LeetCode每日一题(1462. Course Schedule IV)

There are a total of numCourses courses you have to take, labeled from 0 to numCourses - 1. You are given an array prerequisites where prerequisites[i] = [ai, bi] indicates that you must take course ai first if you want to take course bi.

For example, the pair [0, 1] indicates that you have to take course 0 before you can take course 1.
Prerequisites can also be indirect. If course a is a prerequisite of course b, and course b is a prerequisite of course c, then course a is a prerequisite of course c.

You are also given an array queries where queries[j] = [uj, vj]. For the jth query, you should answer whether course uj is a prerequisite of course vj or not.

Return a boolean array answer, where answer[j] is the answer to the jth query.

Example 1:

Input: numCourses = 2, prerequisites = [[1,0]], queries = [[0,1],[1,0]]
Output: [false,true]

Explanation: The pair [1, 0] indicates that you have to take course 1 before you can take course 0.
Course 0 is not a prerequisite of course 1, but the opposite is true.

Example 2:

Input: numCourses = 2, prerequisites = [], queries = [[1,0],[0,1]]
Output: [false,false]

Explanation: There are no prerequisites, and each course is independent.

Example 3:

Input: numCourses = 3, prerequisites = [[1,2],[1,0],[2,0]], queries = [[1,0],[1,2]]
Output: [true,true]

Constraints:

• 2 <= numCourses <= 100
• 0 <= prerequisites.length <= (numCourses * (numCourses - 1) / 2)
• prerequisites[i].length == 2
• 0 <= ai, bi <= n - 1
• ai != bi
• All the pairs [ai, bi] are unique.
• The prerequisites graph has no cycles.
• 1 <= queries.length <= 104
• 0 <= ui, vi <= n - 1
• ui != vi

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开始想用 union-find 的方式来做， 后来发现对于这种注重中间节点的问题，用 union-find 会比较麻烦。然后就改用 dp。整体思路很简单， 就是找到所有 course 的依赖。

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use std::collections::{HashMap, HashSet};

impl Solution {
    fn find(prerequisites: &Vec<Vec<i32>>, course: i32, cache: &mut HashMap<i32, HashSet<i32>>) -> HashSet<i32> {
        if let Some(c) = cache.get(&course) {
            return c.clone();
        }
        let mut ans = HashSet::new();
        for &p in &prerequisites[course as usize] {
            ans.insert(p);
            let next = Solution::find(prerequisites, p, cache);
            ans.extend(&next)
        }
        cache.insert(course, ans.clone());
        ans
    }
    pub fn check_if_prerequisite(num_courses: i32, prerequisites: Vec<Vec<i32>>, queries: Vec<Vec<i32>>) -> Vec<bool> {
        let mut pres: Vec<Vec<i32>> = vec![Vec::new(); num_courses as usize];
        for p in prerequisites {
            pres[p[1] as usize].push(p[0]);
        }
        let mut cache = HashMap::new();
        let ps: Vec<HashSet<i32>> = (0..num_courses).into_iter().map(|c| Solution::find(&pres, c, &mut cache)).collect();
        queries.into_iter().map(|q| ps[q[1] as usize].contains(&q[0])).collect()
    }
}