| #include <iostream> |
| #include <set> |
| #include <vector> |
| using namespace std; |
|
|
| int N, M; |
| vector<vector<int>> adj; |
| vector<bool> visit; |
| vector<int> sizes; |
|
|
| void rec(int u) { |
| sizes.back()++; |
| visit[u] = true; |
| for (int v : adj[u]) { |
| if (!visit[v]) { |
| rec(v); |
| } |
| } |
| } |
|
|
| int tgt; |
| vector<int> groups; |
| multiset<int> state; |
| set<multiset<int>> seen; |
|
|
| bool can_partition(int i) { |
| if (i == (int)sizes.size()) { |
| for (int sz : groups) { |
| if (sz != tgt) { |
| return false; |
| } |
| } |
| return true; |
| } |
| if (seen.count(state)) { |
| return false; |
| } |
| seen.insert(state); |
| for (int &g : groups) { |
| if (g + sizes[i] <= tgt) { |
| state.erase(state.find(g)); |
| g += sizes[i]; |
| state.insert(g); |
| if (can_partition(i + 1)) { |
| return true; |
| } |
| state.erase(state.find(g)); |
| g -= sizes[i]; |
| state.insert(g); |
| } |
| } |
| return false; |
| } |
|
|
| void solve() { |
| cin >> N >> M; |
| adj.assign(N, {}); |
| visit.assign(N, false); |
| sizes.clear(); |
| for (int i = 0, a, b; i < M; i++) { |
| cin >> a >> b; |
| a--; |
| b--; |
| adj[a].push_back(b); |
| adj[b].push_back(a); |
| } |
| for (int i = 0; i < N; i++) { |
| if (!visit[i]) { |
| sizes.push_back(0); |
| rec(i); |
| } |
| } |
| for (int K = 1; K <= N; K++) { |
| if (N % K == 0) { |
| tgt = N / K; |
| groups.assign(K, 0); |
| state.clear(); |
| for (int i = 0; i < K; i++) { |
| state.insert(0); |
| } |
| seen.clear(); |
| if (can_partition(0)) { |
| cout << " " << K; |
| } |
| } |
| } |
| } |
|
|
| int main() { |
| int T; |
| cin >> T; |
| for (int t = 1; t <= T; t++) { |
| cout << "Case #" << t << ":"; |
| solve(); |
| cout << endl; |
| } |
| return 0; |
| } |
