// https://yukicoder.me/problems/no/2319 // really cool problem // // Solution 0. use bitsets and bruteforce // // Solution 1. sqrt over nodes // let K = sqrt(M) // a person is "few" if it has < K friends and "many" if >= K // there are at most 2M / K ~= K people that are "many" // to solve a query where x is few, brute force it // to solve a query where x is many, consider its friends that are: // a. many - you can check ALL many's for the condition // b. few - store this as map f[i][j] = # of few friends of the many i in world j // update naively, it works in O(Q*sqrt M + N*sqrt M + M) // // Solution 2. sqrt over queries #include #pragma GCC optimize("O3") #pragma GCC target("sse4") using namespace std; using HashSet = unordered_set; using FewCounter = unordered_map>; signed main() { cin.tie(0)->sync_with_stdio(0); // cout << "sol 1\n"; // freopen("/Users/drymerge/CLionProjects/DEBUG/a.in", "r", stdin); // freopen("/Users/drymerge/a.out", "w", stdout); int N, M, Q; cin >> N >> M; int K = sqrt(M); vector world(N+1); // world[i] = the world that person i is in FewCounter num_few_of; // num_few_of[i].at(w) = # friends of i in world j with < K friends vector many; // many = [those with >= K friends] vector friends(N+1); auto is_many = [&] (int i) { return friends[i].size() >= K; }; for (int i = 1; i <= N; ++i) cin >> world[i]; for (int i = 1; i <= M; ++i) { int a, b; cin >> a >> b; friends[a].insert(b); friends[b].insert(a); } for (int i = 1; i <= N; ++i) { if (!is_many(i)) continue; many.push_back(i); num_few_of[i].assign(N+1, 0); for (int f : friends[i]) if (!is_many(f)) { int w = world[f]; ++num_few_of[i].at(w); } } auto solve_many = [&] (int x, int y) { int new_world = world[y]; if (num_few_of[x].at(new_world) > 0) goto success; for (int m : many) if (friends[x].count(m) && world[m] == new_world) goto success; return "No\n"; success: world[x] = new_world; return "Yes\n"; }; auto solve_few = [&] (int x, int y) { for (int f : friends[x]) if (world[f] == world[y]) goto success; return "No\n"; success: int old_world = world[x]; int new_world = world[y]; for (int f : friends[x]) { if (!is_many(f)) continue; --num_few_of[f].at(old_world); ++num_few_of[f].at(new_world); } world[x] = new_world; return "Yes\n"; }; cin >> Q; while (Q--) { int x, y; cin >> x >> y; if (world[x] == world[y]) { cout << "No\n"; continue; } auto ans = is_many(x) ? solve_many(x,y) : solve_few(x,y); cout << ans; } } signed main2() { cout << "sol2\n"; freopen("/Users/drymerge/CLionProjects/DEBUG/a.in", "r", stdin); freopen("/Users/drymerge/b.out", "w", stdout); cin.tie(0)->sync_with_stdio(0); int N, M, Q; cin >> N >> M; vector world(N+1); for (int i = 1; i <= N; ++i) cin >> world[i]; vector> friends(N+1); vector> friendships(M); unordered_map> initial_count; // initial_count[i][j] = # of friends of i in world j for (auto& [a,b] : friendships) { cin >> a >> b; friends[a].insert(b); friends[b].insert(a); } auto reset_map = [&] { initial_count.clear(); for (auto [a,b] : friendships) { ++initial_count[a][world[b]]; ++initial_count[b][world[a]]; } }; auto is_friends = [&] (int i, int j) -> bool { if (friends[i].size() > friends[j].size()) swap(i, j); return friends[i].count(j); }; cin >> Q; int K = sqrt(Q); int q = 0; vector> succeeded; while (q < Q) { reset_map(); for (int k = 0; k < K && q < Q; ++k, ++q) { int x, y; cin >> x >> y; if (world[x] == world[y]) { cout << "No\n"; continue; } int start = initial_count[x][world[y]]; for (auto [xl,yl,wx,wy] : succeeded) { if (wx == world[y] && is_friends(x, xl)) --start; if (wy == world[y] && is_friends(x, xl)) ++start; } if (start > 0) { cout << "Yes\n"; succeeded.push_back( {x,y,world[x],world[y]} ); world[x] = world[y]; } else cout << "No\n"; } succeeded.clear(); } return 0; }