// 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; #include using namespace __gnu_pbds; template using HashTable = gp_hash_table; constexpr size_t MXN = 20001; constexpr size_t MXM = 400000; 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]; short X[MXN], Y[MXN]; HashTable 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; } vector whos_involved; 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]]; } } }; cin >> Q; int K = sqrt(Q); int q = 0; HashTable> succeeded_wx, succeeded_wy; while (q < Q) { reset_map(); int last = min(Q, q + K); for (int k = q; k < last; ++k) { cin >> X[k] >> Y[k]; whos_involved.push_back(X[k]); whos_involved.push_back(Y[k]); } 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; }