Course Schedule II.java

M

详细的中文分析，看Course Schedule I

```
/*
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].

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

click to show more hints.

Hints:
This problem is equivalent to finding the topological order in a directed graph. If a cycle exists, no topological ordering exists and therefore it will be impossible to take all courses.
Topological Sort via DFS - A great video tutorial (21 minutes) on Coursera explaining the basic concepts of Topological Sort.
Topological sort could also be done via BFS.
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*/

/*
	http://blog.csdn.net/ljiabin/article/details/45847019

	Based on Course Schedule I, now we need to return all nodes with by the seq number.
	
	Note:
	The map is built based on <most deepest prerequisites, list of course based on that root prerequsites>
*/
public class Solution {
	HashMap<Integer, List<Integer>> map;
	int[] visited;
    int seq;
    int[] order;
    public int[] findOrder(int numCourses, int[][] prerequisites) {
    	order = new int[numCourses];
    	seq = numCourses - 1;
        visited = new int[numCourses];
        map = new HashMap<Integer, List<Integer>>();
        //Put all start node into map.
        for (int i = 0; i < prerequisites.length; i++) {
        	if (!map.containsKey(prerequisites[i][1])) {
        		map.put(prerequisites[i][1], new ArrayList<Integer>());
        	}
        	map.get(prerequisites[i][1]).add(prerequisites[i][0]);
        }
        //dfs on each start node in the pair
        for (int i = 0; i < numCourses; i++) {
        	if (!dfs(i)) {
        		return new int[]{};
        	}
        }
        return order;
    }

    public boolean dfs (int node) {
    	if (visited[node] == 1) {//has been through this path, true.
    		return true;
    	}
    	if (visited[node] == -1) {//visiting a visited node from a deper level node, cycle
    		return false;
    	}
    	//mark it -1 then after dfs mark it 1. Marking and backtracking skills
    	visited[node] = -1;

    	//Visit each child and make sure there is no cycle.
    	if (map.containsKey(node)) {
    		for (int nextNode : map.get(node)) {
    			if (!dfs(nextNode)) {
    				return false;
    			}
    		}
    	}
    	visited[node] = 1;
        order[seq--] = node;
    	return true;
    }

}






```