210. Course Schedule II

There are a total ofncourses you have to take, labeled from0ton - 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 prerequisitepairs, 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:

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.

S1: topological sort + DFS

1. 构建有向图
2. 对图进行拓扑排序并判断环

class Solution {
public:
    vector<int> findOrder(int numCourses, vector<pair<int, int>>& prerequisites) {
        vector<unordered_set<int>> children(numCourses);
        for (const auto& i : prerequisites) {
            children[i.second].insert(i.first);
        }

        vector<bool> visited(numCourses, false);
        vector<bool> ancestor(numCourses, false);
        vector<int> result;
        for (int i = 0; i < numCourses; ++i) {
            if (!dfs(children, result, i, visited, ancestor)) {
                return vector<int>{};
            }
        }
        reverse(result.begin(), result.end());
        return result;
    }

private:
    bool dfs(vector<unordered_set<int>>& children, vector<int>& result, int courseNum, 
             vector<bool>& visited, vector<bool>& ancestor) {
        if (ancestor[courseNum]) {
            return false;
        }
        if (visited[courseNum]) {
            return true;
        }
        visited[courseNum] = true;
        ancestor[courseNum] = true;
        for (int i : children[courseNum]) {
            if (!dfs(children, result, i, visited, ancestor)) {
                return false;
            }
        }
        result.push_back(courseNum);
        ancestor[courseNum] = false;
        return true;
    }
};