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‎Problemset/2050-Parallel Courses III/README.md

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# 2050. Parallel Courses III
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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 <code>relations[j] = [prevCourse<sub>j</sub>, nextCourse<sub>j</sub>]</code> denotes that course <code>prevCourse<sub>j</sub></code> has to be completed before course <code>nextCourse<sub>j</sub></code> (prerequisite relationship). Furthermore, you are given a 0-indexed integer array `time` where `time[i]` denotes how many months it takes to complete the <code>(i+1)<sup>th</sup></code> course.
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You must find the **minimum** number of months needed to complete all the courses following these rules:
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* You may start taking a course at **any time** if the prerequisites are met.
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* **Any number of courses** can be taken at the **same time**.
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Return *the **minimum** number of months needed to complete all the courses*.
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**Note:** The test cases are generated such that it is possible to complete every course (i.e., the graph is a directed acyclic graph).
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#### Example 1:
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![](https://assets.leetcode.com/uploads/2021/10/07/ex1.png)
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<pre>
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<strong>Input:</strong> n = 3, relations = [[1,3],[2,3]], time = [3,2,5]
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<strong>Output:</strong> 8
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<strong>Explanation:</strong> The figure above represents the given graph and the time required to complete each course.
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We start course 1 and course 2 simultaneously at month 0.
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Course 1 takes 3 months and course 2 takes 2 months to complete respectively.
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Thus, the earliest time we can start course 3 is at month 3, and the total time required is 3 + 5 = 8 months.
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</pre>
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#### Example 2:
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![](https://assets.leetcode.com/uploads/2021/10/07/ex2.png)
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<pre>
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<strong>Input:</strong> n = 5, relations = [[1,5],[2,5],[3,5],[3,4],[4,5]], time = [1,2,3,4,5]
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<strong>Output:</strong> 12
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<strong>Explanation:</strong> The figure above represents the given graph and the time required to complete each course.
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You can start courses 1, 2, and 3 at month 0.
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You can complete them after 1, 2, and 3 months respectively.
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Course 4 can be taken only after course 3 is completed, i.e., after 3 months. It is completed after 3 + 4 = 7 months.
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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.
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Thus, the minimum time needed to complete all the courses is 7 + 5 = 12 months.
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</pre>
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#### Constraints:
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* <code>1 <= n <= 5 * 10<sup>4</sup></code>
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* <code>0 <= relations.length <= min(n * (n - 1) / 2, 5 * 10<sup>4</sup>)</code>
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* `relations[j].length == 2`
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* <code>1 <= prevCourse<sub>j</sub>, nextCourse<sub>j</sub> <= n</code>
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* <code>prevCourse<sub>j</sub> != nextCourse<sub>j</sub></code>
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* All the pairs <code>[prevCourse<sub>j</sub>, nextCourse<sub>j</sub>]</code> are **unique**.
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* `time.length == n`
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* <code>1 <= time[i] <= 10<sup>4</sup></code>
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* The given graph is a directed acyclic graph.
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## Solutions (Rust)
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### 1. Solution
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```Rust
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impl Solution {
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pub fn minimum_time(n: i32, relations: Vec<Vec<i32>>, time: Vec<i32>) -> i32 {
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let mut next_courses = vec![vec![]; n as usize];
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let mut indgree = vec![0; n as usize];
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let mut start = vec![0; n as usize];
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let mut stack = vec![];
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let mut ret = 0;
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for relation in &relations {
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let (prev, next) = (relation[0] as usize - 1, relation[1] as usize - 1);
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next_courses[prev].push(next);
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indgree[next] += 1;
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}
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for i in 0..n as usize {
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if indgree[i] == 0 {
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stack.push(i);
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}
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}
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while let Some(prev) = stack.pop() {
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let end = start[prev] + time[prev];
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for &next in &next_courses[prev] {
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indgree[next] -= 1;
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start[next] = start[next].max(end);
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if indgree[next] == 0 {
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stack.push(next);
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}
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}
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ret = ret.max(end);
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}
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ret
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}
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}
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```

‎Problemset/2050-Parallel Courses III/README_CN.md

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# 2050. 并行课程 III
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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 <code>relations[j] = [prevCourse<sub>j</sub>, nextCourse<sub>j</sub>]</code> ，表示课程 <code>prevCourse<sub>j</sub></code> 必须在课程 <code>nextCourse<sub>j</sub></code> 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。
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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：
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* 如果一门课的所有先修课都已经完成，你可以在 **任意** 时间开始这门课程。
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* 你可以 **同时** 上 **任意门课程** 。
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请你返回完成所有课程所需要的 **最少** 月份数。
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**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）。
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#### 示例 1:
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![](https://assets.leetcode.com/uploads/2021/10/07/ex1.png)
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<pre>
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<strong>输入:</strong> n = 3, relations = [[1,3],[2,3]], time = [3,2,5]
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<strong>输出:</strong> 8
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<strong>解释:</strong> 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。
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你可以在月份 0 同时开始课程 1 和 2 。
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课程 1 花费 3 个月，课程 2 花费 2 个月。
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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。
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</pre>
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#### 示例 2:
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![](https://assets.leetcode.com/uploads/2021/10/07/ex2.png)
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<pre>
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<strong>输入:</strong> n = 5, relations = [[1,5],[2,5],[3,5],[3,4],[4,5]], time = [1,2,3,4,5]
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<strong>输出:</strong> 12
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<strong>解释:</strong> 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。
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你可以在月份 0 同时开始课程 1 ，2 和 3 。
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在月份 1，2 和 3 分别完成这三门课程。
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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。
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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。
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所以完成所有课程所需的最少时间为 7 + 5 = 12 个月。
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</pre>
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#### 提示:
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* <code>1 <= n <= 5 * 10<sup>4</sup></code>
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* <code>0 <= relations.length <= min(n * (n - 1) / 2, 5 * 10<sup>4</sup>)</code>
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* `relations[j].length == 2`
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* <code>1 <= prevCourse<sub>j</sub>, nextCourse<sub>j</sub> <= n</code>
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* <code>prevCourse<sub>j</sub> != nextCourse<sub>j</sub></code>
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* 所有的先修课程对 <code>[prevCourse<sub>j</sub>, nextCourse<sub>j</sub>]</code> 都是 **互不相同** 的。
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* `time.length == n`
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* <code>1 <= time[i] <= 10<sup>4</sup></code>
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* 先修课程图是一个有向无环图。
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## 题解 (Rust)
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### 1. 题解
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```Rust
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impl Solution {
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pub fn minimum_time(n: i32, relations: Vec<Vec<i32>>, time: Vec<i32>) -> i32 {
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let mut next_courses = vec![vec![]; n as usize];
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let mut indgree = vec![0; n as usize];
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let mut start = vec![0; n as usize];
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let mut stack = vec![];
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let mut ret = 0;
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for relation in &relations {
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let (prev, next) = (relation[0] as usize - 1, relation[1] as usize - 1);
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next_courses[prev].push(next);
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indgree[next] += 1;
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}
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for i in 0..n as usize {
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if indgree[i] == 0 {
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stack.push(i);
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}
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}
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while let Some(prev) = stack.pop() {
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let end = start[prev] + time[prev];
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for &next in &next_courses[prev] {
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indgree[next] -= 1;
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start[next] = start[next].max(end);
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if indgree[next] == 0 {
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stack.push(next);
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}
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}
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ret = ret.max(end);
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}
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ret
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}
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}
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```

‎Problemset/2050-Parallel Courses III/Solution.rs

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impl Solution {
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pub fn minimum_time(n: i32, relations: Vec<Vec<i32>>, time: Vec<i32>) -> i32 {
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let mut next_courses = vec![vec![]; n as usize];
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let mut indgree = vec![0; n as usize];
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let mut start = vec![0; n as usize];
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let mut stack = vec![];
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let mut ret = 0;
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for relation in &relations {
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let (prev, next) = (relation[0] as usize - 1, relation[1] as usize - 1);
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next_courses[prev].push(next);
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indgree[next] += 1;
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}
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for i in 0..n as usize {
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if indgree[i] == 0 {
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stack.push(i);
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}
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}
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while let Some(prev) = stack.pop() {
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let end = start[prev] + time[prev];
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for &next in &next_courses[prev] {
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indgree[next] -= 1;
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start[next] = start[next].max(end);
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if indgree[next] == 0 {
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stack.push(next);
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}
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}
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ret = ret.max(end);
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}
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ret
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}
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}

‎README.md

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[2047][2047l]|[Number of Valid Words in a Sentence][2047] |![py]
12891289
[2048][2048l]|[Next Greater Numerically Balanced Number][2048] |![rs]
12901290
[2049][2049l]|[Count Nodes With the Highest Score][2049] |![rs]
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[2050][2050l]|[Parallel Courses III][2050] |![rs]
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[2053][2053l]|[Kth Distinct String in an Array][2053] |![py]
12921293
[2054][2054l]|[Two Best Non-Overlapping Events][2054] |![rs]
12931294
[2055][2055l]|[Plates Between Candles][2055] |![rs]
@@ -2911,6 +2912,7 @@
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[2047]:Problemset/2047-Number%20of%20Valid%20Words%20in%20a%20Sentence/README.md#2047-number-of-valid-words-in-a-sentence
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[2048]:Problemset/2048-Next%20Greater%20Numerically%20Balanced%20Number/README.md#2048-next-greater-numerically-balanced-number
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[2049]:Problemset/2049-Count%20Nodes%20With%20the%20Highest%20Score/README.md#2049-count-nodes-with-the-highest-score
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[2050]:Problemset/2050-Parallel%20Courses%20III/README.md#2050-parallel-courses-iii
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[2053]:Problemset/2053-Kth%20Distinct%20String%20in%20an%20Array/README.md#2053-kth-distinct-string-in-an-array
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[2054]:Problemset/2054-Two%20Best%20Non-Overlapping%20Events/README.md#2054-two-best-non-overlapping-events
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[2055]:Problemset/2055-Plates%20Between%20Candles/README.md#2055-plates-between-candles
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[2047l]:https://leetcode.com/problems/number-of-valid-words-in-a-sentence/
45294531
[2048l]:https://leetcode.com/problems/next-greater-numerically-balanced-number/
45304532
[2049l]:https://leetcode.com/problems/count-nodes-with-the-highest-score/
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[2050l]:https://leetcode.com/problems/parallel-courses-iii/
45314534
[2053l]:https://leetcode.com/problems/kth-distinct-string-in-an-array/
45324535
[2054l]:https://leetcode.com/problems/two-best-non-overlapping-events/
45334536
[2055l]:https://leetcode.com/problems/plates-between-candles/

‎README_CN.md

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[2047][2047l]|[句子中的有效单词数][2047] |![py]
12891289
[2048][2048l]|[下一个更大的数值平衡数][2048] |![rs]
12901290
[2049][2049l]|[统计最高分的节点数目][2049] |![rs]
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[2050][2050l]|[并行课程 III][2050] |![rs]
12911292
[2053][2053l]|[数组中第 K 个独一无二的字符串][2053] |![py]
12921293
[2054][2054l]|[两个最好的不重叠活动][2054] |![rs]
12931294
[2055][2055l]|[蜡烛之间的盘子][2055] |![rs]
@@ -2911,6 +2912,7 @@
29112912
[2047]:Problemset/2047-Number%20of%20Valid%20Words%20in%20a%20Sentence/README_CN.md#2047-句子中的有效单词数
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[2048]:Problemset/2048-Next%20Greater%20Numerically%20Balanced%20Number/README_CN.md#2048-下一个更大的数值平衡数
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[2049]:Problemset/2049-Count%20Nodes%20With%20the%20Highest%20Score/README_CN.md#2049-统计最高分的节点数目
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[2050]:Problemset/2050-Parallel%20Courses%20III/README_CN.md#2050-并行课程-iii
29142916
[2053]:Problemset/2053-Kth%20Distinct%20String%20in%20an%20Array/README_CN.md#2053-数组中第-k-个独一无二的字符串
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[2054]:Problemset/2054-Two%20Best%20Non-Overlapping%20Events/README_CN.md#2054-两个最好的不重叠活动
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[2055]:Problemset/2055-Plates%20Between%20Candles/README_CN.md#2055-蜡烛之间的盘子
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[2047l]:https://leetcode.cn/problems/number-of-valid-words-in-a-sentence/
45294531
[2048l]:https://leetcode.cn/problems/next-greater-numerically-balanced-number/
45304532
[2049l]:https://leetcode.cn/problems/count-nodes-with-the-highest-score/
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[2050l]:https://leetcode.cn/problems/parallel-courses-iii/
45314534
[2053l]:https://leetcode.cn/problems/kth-distinct-string-in-an-array/
45324535
[2054l]:https://leetcode.cn/problems/two-best-non-overlapping-events/
45334536
[2055l]:https://leetcode.cn/problems/plates-between-candles/

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