LeetCode-in-All

207. Course Schedule

Medium

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] = [a_i, b_i] indicates that you must take course b_i first if you want to take course a_i.

For example, the pair [0, 1], indicates that to take course 0 you have to first take course 1.

Return true if you can finish all courses. Otherwise, return false.

Example 1:

Input: numCourses = 2, prerequisites = [[1,0]]

Output: true

Explanation: There are a total of 2 courses to take. To take course 1 you should have finished course 0. So it is possible.

Example 2:

Input: numCourses = 2, prerequisites = [[1,0],[0,1]]

Output: false

Explanation: There are a total of 2 courses to take. To take course 1 you should have finished course 0, and to take course 0 you should also have finished course 1. So it is impossible.

Constraints:

1 <= numCourses <= 2000
0 <= prerequisites.length <= 5000
prerequisites[i].length == 2
0 <= a_i, b_i < numCourses
All the pairs prerequisites[i] are unique.

Solution

impl Solution {
    const WHITE: i32 = 0;
    const GRAY: i32 = 1;
    const BLACK: i32 = 2;

    pub fn can_finish(num_courses: i32, prerequisites: Vec<Vec<i32>>) -> bool {
        let num_courses = num_courses as usize;
        let mut adj: Vec<Vec<i32>> = vec![vec![]; num_courses];
        let mut colors: Vec<i32> = vec![Self::WHITE; num_courses];

        for pre in prerequisites.iter() {
            adj[pre[1] as usize].push(pre[0]);
        }

        for i in 0..num_courses {
            if colors[i] == Self::WHITE && !adj[i].is_empty() {
                if Self::has_cycle(&adj, i, &mut colors) {
                    return false;
                }
            }
        }

        true
    }

    fn has_cycle(adj: &Vec<Vec<i32>>, node: usize, colors: &mut Vec<i32>) -> bool {
        colors[node] = Self::GRAY;

        for &neighbor in adj[node].iter() {
            let neighbor = neighbor as usize;
            if colors[neighbor] == Self::GRAY {
                return true;
            }
            if colors[neighbor] == Self::WHITE {
                if Self::has_cycle(adj, neighbor, colors) {
                    return true;
                }
            }
        }

        colors[node] = Self::BLACK;
        false
    }
}

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