README.md

207. 课程表

English Version

题目描述

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

在选修某些课程之前需要一些先修课程。 先修课程按数组 prerequisites 给出，其中 prerequisites[i] = [ai, bi] ，表示如果要学习课程 ai 则 必须 先学习课程  bi 。

• 例如，先修课程对 [0, 1] 表示：想要学习课程 0 ，你需要先完成课程 1 。

请你判断是否可能完成所有课程的学习？如果可以，返回 true ；否则，返回 false 。

 

示例 1：

输入：numCourses = 2, prerequisites = [[1,0]]
输出：true
解释：总共有 2 门课程。学习课程 1 之前，你需要完成课程 0 。这是可能的。

示例 2：

输入：numCourses = 2, prerequisites = [[1,0],[0,1]]
输出：false
解释：总共有 2 门课程。学习课程 1 之前，你需要先完成​课程 0 ；并且学习课程 0 之前，你还应先完成课程 1 。这是不可能的。

 

提示：

• 1 <= numCourses <= 105
• 0 <= prerequisites.length <= 5000
• prerequisites[i].length == 2
• 0 <= ai, bi < numCourses
• prerequisites[i] 中的所有课程对 互不相同

解法

拓扑排序，BFS 实现。

Python3

class Solution:
    def canFinish(self, numCourses: int, prerequisites: List[List[int]]) -> bool:
        edges = collections.defaultdict(list)
        indegree = [0] * numCourses
        for i, j in prerequisites:
            edges[j].append(i)
            indegree[i] += 1
        q = collections.deque()
        for i in range(numCourses):
            if indegree[i] == 0:
                q.append(i)
        cnt = 0
        while q:
            i = q.popleft()
            cnt += 1
            for j in edges[i]:
                indegree[j] -= 1
                if indegree[j] == 0:
                    q.append(j)
        return cnt == numCourses

Java

class Solution {
    public boolean canFinish(int numCourses, int[][] prerequisites) {
        List<Integer>[] edges = new List[numCourses];
        for (int i = 0; i < numCourses; ++i) {
            edges[i] = new ArrayList<>();
        }
        int[] indegree = new int[numCourses];
        for (int[] p : prerequisites) {
            edges[p[1]].add(p[0]);
            ++indegree[p[0]];
        }
        Queue<Integer> q = new LinkedList<>();
        for (int i = 0; i < numCourses; ++i) {
            if (indegree[i] == 0) {
                q.offer(i);
            }
        }
        int cnt = 0;
        while (!q.isEmpty()) {
            int i = q.poll();
            ++cnt;
            for (int j : edges[i]) {
                --indegree[j];
                if (indegree[j] == 0) {
                    q.offer(j);
                }
            }
        }
        return cnt == numCourses;
    }
}

C++

class Solution {
public:
    bool canFinish(int numCourses, vector<vector<int>>& prerequisites) {
        vector<vector<int>> edges(numCourses);
        vector<int> indegree(numCourses);
        for (auto p : prerequisites)
        {
            edges[p[1]].push_back(p[0]);
            ++indegree[p[0]];
        }
        queue<int> q;
        for (int i = 0; i < numCourses; ++i)
        {
            if (indegree[i] == 0) q.push(i);
        }
        int cnt = 0;
        while (!q.empty())
        {
            int i = q.front();
            q.pop();
            ++cnt;
            for (int j : edges[i])
            {
                --indegree[j];
                if (indegree[j] == 0) q.push(j);
            }
        }
        return cnt == numCourses;
    }
};

Go

func canFinish(numCourses int, prerequisites [][]int) bool {
	edges := make([][]int, numCourses)
	indegree := make([]int, numCourses)
	for _, p := range prerequisites {
		edges[p[1]] = append(edges[p[1]], p[0])
		indegree[p[0]]++
	}
	var q []int
	for i := 0; i < numCourses; i++ {
		if indegree[i] == 0 {
			q = append(q, i)
		}
	}
	cnt := 0
	for len(q) > 0 {
		i := q[0]
		q = q[1:]
		cnt++
		for _, j := range edges[i] {
			indegree[j]--
			if indegree[j] == 0 {
				q = append(q, j)
			}
		}
	}
	return cnt == numCourses
}

C#

using System.Collections.Generic;

public class Solution {
    public bool CanFinish(int numCourses, int[][] prerequisites) {
        var indegree = new int[numCourses];
        var edgeCount = prerequisites.Length;
        var edge = new List<int>[numCourses];
        for (var i = 0; i < edgeCount; ++i)
        {
            var child = prerequisites[i][0];
            var parent = prerequisites[i][1];
            if (edge[parent] == null)
            {
                edge[parent] = new List<int>();
            }
            edge[parent].Add(child);
            ++indegree[child];
        }

        var queue = new Queue<int>();
        for (var i = 0; i < numCourses; ++i)
        {
            if (indegree[i] == 0) queue.Enqueue(i);
        }

        var count = 0;
        while (queue.Count > 0)
        {
            var node = queue.Dequeue();
            ++count;
            if (edge[node] != null)
            {
                foreach (var next in edge[node])
                {
                    if (--indegree[next] == 0)
                    {
                        queue.Enqueue(next);
                    }
                }
            }
        }
        return count == numCourses;
    }
}

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