// 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 // for each chunk, recompute a map of for each person i, how many friends they have in world j // then for each query, loop over the previous queries in the chunk and simulate. if by the end, // you still have at least one friend in world[y], ur good // the map computations take M sqrt(Q) time total, the rest is Q sqrt(Q) #include #pragma GCC optimize("O3,unroll-loops") #pragma GCC target("avx2") using namespace std; using HashSet = unordered_set; using FewCounter = unordered_map>; signed main2() { cin.tie(0)->sync_with_stdio(0); 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; } } // SOLUTION 2: TLEs sadly. could not get it to pass #include using namespace __gnu_pbds; constexpr size_t MXN = 20001; constexpr size_t MXM = 400000; // constexpr size_t MXN = 100; // constexpr size_t MXM = 100; signed main() { cin.tie(0)->sync_with_stdio(0); int N, M, Q; cin >> N >> M; short world[MXN]; bitset friends[MXN]; short friendships[MXM]; gp_hash_table initial_count[MXN]; // initial_count[i][j] = # of friends of i in world j for (int i = 1; i <= N; ++i) cin >> world[i]; for (int i = 0; i < M; ++i) { short a, b; cin >> a >> b; friendships[2*i] = a, friendships[2*i+1] = b; friends[a][b] = true; friends[b][a] = true; } auto reset_map = [&] { for (int i = 1; i <= N; ++i) initial_count[i].clear(); for (int i = 0; i < M; ++i) { short a = friendships[2*i]; short b = friendships[2*i+1]; ++initial_count[a][world[b]]; ++initial_count[b][world[a]]; } }; cin >> Q; int K = sqrt(Q); int q = 0; gp_hash_table> succeeded_wx, succeeded_wy; while (q < Q) { reset_map(); for (int k = 0; k < K && q < Q; ++k, ++q) { short x, y; cin >> x >> y; if (world[x] == world[y]) { cout << "No\n"; continue; } int start = initial_count[x][world[y]]; for (int xl : succeeded_wx[ world[y] ]) { start -= (friends[x][xl]); } for (int xl : succeeded_wy[ world[y] ]) { start += (friends[x][xl]); } if (start > 0) { cout << "Yes\n"; succeeded_wx[world[x]].push_back(x); succeeded_wy[world[y]].push_back(x); world[x] = world[y]; } else cout << "No\n"; } succeeded_wx.clear(); succeeded_wy.clear(); } return 0; }