// 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; using HashSet = unordered_set; using FewCounter = HashTable>; signed main() { 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: took forever to make it pass :/ // 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]; // HashTable initial_count[MXN]; // // initial_count[i][j] = # of friends of i in world j // short X[SQR], Y[SQR]; // vector whos_involved; // 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]]; // } // } // }; // 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; // }