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] .
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] .
Note:
- The input prerequisites is a graph represented by a list of edges, not adjacency matrices. Read more about how a graph is represented.
- You may assume that there are no duplicate edges in the input prerequisites.
思路：
这道题可以使用经典的Kahn's Algorithm来解决，即Topological Sorting的生成算法。
class Solution {
public:
vector<int> findOrder(int numCourses, vector<pair<int, int>>& prerequisites) {
vector<vector<int>> admat;
admat = genAdmat(numCourses, prerequisites);
vector<int> L;
set<int> S; //Set of all nodes with no incoming edge
S = findS(admat);
while (!S.empty()) {
int node = *S.begin();
S.erase(node);
L.push_back(node);
update(admat, node, S);
}
if (hasEdge(admat)) return vector<int>();
else return L;
}
private:
// Generate adjasent matrix
vector<vector<int>> genAdmat(int num, vector<pair<int, int>> &prerequisites) {
vector<vector<int>> admat = vector<vector<int>>(num, vector<int>(num, 0));
for (pair<int, int> one : prerequisites) {
admat[one.second][one.first] = 1;
}
return admat;
}
// Find all nodes with no incoming edge
set<int> findS(vector<vector<int>> admat) {
int num = int(admat.size());
set<int> S;
for (int i = 0; i < num; i++) {
bool flag = true;
for (int j = 0; j < num; j++) {
if (admat[j][i] == 1) {
flag = false;
break;
}
}
if (flag) S.insert(i);
}
return S;
}
// Update the adjasent matrix and node set
void update(vector<vector<int>> &admat, int node, set<int> &S) {
int num = int(admat.size());
for (int i = 0; i < num; i++) {
if (admat[node][i] == 1) {
admat[node][i] = 0;
bool flag = true;
for (int j = 0; j < num; j++) {
if (admat[j][i] == 1) {
flag = false;
break;
}
}
if (flag) S.insert(i);
}
}
}
// If there is still an edge
bool hasEdge(const vector<vector<int>> admat) {
int num = int(admat.size());
for (int i = 0; i < num; i++) {
for (int j = 0; j < num; j++) {
if (admat[i][j] == 1) return true;
}
}
return false;
}
};