsp;<code>3</code>&nbsp;的三个组，数字&nbsp;<code>i</code>&nbsp;属于组&nbsp;<code>nums[i]</code>&nbsp;。注意，有的组可能是&nbsp;<strong>空的</strong>&nbsp;。<br />\n<br />\n你可以执行以下操作任意次：</p>\n\n<ul>\n\t<li>选择数字&nbsp;<code>x</code>&nbsp;并改变它的组。更正式的，你可以将&nbsp;<code>nums[x]</code>&nbsp;改为数字&nbsp;<code>1</code>&nbsp;到&nbsp;<code>3</code>&nbsp;中的任意一个。</li>\n</ul>\n\n<p>你将按照以下过程构建一个新的数组&nbsp;<code>res</code>&nbsp;：</p>\n\n<ol>\n\t<li>将每个组中的数字分别排序。</li>\n\t<li>将组&nbsp;<code>1</code>&nbsp;，<code>2</code>&nbsp;和&nbsp;<code>3</code>&nbsp;中的元素&nbsp;<strong>依次</strong>&nbsp;连接以得到&nbsp;<code>res</code>&nbsp;。</li>\n</ol>\n\n<p>如果得到的&nbsp;<code>res</code>&nbsp;是 <strong>非递减</strong>顺序的，那么我们称数组&nbsp;<code>nums</code>&nbsp;是 <strong>美丽数组</strong>&nbsp;。</p>\n\n<p>请你返回将<em>&nbsp;</em><code>nums</code>&nbsp;变为&nbsp;<strong>美丽数组</strong>&nbsp;需要的最少步数。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<pre>\n<b>输入：</b>nums = [2,1,3,2,1]\n<b>输出：</b>3\n<b>解释：</b>以下三步操作是最优方案：\n1. 将 nums[0] 变为 1 。\n2. 将 nums[2] 变为 1 。\n3. 将 nums[3] 变为 1 。\n执行以上操作后，将每组中的数字排序，组 1 为 [0,1,2,3,4] ，组 2 和组 3 都为空。所以 res 等于 [0,1,2,3,4] ，它是非递减顺序的。\n三步操作是最少需要的步数。\n</pre>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<pre>\n<b>输入：</b>nums = [1,3,2,1,3,3]\n<b>输出：</b>2\n<b>解释：</b>以下两步操作是最优方案：\n1. 将 nums[1] 变为 1 。\n2. 将 nums[2] 变为 1 。\n执行以上操作后，将每组中的数字排序，组 1 为 [0,1,2,3] ，组 2 为空，组 3 为 [4,5] 。所以 res 等于 [0,1,2,3,4,5] ，它是非递减顺序的。\n两步操作是最少需要的步数。\n</pre>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n\n<pre>\n<b>输入：</b>nums = [2,2,2,2,3,3]\n<b>输出：</b>0\n<b>解释：</b>不需要执行任何操作。\n组 1 为空，组 2 为 [0,1,2,3] ，组 3 为 [4,5] 。所以 res 等于 [0,1,2,3,4,5] ，它是非递减顺序的。\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;= 100</code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 3</code></li>\n</ul>\n",
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                "The problem asks to change the array nums to make it sorted (i.e., all the 1s are on the left of 2s, and all the 2s are on the left of 3s.).",
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