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**, return the ordering of courses you should take to finish all courses.

There may be multiple correct orders, you just need to return one of them. If it is impossible to finish all courses, return an empty array.

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 the correct course order is `[0,1]`

4, [[1,0],[2,0],[3,1],[3,2]]

There are a total of 4 courses to take. To take course 3 you should have finished both courses 1 and 2. Both courses 1 and 2 should be taken after you finished course 0. So one correct course order is `[0,1,2,3]`

. Another correct ordering is`[0,2,1,3]`

.

**Solution** : I & II are the same idea. This is solution to II, if you want solution I, just change the return from int array to bool and return false instead of return null. Use DFS to solve it without knowing the sinks. it is like reverse of DFS. see here for more information.

bool[] visited; public int[] FindOrder(int numCourses, int[,] prerequisites) { visited = new bool[numCourses]; var res = new List(); for (int i = 0; i < numCourses; i++) { if (!visited[i]) { var returns = FindOrderDFS(numCourses, prerequisites, i, new List()); if(returns == null) return null; res.AddRange(returns); } } res.Reverse(); return res.ToArray(); } private int[] FindOrderDFS(int numCourses, int[,] prerequisites, int start, List parents) { var res = new List(); int rows = prerequisites.GetLength(0); int columns = prerequisites.GetLength(1); for (int i = 0; i < rows; i++) { if (prerequisites[i, 1] == start && !visited[prerequisites[i, 0]]) { if (parents.Contains(prerequisites[i, 0])) { return null; } parents.Add(start); var rest = FindOrderDFS(numCourses, prerequisites, prerequisites[i, 0], parents); if(rest == null) { return null; } res.AddRange(rest); } } res.Add(start); visited[start] = true; return res.ToArray(); }