## Monday, August 7, 2017

### [Leetcode] Course Schedule, Solution

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:
1. The input prerequisites is a graph represented by a list of edges, not adjacency matrices. Read more about how a graph is represented.
2. You may assume that there are no duplicate edges in the input prerequisites.
Hints:
1. This problem is equivalent to finding if a cycle exists in a directed graph. If a cycle exists, no topological ordering exists and therefore it will be impossible to take all courses.
2. Topological Sort via DFS - A great video tutorial (21 minutes) on Coursera explaining the basic concepts of Topological Sort.
3. Topological sort could also be done via BFS.

[Thoughts]

[Code]
``````1:    bool canFinish(int numCourses, vector<pair<int, int>>& prerequisites) {
2:      unordered_map<int, vector<int>> deps(numCourses);
3:
4:      for(auto pair : prerequisites) {
5:        deps[pair.first].push_back(pair.second);
6:      }
7:
8:      vector<int> visited(numCourses, 0);
9:      for(int i =0 ; i< numCourses; i++) {
10:        if(isCycle(i, deps, visited)) return false;
11:      }
12:      return true;
13:    }
14:
15:    bool isCycle(int start, unordered_map<int, vector<int>>& deps, vector<int>& visited) {
16:      if(visited[start] == 1) return true;
17:
18:      visited[start] =1;
19:
20:      for(auto edge: deps[start]) {
21:        if(isCycle(edge, deps, visited)) return true;
22:
23:      }
24:      visited[start] =0;
25:      return false;
26:    }
``````

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