2050. Parallel Courses III Hard

1/**
2 * [2050] Parallel Courses III
3 *
4 * 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.
5 * You must find the minimum number of months needed to complete all the courses following these rules:
6 * 
7 * 	You may start taking a course at any time if the prerequisites are met.
8 * 	Any number of courses can be taken at the same time.
9 * 
10 * Return the minimum number of months needed to complete all the courses.
11 * Note: The test cases are generated such that it is possible to complete every course (i.e., the graph is a directed acyclic graph).
12 *  
13 * Example 1:
14 * <img alt="" src="https://assets.leetcode.com/uploads/2021/10/07/ex1.png" style="width: 392px; height: 232px;" />
15 * 
16 * Input: n = 3, relations = [[1,3],[2,3]], time = [3,2,5]
17 * Output: 8
18 * Explanation: The figure above represents the given graph and the time required to complete each course. 
19 * We start course 1 and course 2 simultaneously at month 0.
20 * Course 1 takes 3 months and course 2 takes 2 months to complete respectively.
21 * Thus, the earliest time we can start course 3 is at month 3, and the total time required is 3 + 5 = 8 months.
22 * 
23 * Example 2:
24 * <img alt="" src="https://assets.leetcode.com/uploads/2021/10/07/ex2.png" style="width: 500px; height: 365px;" />
25 * 
26 * Input: n = 5, relations = [[1,5],[2,5],[3,5],[3,4],[4,5]], time = [1,2,3,4,5]
27 * Output: 12
28 * Explanation: The figure above represents the given graph and the time required to complete each course.
29 * You can start courses 1, 2, and 3 at month 0.
30 * You can complete them after 1, 2, and 3 months respectively.
31 * Course 4 can be taken only after course 3 is completed, i.e., after 3 months. It is completed after 3 + 4 = 7 months.
32 * Course 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.
33 * Thus, the minimum time needed to complete all the courses is 7 + 5 = 12 months.
34 * 
35 *  
36 * Constraints:
37 * 
38 * 	1 <= n <= 5 * 10^4
39 * 	0 <= relations.length <= min(n * (n - 1) / 2, 5 * 10^4)
40 * 	relations[j].length == 2
41 * 	1 <= prevCoursej, nextCoursej <= n
42 * 	prevCoursej != nextCoursej
43 * 	All the pairs [prevCoursej, nextCoursej] are unique.
44 * 	time.length == n
45 * 	1 <= time[i] <= 10^4
46 * 	The given graph is a directed acyclic graph.
47 * 
48 */
49pub struct Solution {}
50
51// problem: https://leetcode.com/problems/parallel-courses-iii/
52// discuss: https://leetcode.com/problems/parallel-courses-iii/discuss/?currentPage=1&orderBy=most_votes&query=
53
54// submission codes start here
55
56impl Solution {
57    pub fn minimum_time(n: i32, relations: Vec<Vec<i32>>, time: Vec<i32>) -> i32 {
58        0
59    }
60}
61
62// submission codes end
63
64#[cfg(test)]
65mod tests {
66    use super::*;
67
68    #[test]
69    fn test_2050() {
70    }
71}
72