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

/**
 * @param {number} numCourses
 * @param {number[][]} prerequisites
 * @return {boolean}
 */
const WHITE = 0;
const GRAY = 1;
const BLACK = 2;

var canFinish = function(numCourses, prerequisites) {
    const adj = Array.from({ length: numCourses }, () => []);

    for (const [course, prerequisite] of prerequisites) {
        adj[prerequisite].push(course);
    }

    const colors = new Array(numCourses).fill(WHITE);

    for (let i = 0; i < numCourses; i++) {
        if (colors[i] === WHITE && adj[i].length > 0 && hasCycle(adj, i, colors)) {
            return false;
        }
    }

    return true;
};

var hasCycle = function(adj, node, colors) {
    colors[node] = GRAY;

    for (const neighbor of adj[node]) {
        if (colors[neighbor] === GRAY) {
            return true;
        }
        if (colors[neighbor] === WHITE && hasCycle(adj, neighbor, colors)) {
            return true;
        }
    }

    colors[node] = BLACK;
    return false;
};

export { canFinish }

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