```
public class Solution {
public boolean canFinish(int numCourses, int[][] prereq) {
int[] visited = new int[numCourses];
//courses that would have the dependency graph
List<List<Integer>> courses = new ArrayList<List<Integer>>();
for(int i=0;i<numCourses;i++){
courses.add(new ArrayList<Integer>());
}
//add dependencies
for(int i=0;i< prereq.length;i++){
// for a course, add all the courses that are dependent on it
courses.get(prereq[i][1]).add(prereq[i][0]);
}
for(int i=0;i<numCourses;i++){
if(visited[i]==0){
if(!dfs(i,courses,visited)) return false;
}
}
return true;
}
public boolean dfs(int i,List<List<Integer>> courses, int[]visited){
visited[i] = 1;
// these are all the courses which are eligible
//when we take their prerequisite, which is course i
List<Integer> eligibleCourses = courses.get(i);
for(int j=0;j<eligibleCourses.size();j++){
int eligibleCourse = eligibleCourses.get(j);
//it is already visited, during previous dfs call, so its a cycle
if(visited[eligibleCourse] == 1) return false;
if(visited[eligibleCourse] == 2) continue;
if(!dfs(eligibleCourse,courses,visited)){
return false;
}
}
//it is totally complete and no cycle found in its depth first traversal
visited[i] = 2;
return true;
}
}
```