207. Course Schedule

[Tcdian]

207. Course Schedule

你这个学期必须选修 numCourse 门课程，记为 0 到 numCourse-1 。

在选修某些课程之前需要一些先修课程。 例如，想要学习课程 0 ，你需要先完成课程 1 ，我们用一个匹配来表示他们：[0,1]

给定课程总量以及它们的先决条件，请你判断是否可能完成所有课程的学习？

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.

Note:

• 输入的先决条件是由 边缘列表 表示的图形，而不是 邻接矩阵 。
• 你可以假定输入的先决条件中没有重复的边。
• 1 <= numCourses <= 10^5

[Tcdian]

Solution

• JavaScript Solution

const Status = {
    initial: 0,
    visiting: 1,
    visited: 2,
}

/**
 * @param {number} numCourses
 * @param {number[][]} prerequisites
 * @return {boolean}
 */
var canFinish = function(numCourses, prerequisites) {
    const graph = Array.from(new Array(numCourses), () => []);
    for (let i = 0; i < prerequisites.length; i++) {
        const [course, preCourse] = prerequisites[i];
        graph[preCourse].push(course);
    }
    const statuses = new Array(numCourses).fill(Status.initial);
    for (let i = 0; i < numCourses; i++) {
        if (hasCycle(i)) {
            return false;
        }
    }
    return true;

    function hasCycle(course) {
        if (statuses[course] === Status.visited) {
            return false;
        }
        if (statuses[course] === Status.visiting) {
            return true;
        }
        statuses[course] = Status.visiting;
        const courses = graph[course];
        for (let i = 0; i < courses.length; i++) {
            if (hasCycle(courses[i])) {
                return true;
            }
        }
        statuses[course] = Status.visited;
        return false;
    }
};

• TypeScript Solution

enum Status {
    initial,
    visiting,
    visited,
}

function canFinish(numCourses: number, prerequisites: number[][]): boolean {
    const graph: number[][] = Array.from(new Array(numCourses), () => []);
    for (let i = 0; i < prerequisites.length; i++) {
        const [course, preCourse] = prerequisites[i];
        graph[preCourse].push(course);
    }
    const statuses: Status[] = new Array(numCourses).fill(Status.initial);
    for (let i = 0; i < numCourses; i++) {
        if (hasCycle(i)) {
            return false;
        }
    }
    return true;

    function hasCycle(course: number): boolean {
        if (statuses[course] === Status.visited) {
            return false;
        }
        if (statuses[course] === Status.visiting) {
            return true;
        }
        statuses[course] = Status.visiting;
        const courses = graph[course];
        for (let i = 0; i < courses.length; i++) {
            if (hasCycle(courses[i])) {
                return true;
            }
        }
        statuses[course] = Status.visited;
        return false;
    }
};