leetcode-problemset/leetcode-cn/originData/minimum-number-of-groups-to-create-a-valid-assignment.json

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        "question": {
            "questionId": "3166",
            "questionFrontendId": "2910",
            "categoryTitle": "Algorithms",
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            "title": "Minimum Number of Groups to Create a Valid Assignment",
            "titleSlug": "minimum-number-of-groups-to-create-a-valid-assignment",
            "content": "<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code> of length <code>n</code>.</p>\n\n<p>We want to group the indices so for each index <code>i</code> in the range <code>[0, n - 1]</code>, it is assigned to <strong>exactly one</strong> group.</p>\n\n<p>A group<strong> </strong>assignment is <strong>valid</strong> if the following conditions hold:</p>\n\n<ul>\n\t<li>For every group <code>g</code>, all indices <code>i</code> assigned to group <code>g</code> have the same value in <code>nums</code>.</li>\n\t<li>For any two groups <code>g<sub>1</sub></code> and <code>g<sub>2</sub></code>, the <strong>difference</strong> between the <strong>number of indices</strong> assigned to <code>g<sub>1</sub></code> and <code>g<sub>2</sub></code> should <strong>not exceed</strong> <code>1</code>.</li>\n</ul>\n\n<p>Return <em>an integer denoting </em><em>the <strong>minimum</strong> number of groups needed to create a valid group assignment.</em></p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [3,2,3,2,3]\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> One way the indices can be assigned to 2 groups is as follows, where the values in square brackets are indices:\ngroup 1 -&gt; [0,2,4]\ngroup 2 -&gt; [1,3]\nAll indices are assigned to one group.\nIn group 1, nums[0] == nums[2] == nums[4], so all indices have the same value.\nIn group 2, nums[1] == nums[3], so all indices have the same value.\nThe number of indices assigned to group 1 is 3, and the number of indices assigned to group 2 is 2.\nTheir difference doesn&#39;t exceed 1.\nIt is not possible to use fewer than 2 groups because, in order to use just 1 group, all indices assigned to that group must have the same value.\nHence, the answer is 2.</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [10,10,10,3,1,1]\n<strong>Output:</strong> 4\n<strong>Explanation:</strong> One way the indices can be assigned to 4 groups is as follows, where the values in square brackets are indices:\ngroup 1 -&gt; [0]\ngroup 2 -&gt; [1,2]\ngroup 3 -&gt; [3]\ngroup 4 -&gt; [4,5]\nThe group assignment above satisfies both conditions.\nIt can be shown that it is not possible to create a valid assignment using fewer than 4 groups.\nHence, the answer is 4.</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",
            "translatedTitle": "合法分组的最少组数",
            "translatedContent": "<p>给你一个长度为 <code>n</code>&nbsp;下标从 <strong>0</strong>&nbsp;开始的整数数组&nbsp;<code>nums</code>&nbsp;。</p>\n\n<p>我们想将下标进行分组，使得&nbsp;<code>[0, n - 1]</code>&nbsp;内所有下标&nbsp;<code>i</code>&nbsp;都 <strong>恰好</strong> 被分到其中一组。</p>\n\n<p>如果以下条件成立，我们说这个分组方案是合法的：</p>\n\n<ul>\n\t<li>对于每个组&nbsp;<code>g</code>&nbsp;，同一组内所有下标在&nbsp;<code>nums</code>&nbsp;中对应的数值都相等。</li>\n\t<li>对于任意两个组&nbsp;<code>g<sub>1</sub></code> 和&nbsp;<code>g<sub>2</sub></code>&nbsp;，两个组中&nbsp;<strong>下标数量</strong> 的&nbsp;<strong>差值不超过&nbsp;</strong><code>1</code>&nbsp;。</li>\n</ul>\n\n<p>请你返回一个整数，表示得到一个合法分组方案的 <strong>最少</strong>&nbsp;组数。</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 = [3,2,3,2,3]\n<b>输出：</b>2\n<b>解释：</b>一个得到 2 个分组的方案如下，中括号内的数字都是下标：\n组 1 -&gt; [0,2,4]\n组 2 -&gt; [1,3]\n所有下标都只属于一个组。\n组 1 中，nums[0] == nums[2] == nums[4] ，所有下标对应的数值都相等。\n组 2 中，nums[1] == nums[3] ，所有下标对应的数值都相等。\n组 1 中下标数目为 3 ，组 2 中下标数目为 2 。\n两者之差不超过 1 。\n无法得到一个小于 2 组的答案，因为如果只有 1 组，组内所有下标对应的数值都要相等。\n所以答案为 2 。</pre>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<pre>\n<b>输入：</b>nums = [10,10,10,3,1,1]\n<b>输出：</b>4\n<b>解释：</b>一个得到 2 个分组的方案如下，中括号内的数字都是下标：\n组 1 -&gt; [0]\n组 2 -&gt; [1,2]\n组 3 -&gt; [3]\n组 4 -&gt; [4,5]\n分组方案满足题目要求的两个条件。\n无法得到一个小于 4 组的答案。\n所以答案为 4 。</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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            "hints": [
                "Calculate the frequency of each number.",
                "For each <code>x</code> in the range <code>[1, minimum_frequency]</code>, try to create groups with either <code>x</code> or <code>x + 1</code> indices assigned to them while minimizing the total number of groups.",
                "For each distinct number, using its frequency, check that all its occurrences can be assigned to groups of size <code>x</code> or <code>x + 1</code> while minimizing the number of groups used.",
                "To get the minimum number of groups needed for a number having frequency <code>f</code> to be assigned to groups of size <code>x</code> or <code>x + 1</code>, let <code>a = f / (x + 1)</code> and <code>b = f % (x + 1)</code>. <ul> <li>If <code>b == 0</code>, then we can simply create <code>a</code> groups of size <code>x + 1</code>.</li> <li>If <code>x - b <= a</code>, we can have <code>a - (x - b)</code> groups of size <code>x + 1</code> and <code>x - b + 1</code> groups of size <code>x</code>. So, in total, we have <code>a + 1</code> groups.</li> <li>Otherwise, it's impossible.</li> </ul>",
                "The minimum number of groups needed for some <code>x</code> is the total minimized number of groups needed for each distinct number.",
                "The answer is the minimum number of groups needed for each <code>x</code> in the range <code>[1, minimum_frequency]</code>."
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