README_EN.md

210. Course Schedule II

中文文档

Description

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.

• For example, the pair [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.

 

Example 1:

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].

Example 2:

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].

Example 3:

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

 

Constraints:

• 1 <= numCourses <= 2000
• 0 <= prerequisites.length <= numCourses * (numCourses - 1)
• prerequisites[i].length == 2
• 0 <= ai, bi < numCourses
• ai != bi
• All the pairs [ai, bi] are distinct.

Solutions

Python3

class Solution:
    def findOrder(self, numCourses: int, prerequisites: List[List[int]]) -> List[int]:
        g = defaultdict(list)
        indeg = [0] * numCourses
        for a, b in prerequisites:
            g[b].append(a)
            indeg[a] += 1
        ans = []
        q = deque(i for i, x in enumerate(indeg) if x == 0)
        while q:
            i = q.popleft()
            ans.append(i)
            for j in g[i]:
                indeg[j] -= 1
                if indeg[j] == 0:
                    q.append(j)
        return ans if len(ans) == numCourses else []

Java

class Solution {
    public int[] findOrder(int numCourses, int[][] prerequisites) {
        List<Integer>[] g = new List[numCourses];
        Arrays.setAll(g, k -> new ArrayList<>());
        int[] indeg = new int[numCourses];
        for (var p : prerequisites) {
            int a = p[0], b = p[1];
            g[b].add(a);
            ++indeg[a];
        }
        Deque<Integer> q = new ArrayDeque<>();
        for (int i = 0; i < numCourses; ++i) {
            if (indeg[i] == 0) {
                q.offer(i);
            }
        }
        int[] ans = new int[numCourses];
        int cnt = 0;
        while (!q.isEmpty()) {
            int i = q.poll();
            ans[cnt++] = i;
            for (int j : g[i]) {
                if (--indeg[j] == 0) {
                    q.offer(j);
                }
            }
        }
        return cnt == numCourses ? ans : new int[0];
    }
}

C++

class Solution {
public:
    vector<int> findOrder(int numCourses, vector<vector<int>>& prerequisites) {
        vector<vector<int>> g(numCourses);
        vector<int> indeg(numCourses);
        for (auto& p : prerequisites) {
            int a = p[0], b = p[1];
            g[b].push_back(a);
            ++indeg[a];
        }
        queue<int> q;
        for (int i = 0; i < numCourses; ++i) {
            if (indeg[i] == 0) {
                q.push(i);
            }
        }
        vector<int> ans;
        while (!q.empty()) {
            int i = q.front();
            q.pop();
            ans.push_back(i);
            for (int j : g[i]) {
                if (--indeg[j] == 0) {
                    q.push(j);
                }
            }
        }
        return ans.size() == numCourses ? ans : vector<int>();
    }
};

Go

func findOrder(numCourses int, prerequisites [][]int) []int {
	g := make([][]int, numCourses)
	indeg := make([]int, numCourses)
	for _, p := range prerequisites {
		a, b := p[0], p[1]
		g[b] = append(g[b], a)
		indeg[a]++
	}
	q := []int{}
	for i, x := range indeg {
		if x == 0 {
			q = append(q, i)
		}
	}
	ans := []int{}
	for len(q) > 0 {
		i := q[0]
		q = q[1:]
		ans = append(ans, i)
		for _, j := range g[i] {
			indeg[j]--
			if indeg[j] == 0 {
				q = append(q, j)
			}
		}
	}
	if len(ans) == numCourses {
		return ans
	}
	return []int{}
}

TypeScript

function findOrder(numCourses: number, prerequisites: number[][]): number[] {
    const g: number[][] = new Array(numCourses).fill(0).map(() => []);
    const indeg: number[] = new Array(numCourses).fill(0);
    for (const [a, b] of prerequisites) {
        g[b].push(a);
        indeg[a]++;
    }
    const q: number[] = [];
    for (let i = 0; i < numCourses; ++i) {
        if (indeg[i] == 0) {
            q.push(i);
        }
    }
    const ans: number[] = [];
    while (q.length) {
        const i = q.shift()!;
        ans.push(i);
        for (const j of g[i]) {
            if (--indeg[j] == 0) {
                q.push(j);
            }
        }
    }
    return ans.length === numCourses ? ans : [];
}

C#

public class Solution {
    public int[] FindOrder(int numCourses, int[][] prerequisites) {
        var g = new List<int>[numCourses];
        for (int i = 0; i < numCourses; ++i) {
            g[i] = new List<int>();
        }
        var indeg = new int[numCourses];
        foreach (var p in prerequisites) {
            int a = p[0], b = p[1];
            g[b].Add(a);
            ++indeg[a];
        }
        var q = new Queue<int>();
        for (int i = 0; i < numCourses; ++i) {
            if (indeg[i] == 0) {
                q.Enqueue(i);
            }
        }
        var ans = new int[numCourses];
        var cnt = 0;
        while (q.Count > 0) {
            int i = q.Dequeue();
            ans[cnt++] = i;
            foreach (int j in g[i]) {
                if (--indeg[j] == 0) {
                    q.Enqueue(j);
                }
            }
        }
        return cnt == numCourses ? ans : new int[0];
    }
}

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