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.

Example 1:

Input: 2, [[1,0]] 
Output: [0,1]
Explanation: 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] .
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Example 2:

Input: 4, [[1,0],[2,0],[3,1],[3,2]]
Output: [0,1,2,3] or [0,2,1,3]
Explanation: 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] .

有n門課程，標號0~n-1，修某些課程之前，需要先修另外一些課程，用prerequisites表示。

輸出修課順序，如果不能修完，輸出空。

典型的拓撲排序。

 1 class Solution {
 2     vector<vector<int>> graph;
 3     vector<int> in_degree;
 4     queue<int> q;
 5     vector<int> ans;
 6 public:
 7     void BuildGraph(int numCourses, vector<pair<int, int>>& prerequisites) {
 8         graph = vector<vector<int>>(numCourses);
 9         in_degree = vector<int>(numCourses);
10         for (auto &p: prerequisites) {
11             int e = p.first;
12             int s = p.second;
13             graph[s].push_back(e);
14             ++in_degree[e];
15         }
16     }
17     
18     void TopoSort(int numCourses) {
19         for (int i = 0; i < numCourses; ++i) {
20             if (in_degree[i] == 0)
21                 q.push(i);
22         }
23         
24         while (!q.empty()) {
25             int idx = q.front();
26             q.pop();
27             ans.push_back(idx);
28             
29             for (auto &p: graph[idx]) {
30                 if (--in_degree[p] == 0)
31                     q.push(p);
32             }
33         }
34     }
35     vector<int> findOrder(int numCourses, vector<pair<int, int>>& prerequisites) {
36         BuildGraph(numCourses, prerequisites);
37         TopoSort(numCourses);
38         if (ans.size() == numCourses)
39             return ans;
40         return {};
41     }
42 };

210. Course Schedule II