# Course Schedule

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.

Note:

The input prerequisites is a graph represented by a list of edges, not adjacency matrices. Read more about how a graph is represented

## Code

BFS

``````public class Solution {
public boolean canFinish(int numCourses, int[][] prerequisites) {
if(prerequisites == null){
throw new IllegalArgumentException("illegal prerequisites array");
}

int len = prerequisites.length;

if(numCourses == 0 || len == 0){
return true;
}

// counter for number of prerequisites
int[] pCounter = new int[numCourses];
for(int i=0; i<len; i++){
pCounter[prerequisites[i][0]]++;
}

//store courses that have no prerequisites
for(int i=0; i<numCourses; i++){
if(pCounter[i]==0){
}
}

// number of courses that have no prerequisites
int numNoPre = queue.size();

while(!queue.isEmpty()){
int top = queue.remove();
for(int i=0; i<len; i++){
// if a course's prerequisite can be satisfied by a course in queue
if(prerequisites[i][1]==top){
pCounter[prerequisites[i][0]]--;
if(pCounter[prerequisites[i][0]]==0){
numNoPre++;
}
}
}
}

return numNoPre == numCourses;
}
}
``````

DFS

``````public class Solution {
public boolean canFinish(int numCourses, int[][] prerequisites) {
if(prerequisites == null){
throw new IllegalArgumentException("illegal prerequisites array");
}

int len = prerequisites.length;

if(numCourses == 0 || len == 0){
return true;
}

//track visited courses
int[] visit = new int[numCourses];

// use the map to store what courses depend on a course
HashMap<Integer,ArrayList<Integer>> map = new HashMap<Integer,ArrayList<Integer>>();
for(int[] a: prerequisites){
if(map.containsKey(a[1])){
}else{
ArrayList<Integer> l = new ArrayList<Integer>();
map.put(a[1], l);
}
}

for(int i=0; i<numCourses; i++){
if(!canFinishDFS(map, visit, i))
return false;
}

return true;
}

private boolean canFinishDFS(HashMap<Integer,ArrayList<Integer>> map, int[] visit, int i){
if(visit[i]==-1)
return false;
if(visit[i]==1)
return true;

visit[i]=-1;
if(map.containsKey(i)){
for(int j: map.get(i)){
if(!canFinishDFS(map, visit, j))
return false;
}
}

visit[i]=1;

return true;
}
}
``````