Published May 23, 2022
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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 bi first if
you want to take course ai.
[0, 1], indicates that to take course 0 you have
to first take course 1.Return the ordering of courses you should take to finish all courses. If there are many valid answers, return any of them. If it is impossible to finish all courses, return an empty array.
Input: numCourses = 2, prerequisites = [[1,0]]
Output: [0,1]
Explanation: There are a total of 2 courses to take. To take course 1 you should have finished course 0. So the correct course order is [0,1].
Input: numCourses = 4, prerequisites = [[1,0],[2,0],[3,1],[3,2]]
Output: [0,2,1,3]
Explanation: There are a total of 4 courses to take. To take course 3 you should have finished both courses 1 and 2. Both courses 1 and 2 should be taken after you finished course 0.
So one correct course order is [0,1,2,3]. Another correct ordering is [0,2,1,3].
Input: numCourses = 1, prerequisites = []
Output: [0]
1 <= numCourses <= 20000 <= prerequisites.length <= numCourses * (numCourses - 1)prerequisites[i].length == 20 <= ai, bi < numCoursesai != bi[ai, bi] are distinct.function findOrder(numCourses: number, prerequisites: number[][]): number[] {
const res: Set<number> = new Set<number>();
const graph: number[][] = Array.from({length: numCourses}, () => []);
const visited: Set<number> = new Set<number>();
for(const [course, pre] of prerequisites){
graph[course].push(pre);
}
const dfs = (course: number): boolean => {
if(graph[course].length === 0){
res.add(course);
return true;
}
if(visited.has(course)) return false;
visited.add(course);
for(const pre of graph[course]){
if(dfs(pre) === false){
return false;
}
}
graph[course] = [];
res.add(course);
return true;
}
for(let i = 0; i < numCourses; i++){
if(dfs(i) === false){
return []
}
}
return [...res];
};
function findOrder(numCourses: number, prerequisites: number[][]): number[] {
const res: number[] = [];
const coursePreCounts: number[] = Array(numCourses).fill(0);
const graph: number[][] = Array.from({length: numCourses}, () => []);
const queue: number[] = [];
for(let [course, pre] of prerequisites){
graph[pre].push(course);
coursePreCounts[course]++;
}
coursePreCounts.forEach((count, index) => {
if(count === 0){
res.push(index);
queue.push(index)
}
})
while(queue.length > 0){
const curCourse = queue.shift();
numCourses--;
graph[curCourse].forEach(course => {
if(--coursePreCounts[course] === 0){
res.push(course);
queue.push(course)
}
})
}
return numCourses ? [] : res;
};