{ "data": { "question": { "questionId": "2176", "questionFrontendId": "2050", "categoryTitle": "Algorithms", "boundTopicId": 1058758, "title": "Parallel Courses III", "titleSlug": "parallel-courses-iii", "content": "

You are given an integer n, which indicates that there are n courses labeled from 1 to n. You are also given a 2D integer array relations where relations[j] = [prevCoursej, nextCoursej] denotes that course prevCoursej has to be completed before course nextCoursej (prerequisite relationship). Furthermore, you are given a 0-indexed integer array time where time[i] denotes how many months it takes to complete the (i+1)th course.

\n\n

You must find the minimum number of months needed to complete all the courses following these rules:

\n\n\n\n

Return the minimum number of months needed to complete all the courses.

\n\n

Note: The test cases are generated such that it is possible to complete every course (i.e., the graph is a directed acyclic graph).

\n\n

 

\n

Example 1:

\n\"\"\n\n
\nInput: n = 3, relations = [[1,3],[2,3]], time = [3,2,5]\nOutput: 8\nExplanation: The figure above represents the given graph and the time required to complete each course. \nWe start course 1 and course 2 simultaneously at month 0.\nCourse 1 takes 3 months and course 2 takes 2 months to complete respectively.\nThus, the earliest time we can start course 3 is at month 3, and the total time required is 3 + 5 = 8 months.\n
\n\n

Example 2:

\n\"\"\n\n
\nInput: n = 5, relations = [[1,5],[2,5],[3,5],[3,4],[4,5]], time = [1,2,3,4,5]\nOutput: 12\nExplanation: The figure above represents the given graph and the time required to complete each course.\nYou can start courses 1, 2, and 3 at month 0.\nYou can complete them after 1, 2, and 3 months respectively.\nCourse 4 can be taken only after course 3 is completed, i.e., after 3 months. It is completed after 3 + 4 = 7 months.\nCourse 5 can be taken only after courses 1, 2, 3, and 4 have been completed, i.e., after max(1,2,3,7) = 7 months.\nThus, the minimum time needed to complete all the courses is 7 + 5 = 12 months.\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "并行课程 III", "translatedContent": "

给你一个整数 n ，表示有 n 节课，课程编号从 1 到 n 。同时给你一个二维整数数组 relations ，其中 relations[j] = [prevCoursej, nextCoursej] ，表示课程 prevCoursej 必须在课程 nextCoursej 之前 完成（先修课的关系）。同时给你一个下标从 0 开始的整数数组 time ，其中 time[i] 表示完成第 (i+1) 门课程需要花费的 月份 数。

\n\n

请你根据以下规则算出完成所有课程所需要的 最少 月份数：

\n\n\n\n

请你返回完成所有课程所需要的 最少 月份数。

\n\n

注意：测试数据保证一定可以完成所有课程（也就是先修课的关系构成一个有向无环图）。

\n\n

 

\n\n

示例 1:

\n\n

\"\"

\n\n
输入：n = 3, relations = [[1,3],[2,3]], time = [3,2,5]\n输出：8\n解释：上图展示了输入数据所表示的先修关系图，以及完成每门课程需要花费的时间。\n你可以在月份 0 同时开始课程 1 和 2 。\n课程 1 花费 3 个月，课程 2 花费 2 个月。\n所以，最早开始课程 3 的时间是月份 3 ，完成所有课程所需时间为 3 + 5 = 8 个月。\n
\n\n

示例 2：

\n\n

\"\"

\n\n
输入：n = 5, relations = [[1,5],[2,5],[3,5],[3,4],[4,5]], time = [1,2,3,4,5]\n输出：12\n解释：上图展示了输入数据所表示的先修关系图，以及完成每门课程需要花费的时间。\n你可以在月份 0 同时开始课程 1 ，2 和 3 。\n在月份 1，2 和 3 分别完成这三门课程。\n课程 4 需在课程 3 之后开始，也就是 3 个月后。课程 4 在 3 + 4 = 7 月完成。\n课程 5 需在课程 1，2，3 和 4 之后开始，也就是在 max(1,2,3,7) = 7 月开始。\n所以完成所有课程所需的最少时间为 7 + 5 = 12 个月。\n
\n\n

 

\n\n

提示：

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