// https://yukicoder.me/problems/no/2319 // really cool problem // // Solution 0. use bitsets and bruteforce (cheating) // // 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. ft. Jerry -> 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; struct chash { const int RANDOM = (long long)(make_unique().get()) ^ chrono::high_resolution_clock::now().time_since_epoch().count(); static unsigned long long hash_f(unsigned long long x) { x += 0x9e3779b97f4a7c15; x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9; x = (x ^ (x >> 27)) * 0x94d049bb133111eb; return x ^ (x >> 31); } static unsigned hash_combine(unsigned a, unsigned b) { return a * 31 + b; } int operator()(int x) const { return hash_f(x)^RANDOM; } }; template using HashTable = gp_hash_table; // template // using HashTable = unordered_map; constexpr size_t MXN = 20001; constexpr size_t MXM = 400000; // constexpr size_t MXN = 100; // constexpr size_t MXM = 100; constexpr size_t SQR = 450; #define all(x) begin(x), end(x) signed main() { cin.tie(0)->sync_with_stdio(0); int N, M, Q; cin >> N >> M; short world[MXN]; bitset friends[MXN]; vector friendss[MXN]; short friendships[MXM]; HashTable initial_count[MXN]; // short initial_count[MXN][SQR]; short X[SQR], Y[SQR]; vector whos_involved; // 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; friendss[a].push_back(b); friendss[b].push_back(a); friendships[2*i] = a, friendships[2*i+1] = b; friends[a][b] = true; friends[b][a] = true; } auto reset_map = [&] { sort( all(whos_involved) ); whos_involved.resize(unique(all(whos_involved)) - begin(whos_involved)); for (int c : whos_involved) { if (!initial_count[c].empty()) initial_count[c].clear(); for (int f : friendss[c]) { ++initial_count[c][world[f]]; } } // 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; HashTable> succeeded_wx, succeeded_wy; while (q < Q) { int last = min(Q, q + K); for (int k = q; k < last; ++k) { cin >> X[k-q] >> Y[k-q]; whos_involved.push_back(X[k-q]); whos_involved.push_back(Y[k-q]); } reset_map(); for (int k = 0; k < K && q < Q; ++k, ++q) { short x = X[k], y = Y[k]; 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(); whos_involved.clear(); } return 0; }