leetcode-problemset/leetcode-cn/originData/number-of-ways-to-wear-different-hats-to-each-other.json

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            "questionId": "1531",
            "questionFrontendId": "1434",
            "categoryTitle": "Algorithms",
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            "title": "Number of Ways to Wear Different Hats to Each Other",
            "titleSlug": "number-of-ways-to-wear-different-hats-to-each-other",
            "content": "<p>There are <code>n</code> people and <code>40</code> types of hats labeled from <code>1</code> to <code>40</code>.</p>\n\n<p>Given a 2D integer array <code>hats</code>, where <code>hats[i]</code> is a list of all hats preferred by the <code>i<sup>th</sup></code> person.</p>\n\n<p>Return <em>the number of ways that the <code>n</code> people wear different hats to each other</em>.</p>\n\n<p>Since the answer may be too large, return it modulo <code>10<sup>9</sup> + 7</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> hats = [[3,4],[4,5],[5]]\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> There is only one way to choose hats given the conditions. \nFirst person choose hat 3, Second person choose hat 4 and last one hat 5.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> hats = [[3,5,1],[3,5]]\n<strong>Output:</strong> 4\n<strong>Explanation:</strong> There are 4 ways to choose hats:\n(3,5), (5,3), (1,3) and (1,5)\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> hats = [[1,2,3,4],[1,2,3,4],[1,2,3,4],[1,2,3,4]]\n<strong>Output:</strong> 24\n<strong>Explanation:</strong> Each person can choose hats labeled from 1 to 4.\nNumber of Permutations of (1,2,3,4) = 24.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == hats.length</code></li>\n\t<li><code>1 &lt;= n &lt;= 10</code></li>\n\t<li><code>1 &lt;= hats[i].length &lt;= 40</code></li>\n\t<li><code>1 &lt;= hats[i][j] &lt;= 40</code></li>\n\t<li><code>hats[i]</code> contains a list of <strong>unique</strong> integers.</li>\n</ul>\n",
            "translatedTitle": "每个人戴不同帽子的方案数",
            "translatedContent": "<p>总共有 <code>n</code>&nbsp;个人和 <code>40</code> 种不同的帽子，帽子编号从 <code>1</code> 到 <code>40</code> 。</p>\n\n<p>给你一个整数列表的列表&nbsp;<code>hats</code>&nbsp;，其中&nbsp;<code>hats[i]</code>&nbsp;是第 <code>i</code>&nbsp;个人所有喜欢帽子的列表。</p>\n\n<p>请你给每个人安排一顶他喜欢的帽子，确保每个人戴的帽子跟别人都不一样，并返回方案数。</p>\n\n<p>由于答案可能很大，请返回它对&nbsp;<code>10^9 + 7</code>&nbsp;取余后的结果。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<strong>输入：</strong>hats = [[3,4],[4,5],[5]]\n<strong>输出：</strong>1\n<strong>解释：</strong>给定条件下只有一种方法选择帽子。\n第一个人选择帽子 3，第二个人选择帽子 4，最后一个人选择帽子 5。</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>hats = [[3,5,1],[3,5]]\n<strong>输出：</strong>4\n<strong>解释：</strong>总共有 4 种安排帽子的方法：\n(3,5)，(5,3)，(1,3) 和 (1,5)\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre>\n<strong>输入：</strong>hats = [[1,2,3,4],[1,2,3,4],[1,2,3,4],[1,2,3,4]]\n<strong>输出：</strong>24\n<strong>解释：</strong>每个人都可以从编号为 1 到 4 的帽子中选。\n(1,2,3,4) 4 个帽子的排列方案数为 24 。\n</pre>\n\n<p><strong>示例 4：</strong></p>\n\n<pre>\n<strong>输入：</strong>hats = [[1,2,3],[2,3,5,6],[1,3,7,9],[1,8,9],[2,5,7]]\n<strong>输出：</strong>111\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>n == hats.length</code></li>\n\t<li><code>1 &lt;= n &lt;= 10</code></li>\n\t<li><code>1 &lt;= hats[i].length &lt;= 40</code></li>\n\t<li><code>1 &lt;= hats[i][j] &lt;= 40</code></li>\n\t<li><code>hats[i]</code>&nbsp;包含一个数字互不相同的整数列表。</li>\n</ul>\n",
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