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?

For example:

2, [[1,0]]
There are a total of 2 courses to take. To take course 1 you should have finished course 0. So it is possible.

2, [[1,0],[0,1]]
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.

答案
重点: if u->v, and v is already on recursion stack, a cycle is found

class Solution {
    public boolean canFinish(int numCourses, int[][] prerequisites) {
        boolean[][] adj_mat = new boolean[numCourses][numCourses];
        boolean[] visited = new boolean[numCourses];    
        boolean[] rec = new boolean[numCourses];
                    
        for(int i = 0; i < prerequisites.length; i++)
            adj_mat[prerequisites[i][0]][prerequisites[i][1]] = true;
        
        for(int i = 0; i < numCourses; i++) {
            boolean ret = dfs_has_cycle(i, visited, rec, adj_mat);
            if(ret) return false;
        }
        return true;
    }
    
    public boolean dfs_has_cycle(int v, boolean[] visited, boolean[] rec, boolean[][] adj_mat) {
        visited[v] = true;
        rec[v] = true;
        
        
        for(int i = 0; i < visited.length; i++) {
            if(i == v || !adj_mat[v][i]) continue;
            if(adj_mat[v][i] && rec[i]) return true;
            if(!visited[i]) {
                boolean ret = dfs_has_cycle(i, visited, rec, adj_mat);
                if(ret) return true;
            }   
        }
        
        rec[v] = false;
        return false;
    }
}