The hints of the problem has given detailed information to implement the topological sorting algorithm. In fact, the toposort algorithm of the hint is the BFS version, which uses the indegrees of each node.
The code is as follows.
1 #include <iostream> 2 #include <vector> 3 #include <queue> 4 5 using namespace std; 6 7 struct DirectedGraphNode { 8 int label; 9 vector<int> neighbors; 10 DirectedGraphNode(int i) : label(i) {} 11 }; 12 13 vector<DirectedGraphNode*> init_graph(int nodes) { 14 vector<DirectedGraphNode*> graph(nodes); 15 for (int i = 0; i < nodes; i++) 16 graph[i] = new DirectedGraphNode(i); 17 return graph; 18 } 19 20 vector<int> compute_indegree(vector<DirectedGraphNode*>& graph) { 21 vector<int> degrees(graph.size(), 0); 22 for (int i = 0; i < (int)graph.size(); i++) 23 for (int j = 0; j < (int)graph[i] -> neighbors.size(); j++) 24 degrees[graph[i] -> neighbors[j]]++; 25 return degrees; 26 } 27 28 bool noCycle(vector<DirectedGraphNode*>& graph) { 29 vector<int> degrees = compute_indegree(graph); 30 int nodes = graph.size(); 31 queue<int> zeros; 32 for (int i = 0; i < (int)degrees.size(); i++) 33 if (!degrees[i]) zeros.push(i); 34 while (!zeros.empty()) { 35 int zero = zeros.front(); 36 zeros.pop(); 37 for (int i = 0; i < (int)graph[zero] -> neighbors.size(); i++) 38 if (--degrees[graph[zero] -> neighbors[i]] == 0) 39 zeros.push(graph[zero] -> neighbors[i]); 40 nodes--; 41 } 42 return nodes == 0; 43 } 44 45 int main(void) { 46 int cases; 47 scanf("%d", &cases); 48 for (int i = 0; i < cases; i++) { 49 int nodes, edges; 50 scanf("%d %d", &nodes, &edges); 51 vector<DirectedGraphNode*> graph = init_graph(nodes); 52 int node, neigh; 53 for (int j = 0; j < edges; j++) { 54 scanf("%d %d", &node, &neigh); 55 graph[node - 1] -> neighbors.push_back(neigh - 1); 56 } 57 if (noCycle(graph)) printf("Correct\n"); 58 else printf("Wrong\n"); 59 } 60 return 0; 61 }