{ "data": { "question": { "questionId": "1531", "questionFrontendId": "1434", "categoryTitle": "Algorithms", "boundTopicId": 226092, "title": "Number of Ways to Wear Different Hats to Each Other", "titleSlug": "number-of-ways-to-wear-different-hats-to-each-other", "content": "

There are n people and 40 types of hats labeled from 1 to 40.

\n\n

Given a 2D integer array hats, where hats[i] is a list of all hats preferred by the ith person.

\n\n

Return the number of ways that the n people wear different hats to each other.

\n\n

Since the answer may be too large, return it modulo 109 + 7.

\n\n

 

\n

Example 1:

\n\n
\nInput: hats = [[3,4],[4,5],[5]]\nOutput: 1\nExplanation: 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
\n\n

Example 2:

\n\n
\nInput: hats = [[3,5,1],[3,5]]\nOutput: 4\nExplanation: There are 4 ways to choose hats:\n(3,5), (5,3), (1,3) and (1,5)\n
\n\n

Example 3:

\n\n
\nInput: hats = [[1,2,3,4],[1,2,3,4],[1,2,3,4],[1,2,3,4]]\nOutput: 24\nExplanation: Each person can choose hats labeled from 1 to 4.\nNumber of Permutations of (1,2,3,4) = 24.\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "每个人戴不同帽子的方案数", "translatedContent": "

总共有 n 个人和 40 种不同的帽子，帽子编号从 1 到 40 。

\n\n

给你一个整数列表的列表 hats ，其中 hats[i] 是第 i 个人所有喜欢帽子的列表。

\n\n

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。

\n\n

由于答案可能很大，请返回它对 10^9 + 7 取余后的结果。

\n\n

 

\n\n

示例 1：

\n\n
\n输入：hats = [[3,4],[4,5],[5]]\n输出：1\n解释：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。
\n\n

示例 2：

\n\n
\n输入：hats = [[3,5,1],[3,5]]\n输出：4\n解释：总共有 4 种安排帽子的方法：\n(3,5)，(5,3)，(1,3) 和 (1,5)\n
\n\n

示例 3：

\n\n
\n输入：hats = [[1,2,3,4],[1,2,3,4],[1,2,3,4],[1,2,3,4]]\n输出：24\n解释：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
\n\n

示例 4：

\n\n
\n输入：hats = [[1,2,3],[2,3,5,6],[1,3,7,9],[1,8,9],[2,5,7]]\n输出：111\n
\n\n

 

\n\n

提示：

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