mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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180 lines
18 KiB
JSON
180 lines
18 KiB
JSON
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"questionId": "1587",
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"questionFrontendId": "1494",
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"title": "Parallel Courses II",
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"titleSlug": "parallel-courses-ii",
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"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> </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> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= n <= 15</code></li>\n\t<li><code>1 <= k <= n</code></li>\n\t<li><code>0 <= relations.length <= n * (n-1) / 2</code></li>\n\t<li><code>relations[i].length == 2</code></li>\n\t<li><code>1 <= prevCourse<sub>i</sub>, nextCourse<sub>i</sub> <= 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",
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"difficulty": "Hard",
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"exampleTestcases": "4\n[[2,1],[3,1],[1,4]]\n2\n5\n[[2,1],[3,1],[4,1],[1,5]]\n2\n11\n[]\n2",
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"categoryTitle": "Algorithms",
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"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 ",
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"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",
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"code": "class Solution {\n func minNumberOfSemesters(_ n: Int, _ relations: [[Int]], _ k: Int) -> Int {\n \n }\n}",
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"code": "object Solution {\n def minNumberOfSemesters(n: Int, relations: Array[Array[Int]], k: Int): Int = {\n \n }\n}",
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"code": "class Solution {\n fun minNumberOfSemesters(n: Int, relations: Array<IntArray>, k: Int): Int {\n \n }\n}",
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"code": "impl Solution {\n pub fn min_number_of_semesters(n: i32, relations: Vec<Vec<i32>>, k: i32) -> i32 {\n \n }\n}",
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"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}",
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"code": "(define/contract (min-number-of-semesters n relations k)\n (-> exact-integer? (listof (listof exact-integer?)) exact-integer? exact-integer?)\n\n )",
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"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).",
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"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."
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