{
    "data": {
        "question": {
            "questionId": "1587",
            "questionFrontendId": "1494",
            "boundTopicId": null,
            "title": "Parallel Courses II",
            "titleSlug": "parallel-courses-ii",
            "content": "<p>You are given an integer <code>n</code>, which indicates that there are <code>n</code> courses labeled from <code>1</code> to <code>n</code>. You are also given an array <code>relations</code> where <code>relations[i] = [prevCourse<sub>i</sub>, nextCourse<sub>i</sub>]</code>, representing a prerequisite relationship between course <code>prevCourse<sub>i</sub></code> and course <code>nextCourse<sub>i</sub></code>: course <code>prevCourse<sub>i</sub></code> has to be taken before course <code>nextCourse<sub>i</sub></code>. Also, you are given the integer <code>k</code>.</p>\n\n<p>In one semester, you can take <strong>at most</strong> <code>k</code> courses as long as you have taken all the prerequisites in the <strong>previous</strong> semester for the courses you are taking.</p>\n\n<p>Return <em>the <strong>minimum</strong> number of semesters needed to take all courses</em>. The testcases will be generated such that it is possible to take every course.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/05/22/leetcode_parallel_courses_1.png\" style=\"width: 300px; height: 164px;\" /></strong></p>\n\n<pre>\n<strong>Input:</strong> n = 4, dependencies = [[2,1],[3,1],[1,4]], k = 2\n<strong>Output:</strong> 3 \n<strong>Explanation:</strong> The figure above represents the given graph.\nIn the first semester, you can take courses 2 and 3.\nIn the second semester, you can take course 1.\nIn the third semester, you can take course 4.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/05/22/leetcode_parallel_courses_2.png\" style=\"width: 300px; height: 234px;\" /></strong></p>\n\n<pre>\n<strong>Input:</strong> n = 5, dependencies = [[2,1],[3,1],[4,1],[1,5]], k = 2\n<strong>Output:</strong> 4 \n<strong>Explanation:</strong> The figure above represents the given graph.\nIn the first semester, you can take courses 2 and 3 only since you cannot take more than two per semester.\nIn the second semester, you can take course 4.\nIn the third semester, you can take course 1.\nIn the fourth semester, you can take course 5.\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 11, dependencies = [], k = 2\n<strong>Output:</strong> 6\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 15</code></li>\n\t<li><code>1 &lt;= k &lt;= n</code></li>\n\t<li><code>0 &lt;= relations.length &lt;= n * (n-1) / 2</code></li>\n\t<li><code>relations[i].length == 2</code></li>\n\t<li><code>1 &lt;= prevCourse<sub>i</sub>, nextCourse<sub>i</sub> &lt;= n</code></li>\n\t<li><code>prevCourse<sub>i</sub> != nextCourse<sub>i</sub></code></li>\n\t<li>All the pairs <code>[prevCourse<sub>i</sub>, nextCourse<sub>i</sub>]</code> are <strong>unique</strong>.</li>\n\t<li>The given graph is a directed acyclic graph.</li>\n</ul>\n",
            "translatedTitle": null,
            "translatedContent": null,
            "isPaidOnly": false,
            "difficulty": "Hard",
            "likes": 573,
            "dislikes": 46,
            "isLiked": null,
            "similarQuestions": "[{\"title\": \"Parallel Courses\", \"titleSlug\": \"parallel-courses\", \"difficulty\": \"Medium\", \"translatedTitle\": null}]",
            "exampleTestcases": "4\n[[2,1],[3,1],[1,4]]\n2\n5\n[[2,1],[3,1],[4,1],[1,5]]\n2\n11\n[]\n2",
            "categoryTitle": "Algorithms",
            "contributors": [],
            "topicTags": [
                {
                    "name": "Dynamic Programming",
                    "slug": "dynamic-programming",
                    "translatedName": null,
                    "__typename": "TopicTagNode"
                },
                {
                    "name": "Bit Manipulation",
                    "slug": "bit-manipulation",
                    "translatedName": null,
                    "__typename": "TopicTagNode"
                },
                {
                    "name": "Graph",
                    "slug": "graph",
                    "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 minNumberOfSemesters(int n, vector<vector<int>>& relations, int k) {\n        \n    }\n};",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Java",
                    "langSlug": "java",
                    "code": "class Solution {\n    public int minNumberOfSemesters(int n, int[][] relations, int k) {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Python",
                    "langSlug": "python",
                    "code": "class Solution(object):\n    def minNumberOfSemesters(self, n, relations, k):\n        \"\"\"\n        :type n: int\n        :type relations: List[List[int]]\n        :type k: int\n        :rtype: int\n        \"\"\"\n        ",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Python3",
                    "langSlug": "python3",
                    "code": "class Solution:\n    def minNumberOfSemesters(self, n: int, relations: List[List[int]], k: int) -> int:\n        ",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "C",
                    "langSlug": "c",
                    "code": "\n\nint minNumberOfSemesters(int n, int** relations, int relationsSize, int* relationsColSize, int k){\n\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "C#",
                    "langSlug": "csharp",
                    "code": "public class Solution {\n    public int MinNumberOfSemesters(int n, int[][] relations, int k) {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "JavaScript",
                    "langSlug": "javascript",
                    "code": "/**\n * @param {number} n\n * @param {number[][]} relations\n * @param {number} k\n * @return {number}\n */\nvar minNumberOfSemesters = function(n, relations, k) {\n    \n};",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Ruby",
                    "langSlug": "ruby",
                    "code": "# @param {Integer} n\n# @param {Integer[][]} relations\n# @param {Integer} k\n# @return {Integer}\ndef min_number_of_semesters(n, relations, k)\n    \nend",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Swift",
                    "langSlug": "swift",
                    "code": "class Solution {\n    func minNumberOfSemesters(_ n: Int, _ relations: [[Int]], _ k: Int) -> Int {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Go",
                    "langSlug": "golang",
                    "code": "func minNumberOfSemesters(n int, relations [][]int, k int) int {\n    \n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Scala",
                    "langSlug": "scala",
                    "code": "object Solution {\n    def minNumberOfSemesters(n: Int, relations: Array[Array[Int]], k: Int): Int = {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Kotlin",
                    "langSlug": "kotlin",
                    "code": "class Solution {\n    fun minNumberOfSemesters(n: Int, relations: Array<IntArray>, k: Int): Int {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Rust",
                    "langSlug": "rust",
                    "code": "impl Solution {\n    pub fn min_number_of_semesters(n: i32, relations: Vec<Vec<i32>>, k: i32) -> i32 {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "PHP",
                    "langSlug": "php",
                    "code": "class Solution {\n\n    /**\n     * @param Integer $n\n     * @param Integer[][] $relations\n     * @param Integer $k\n     * @return Integer\n     */\n    function minNumberOfSemesters($n, $relations, $k) {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "TypeScript",
                    "langSlug": "typescript",
                    "code": "function minNumberOfSemesters(n: number, relations: number[][], k: number): number {\n\n};",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Racket",
                    "langSlug": "racket",
                    "code": "(define/contract (min-number-of-semesters n relations k)\n  (-> exact-integer? (listof (listof exact-integer?)) exact-integer? exact-integer?)\n\n  )",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Erlang",
                    "langSlug": "erlang",
                    "code": "-spec min_number_of_semesters(N :: integer(), Relations :: [[integer()]], K :: integer()) -> integer().\nmin_number_of_semesters(N, Relations, K) ->\n  .",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Elixir",
                    "langSlug": "elixir",
                    "code": "defmodule Solution do\n  @spec min_number_of_semesters(n :: integer, relations :: [[integer]], k :: integer) :: integer\n  def min_number_of_semesters(n, relations, k) do\n\n  end\nend",
                    "__typename": "CodeSnippetNode"
                }
            ],
            "stats": "{\"totalAccepted\": \"10.4K\", \"totalSubmission\": \"32.8K\", \"totalAcceptedRaw\": 10412, \"totalSubmissionRaw\": 32841, \"acRate\": \"31.7%\"}",
            "hints": [
                "Use backtracking with states (bitmask, degrees) where bitmask represents the set of courses, if the ith bit is 1 then the ith course was taken, otherwise, you can take the ith course. Degrees represent the degree for each course (nodes in the graph).",
                "Note that you can only take nodes (courses) with degree = 0 and it is optimal at every step in the backtracking take the maximum number of courses limited by k."
            ],
            "solution": null,
            "status": null,
            "sampleTestCase": "4\n[[2,1],[3,1],[1,4]]\n2",
            "metaData": "{\n  \"name\": \"minNumberOfSemesters\",\n  \"params\": [\n    {\n      \"name\": \"n\",\n      \"type\": \"integer\"\n    },\n    {\n      \"type\": \"integer[][]\",\n      \"name\": \"relations\"\n    },\n    {\n      \"type\": \"integer\",\n      \"name\": \"k\"\n    }\n  ],\n  \"return\": {\n    \"type\": \"integer\"\n  }\n}",
            "judgerAvailable": true,
            "judgeType": "large",
            "mysqlSchemas": [],
            "enableRunCode": true,
            "enableTestMode": false,
            "enableDebugger": true,
            "envInfo": "{\"cpp\": [\"C++\", \"<p>Compiled with <code> clang 11 </code> using the latest C++ 17 standard.</p>\\r\\n\\r\\n<p>Your code is compiled with level two optimization (<code>-O2</code>). <a href=\\\"https://github.com/google/sanitizers/wiki/AddressSanitizer\\\" target=\\\"_blank\\\">AddressSanitizer</a> is also enabled to help detect out-of-bounds and use-after-free bugs.</p>\\r\\n\\r\\n<p>Most standard library headers are already included automatically for your convenience.</p>\"], \"java\": [\"Java\", \"<p><code> OpenJDK 17 </code>. Java 8 features such as lambda expressions and stream API can be used. </p>\\r\\n\\r\\n<p>Most standard library headers are already included automatically for your convenience.</p>\\r\\n<p>Includes <code>Pair</code> class from https://docs.oracle.com/javase/8/javafx/api/javafx/util/Pair.html.</p>\"], \"python\": [\"Python\", \"<p><code>Python 2.7.12</code>.</p>\\r\\n\\r\\n<p>Most libraries are already imported automatically for your convenience, such as <a href=\\\"https://docs.python.org/2/library/array.html\\\" target=\\\"_blank\\\">array</a>, <a href=\\\"https://docs.python.org/2/library/bisect.html\\\" target=\\\"_blank\\\">bisect</a>, <a href=\\\"https://docs.python.org/2/library/collections.html\\\" target=\\\"_blank\\\">collections</a>. If you need more libraries, you can import it yourself.</p>\\r\\n\\r\\n<p>For Map/TreeMap data structure, you may use <a href=\\\"http://www.grantjenks.com/docs/sortedcontainers/\\\" target=\\\"_blank\\\">sortedcontainers</a> library.</p>\\r\\n\\r\\n<p>Note that Python 2.7 <a href=\\\"https://www.python.org/dev/peps/pep-0373/\\\" target=\\\"_blank\\\">will not be maintained past 2020</a>. For the latest Python, please choose Python3 instead.</p>\"], \"c\": [\"C\", \"<p>Compiled with <code>gcc 8.2</code> using the gnu99 standard.</p>\\r\\n\\r\\n<p>Your code is compiled with level one optimization (<code>-O1</code>). <a href=\\\"https://github.com/google/sanitizers/wiki/AddressSanitizer\\\" target=\\\"_blank\\\">AddressSanitizer</a> is also enabled to help detect out-of-bounds and use-after-free bugs.</p>\\r\\n\\r\\n<p>Most standard library headers are already included automatically for your convenience.</p>\\r\\n\\r\\n<p>For hash table operations, you may use <a href=\\\"https://troydhanson.github.io/uthash/\\\" target=\\\"_blank\\\">uthash</a>. \\\"uthash.h\\\" is included by default. Below are some examples:</p>\\r\\n\\r\\n<p><b>1. Adding an item to a hash.</b>\\r\\n<pre>\\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</pre>\\r\\n</p>\\r\\n\\r\\n<p><b>2. Looking up an item in a hash:</b>\\r\\n<pre>\\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</pre>\\r\\n</p>\\r\\n\\r\\n<p><b>3. Deleting an item in a hash:</b>\\r\\n<pre>\\r\\nvoid delete_user(struct hash_entry *user) {\\r\\n    HASH_DEL(users, user);  \\r\\n}\\r\\n</pre>\\r\\n</p>\"], \"csharp\": [\"C#\", \"<p><a href=\\\"https://docs.microsoft.com/en-us/dotnet/csharp/whats-new/csharp-9\\\" target=\\\"_blank\\\">C# 10 with .NET 6 runtime</a></p>\\r\\n\\r\\n<p>Your code is compiled with debug flag enabled (<code>/debug</code>).</p>\"], \"javascript\": [\"JavaScript\", \"<p><code>Node.js 16.13.2</code>.</p>\\r\\n\\r\\n<p>Your code is run with <code>--harmony</code> flag, enabling <a href=\\\"http://node.green/\\\" target=\\\"_blank\\\">new ES6 features</a>.</p>\\r\\n\\r\\n<p><a href=\\\"https://lodash.com\\\" target=\\\"_blank\\\">lodash.js</a> library is included by default.</p>\\r\\n\\r\\n<p>For Priority Queue / Queue data structures, you may use <a href=\\\"https://github.com/datastructures-js/priority-queue\\\" target=\\\"_blank\\\">datastructures-js/priority-queue</a> and <a href=\\\"https://github.com/datastructures-js/queue\\\" target=\\\"_blank\\\">datastructures-js/queue</a>.</p>\"], \"ruby\": [\"Ruby\", \"<p><code>Ruby 3.1</code></p>\\r\\n\\r\\n<p>Some common data structure implementations are provided in the Algorithms module: https://www.rubydoc.info/github/kanwei/algorithms/Algorithms</p>\"], \"swift\": [\"Swift\", \"<p><code>Swift 5.5.2</code>.</p>\"], \"golang\": [\"Go\", \"<p><code>Go 1.17.6</code>.</p>\\r\\n\\r\\n<p>Support <a href=\\\"https://godoc.org/github.com/emirpasic/gods\\\" target=\\\"_blank\\\">https://godoc.org/github.com/emirpasic/gods</a> library.</p>\"], \"python3\": [\"Python3\", \"<p><code>Python 3.10</code>.</p>\\r\\n\\r\\n<p>Most libraries are already imported automatically for your convenience, such as <a href=\\\"https://docs.python.org/3/library/array.html\\\" target=\\\"_blank\\\">array</a>, <a href=\\\"https://docs.python.org/3/library/bisect.html\\\" target=\\\"_blank\\\">bisect</a>, <a href=\\\"https://docs.python.org/3/library/collections.html\\\" target=\\\"_blank\\\">collections</a>. If you need more libraries, you can import it yourself.</p>\\r\\n\\r\\n<p>For Map/TreeMap data structure, you may use <a href=\\\"http://www.grantjenks.com/docs/sortedcontainers/\\\" target=\\\"_blank\\\">sortedcontainers</a> library.</p>\"], \"scala\": [\"Scala\", \"<p><code>Scala 2.13.7</code>.</p>\"], \"kotlin\": [\"Kotlin\", \"<p><code>Kotlin 1.3.10</code>.</p>\"], \"rust\": [\"Rust\", \"<p><code>Rust 1.58.1</code></p>\\r\\n\\r\\n<p>Supports <a href=\\\"https://crates.io/crates/rand\\\" target=\\\"_blank\\\">rand </a> v0.6\\u00a0from crates.io</p>\"], \"php\": [\"PHP\", \"<p><code>PHP 8.1</code>.</p>\\r\\n<p>With bcmath module</p>\"], \"typescript\": [\"Typescript\", \"<p><code>TypeScript 4.5.4, Node.js 16.13.2</code>.</p>\\r\\n\\r\\n<p>Your code is run with <code>--harmony</code> flag, enabling <a href=\\\"http://node.green/\\\" target=\\\"_blank\\\">new ES2020 features</a>.</p>\\r\\n\\r\\n<p><a href=\\\"https://lodash.com\\\" target=\\\"_blank\\\">lodash.js</a> library is included by default.</p>\"], \"racket\": [\"Racket\", \"<p>Run with <code>Racket 8.3</code>.</p>\"], \"erlang\": [\"Erlang\", \"Erlang/OTP 24.2\"], \"elixir\": [\"Elixir\", \"Elixir 1.13.0 with Erlang/OTP 24.2\"]}",
            "libraryUrl": null,
            "adminUrl": null,
            "challengeQuestion": null,
            "__typename": "QuestionNode"
        }
    }
}