LeetCode 207. Course Schedule 课程表 (C++/Java)

题目：

There are a total of n courses you have to take, labeled from 0 to n-1.

Some courses may have prerequisites, for example to take course 0 you have to first take course 1, which is expressed as a pair: [0,1]

Given the total number of courses and a list of prerequisite pairs, is it possible for you to finish all courses?

Example 1:

Input: 2, [[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: 2, [[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.

分析：

给定n门课程和他们之间的先修关系，例如[1, 0]就表示修1这门课程要先修完0，判断能否学完所有的课程。

很明显，如果课程中存在循环，就不能完成全部课程。记录每门课程之间的先后顺序，用map存储起来。遍历所有的课程，使用visit数组用来记录每门课程的访问状态，1表示正在访问，2表示已经访问过，访问课程后，在遍历这门课的后续课程，递归执行，如果出现访问的课程状态为1，也就是正在访问，那么表示图中存在环，返回false即可。

程序：

C++

class Solution {
public:
    bool canFinish(int numCourses, vector<vector<int>>& prerequisites) {
        courses = vector<vector<int>> (numCourses);
        for(auto a:prerequisites){
            courses[a[1]].push_back(a[0]);
        }
        vector<int> visit(numCourses);
        for(int i = 0; i < numCourses; ++i)
            if(dfs(i, visit))
                return false;
        return true;
    }
private:
    bool dfs(int curr, vector<int>& visit){
        if(visit[curr] == 1)
            return true;
        if(visit[curr] == 2)
            return false;
        visit[curr] = 1;
        for(auto i:courses[curr])
            if(dfs(i, visit))
                return true;
        visit[curr] = 2;
        return false;
    }
    vector<vector<int>> courses;
};

Java

class Solution {
    public boolean canFinish(int numCourses, int[][] prerequisites) {
        for(int[] arr:prerequisites){
            List<Integer> list = courses.getOrDefault(arr[1], new ArrayList<>());
            list.add(arr[0]);
            courses.put(arr[1], list);
        }
        int[] visit = new int[numCourses];
        for(int i = 0; i < numCourses; ++i){
            if(dfs(i, visit))
                return false;
        }
        return true;
    }
    private boolean dfs(int curr, int[] visit){
        if(visit[curr] == 1)
            return true;
        if(visit[curr] == 2)
            return false;
        visit[curr] = 1;
        List<Integer> list = courses.get(curr);
        if(list != null){
            for(int i:list){
                if(dfs(i, visit))
                    return true;
            }
        }
         visit[curr] = 2;
        return false;
    }
    private Map<Integer, List<Integer>> courses = new HashMap<>();
}