{ "data": { "question": { "questionId": "1531", "questionFrontendId": "1434", "boundTopicId": null, "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": null, "translatedContent": null, "isPaidOnly": false, "difficulty": "Hard", "likes": 864, "dislikes": 9, "isLiked": null, "similarQuestions": "[{\"title\": \"The Number of Good Subsets\", \"titleSlug\": \"the-number-of-good-subsets\", \"difficulty\": \"Hard\", \"translatedTitle\": null}]", "exampleTestcases": "[[3,4],[4,5],[5]]\n[[3,5,1],[3,5]]\n[[1,2,3,4],[1,2,3,4],[1,2,3,4],[1,2,3,4]]", "categoryTitle": "Algorithms", "contributors": [], "topicTags": [ { "name": "Array", "slug": "array", "translatedName": null, "__typename": "TopicTagNode" }, { "name": "Dynamic Programming", "slug": "dynamic-programming", "translatedName": null, "__typename": "TopicTagNode" }, { "name": "Bit Manipulation", "slug": "bit-manipulation", "translatedName": null, "__typename": "TopicTagNode" }, { "name": "Bitmask", "slug": "bitmask", "translatedName": null, "__typename": "TopicTagNode" } ], "companyTagStats": null, "codeSnippets": [ { "lang": "C++", "langSlug": "cpp", "code": "class Solution {\npublic:\n int numberWays(vector>& hats) {\n \n }\n};", "__typename": "CodeSnippetNode" }, { "lang": "Java", "langSlug": "java", "code": "class Solution {\n public int numberWays(List> hats) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Python", "langSlug": "python", "code": "class Solution(object):\n def numberWays(self, hats):\n \"\"\"\n :type hats: List[List[int]]\n :rtype: int\n \"\"\"\n ", "__typename": "CodeSnippetNode" }, { "lang": "Python3", "langSlug": "python3", "code": "class Solution:\n def numberWays(self, hats: List[List[int]]) -> int:\n ", "__typename": "CodeSnippetNode" }, { "lang": "C", "langSlug": "c", "code": "int numberWays(int** hats, int hatsSize, int* hatsColSize) {\n \n}", "__typename": "CodeSnippetNode" }, { "lang": "C#", "langSlug": "csharp", "code": "public class Solution {\n public int NumberWays(IList> hats) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "JavaScript", "langSlug": "javascript", "code": "/**\n * @param {number[][]} hats\n * @return {number}\n */\nvar numberWays = function(hats) {\n \n};", "__typename": "CodeSnippetNode" }, { "lang": "TypeScript", "langSlug": "typescript", "code": "function numberWays(hats: number[][]): number {\n \n};", "__typename": "CodeSnippetNode" }, { "lang": "PHP", "langSlug": "php", "code": "class Solution {\n\n /**\n * @param Integer[][] $hats\n * @return Integer\n */\n function numberWays($hats) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Swift", "langSlug": "swift", "code": "class Solution {\n func numberWays(_ hats: [[Int]]) -> Int {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Kotlin", "langSlug": "kotlin", "code": "class Solution {\n fun numberWays(hats: List>): Int {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Dart", "langSlug": "dart", "code": "class Solution {\n int numberWays(List> hats) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Go", "langSlug": "golang", "code": "func numberWays(hats [][]int) int {\n \n}", "__typename": "CodeSnippetNode" }, { "lang": "Ruby", "langSlug": "ruby", "code": "# @param {Integer[][]} hats\n# @return {Integer}\ndef number_ways(hats)\n \nend", "__typename": "CodeSnippetNode" }, { "lang": "Scala", "langSlug": "scala", "code": "object Solution {\n def numberWays(hats: List[List[Int]]): Int = {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Rust", "langSlug": "rust", "code": "impl Solution {\n pub fn number_ways(hats: Vec>) -> i32 {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Racket", "langSlug": "racket", "code": "(define/contract (number-ways hats)\n (-> (listof (listof exact-integer?)) exact-integer?)\n )", "__typename": "CodeSnippetNode" }, { "lang": "Elixir", "langSlug": "elixir", "code": "defmodule Solution do\n @spec number_ways(hats :: [[integer]]) :: integer\n def number_ways(hats) do\n \n end\nend", "__typename": "CodeSnippetNode" } ], "stats": "{\"totalAccepted\": \"13.7K\", \"totalSubmission\": \"31.3K\", \"totalAcceptedRaw\": 13748, \"totalSubmissionRaw\": 31312, \"acRate\": \"43.9%\"}", "hints": [ "Dynamic programming + bitmask.", "dp(peopleMask, idHat) number of ways to wear different hats given a bitmask (people visited) and used hats from 1 to idHat-1." ], "solution": { "id": "1982", "canSeeDetail": true, "paidOnly": false, "hasVideoSolution": false, "paidOnlyVideo": true, "__typename": "ArticleNode" }, "status": null, "sampleTestCase": "[[3,4],[4,5],[5]]", "metaData": "{\n \"name\": \"numberWays\",\n \"params\": [\n {\n \"name\": \"hats\",\n \"type\": \"list>\"\n }\n ],\n \"return\": {\n \"type\": \"integer\"\n }\n}", "judgerAvailable": true, "judgeType": "large", "mysqlSchemas": [], "enableRunCode": true, "enableTestMode": false, "enableDebugger": true, "envInfo": "{\"cpp\": [\"C++\", \"

Compiled with clang 11 using the latest C++ 20 standard.

\\r\\n\\r\\n

Your code is compiled with level two optimization (-O2). AddressSanitizer is also enabled to help detect out-of-bounds and use-after-free bugs.

\\r\\n\\r\\n

Most standard library headers are already included automatically for your convenience.

\"], \"java\": [\"Java\", \"

OpenJDK 17. Java 8 features such as lambda expressions and stream API can be used.

\\r\\n\\r\\n

Most standard library headers are already included automatically for your convenience.

\\r\\n

Includes Pair class from https://docs.oracle.com/javase/8/javafx/api/javafx/util/Pair.html.

\"], \"python\": [\"Python\", \"

Python 2.7.12.

\\r\\n\\r\\n

Most libraries are already imported automatically for your convenience, such as array, bisect, collections. If you need more libraries, you can import it yourself.

\\r\\n\\r\\n

For Map/TreeMap data structure, you may use sortedcontainers library.

\\r\\n\\r\\n

Note that Python 2.7 will not be maintained past 2020. For the latest Python, please choose Python3 instead.

\"], \"c\": [\"C\", \"

Compiled with gcc 8.2 using the gnu11 standard.

\\r\\n\\r\\n

Your code is compiled with level one optimization (-O1). AddressSanitizer is also enabled to help detect out-of-bounds and use-after-free bugs.

\\r\\n\\r\\n

Most standard library headers are already included automatically for your convenience.

\\r\\n\\r\\n

For hash table operations, you may use uthash. \\\"uthash.h\\\" is included by default. Below are some examples:

\\r\\n\\r\\n

1. Adding an item to a hash.\\r\\n

\\r\\nstruct hash_entry {\\r\\n    int id;            /* we'll use this field as the key */\\r\\n    char name[10];\\r\\n    UT_hash_handle hh; /* makes this structure hashable */\\r\\n};\\r\\n\\r\\nstruct hash_entry *users = NULL;\\r\\n\\r\\nvoid add_user(struct hash_entry *s) {\\r\\n    HASH_ADD_INT(users, id, s);\\r\\n}\\r\\n
\\r\\n

\\r\\n\\r\\n

2. Looking up an item in a hash:\\r\\n

\\r\\nstruct hash_entry *find_user(int user_id) {\\r\\n    struct hash_entry *s;\\r\\n    HASH_FIND_INT(users, &user_id, s);\\r\\n    return s;\\r\\n}\\r\\n
\\r\\n

\\r\\n\\r\\n

3. Deleting an item in a hash:\\r\\n

\\r\\nvoid delete_user(struct hash_entry *user) {\\r\\n    HASH_DEL(users, user);  \\r\\n}\\r\\n
\\r\\n

\"], \"csharp\": [\"C#\", \"

C# 10 with .NET 6 runtime

\"], \"javascript\": [\"JavaScript\", \"

Node.js 16.13.2.

\\r\\n\\r\\n

Your code is run with --harmony flag, enabling new ES6 features.

\\r\\n\\r\\n

lodash.js library is included by default.

\\r\\n\\r\\n

For Priority Queue / Queue data structures, you may use 5.3.0 version of datastructures-js/priority-queue and 4.2.1 version of datastructures-js/queue.

\"], \"ruby\": [\"Ruby\", \"

Ruby 3.1

\\r\\n\\r\\n

Some common data structure implementations are provided in the Algorithms module: https://www.rubydoc.info/github/kanwei/algorithms/Algorithms

\"], \"swift\": [\"Swift\", \"

Swift 5.5.2.

\"], \"golang\": [\"Go\", \"

Go 1.21

\\r\\n

Support https://godoc.org/github.com/emirpasic/gods@v1.18.1 library.

\"], \"python3\": [\"Python3\", \"

Python 3.10.

\\r\\n\\r\\n

Most libraries are already imported automatically for your convenience, such as array, bisect, collections. If you need more libraries, you can import it yourself.

\\r\\n\\r\\n

For Map/TreeMap data structure, you may use sortedcontainers library.

\"], \"scala\": [\"Scala\", \"

Scala 2.13.7.

\"], \"kotlin\": [\"Kotlin\", \"

Kotlin 1.9.0.

\"], \"rust\": [\"Rust\", \"

Rust 1.58.1

\\r\\n\\r\\n

Supports rand v0.6\\u00a0from crates.io

\"], \"php\": [\"PHP\", \"

PHP 8.1.

\\r\\n

With bcmath module

\"], \"typescript\": [\"Typescript\", \"

TypeScript 5.1.6, Node.js 16.13.2.

\\r\\n\\r\\n

Your code is run with --harmony flag, enabling new ES2022 features.

\\r\\n\\r\\n

lodash.js library is included by default.

\"], \"racket\": [\"Racket\", \"

Run with Racket 8.3.

\"], \"elixir\": [\"Elixir\", \"Elixir 1.13.4 with Erlang/OTP 25.0\"], \"dart\": [\"Dart\", \"

Dart 2.17.3

\\r\\n\\r\\n

Your code will be run directly without compiling

\"]}", "libraryUrl": null, "adminUrl": null, "challengeQuestion": null, "__typename": "QuestionNode" } } }