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4.97 kB
| using namespace std; | |
| using ull = unsigned long long; | |
| struct Solver { | |
| int n, q; | |
| int B; // heavy threshold | |
| int W; // words in a bitset = (n+63)/64 | |
| vector<vector<int>> adj; | |
| vector<int> deg; | |
| vector<char> isHeavy; | |
| vector<int> hId; | |
| vector<vector<ull>> hBits; // bitsets for heavy rows | |
| vector<vector<int>> hDiff; // hDiff[i][j] = |heavy_i \ heavy_j| | |
| vector<int> heavyRows; // heavyRows[i] = row id | |
| vector<int> tag; | |
| int timer; | |
| set<pair<int,int>> ord; // (degree, row id) | |
| long long bad; // number of incomparable adjacent pairs | |
| Solver(int n_, int q_) : n(n_), q(q_) { | |
| B = max(1, (int)std::sqrt((double)q)); | |
| W = (n + 63) >> 6; | |
| adj.assign(n, {}); | |
| deg.assign(n, 0); | |
| isHeavy.assign(n, 0); | |
| hId.assign(n, -1); | |
| heavyRows.clear(); | |
| tag.assign(n, 0); | |
| timer = 1; | |
| ord.clear(); | |
| for (int i = 0; i < n; ++i) ord.insert({0, i}); | |
| bad = 0; | |
| } | |
| // return true iff N(a) ⊆ N(b) or N(b) ⊆ N(a) | |
| bool comp(int a, int b) { | |
| if (a == b) return true; | |
| if (deg[a] > deg[b]) swap(a, b); // a is the smaller (or equal) set | |
| if (deg[a] > B) { // both are heavy | |
| int ha = hId[a], hb = hId[b]; | |
| return hDiff[ha][hb] == 0; // a ⊆ b | |
| } | |
| if (isHeavy[b]) { // a light, b heavy | |
| const auto &bits = hBits[hId[b]]; | |
| for (int col : adj[a]) { | |
| if ( ((bits[col >> 6] >> (col & 63)) & 1ULL) == 0 ) | |
| return false; | |
| } | |
| return true; | |
| } | |
| // both light | |
| ++timer; | |
| for (int col : adj[b]) tag[col] = timer; | |
| for (int col : adj[a]) if (tag[col] != timer) return false; | |
| return true; | |
| } | |
| void makeHeavy(int r) { | |
| int id = (int)hBits.size(); | |
| hId[r] = id; | |
| isHeavy[r] = 1; | |
| vector<ull> bits(W, 0); | |
| for (int col : adj[r]) bits[col >> 6] |= 1ULL << (col & 63); | |
| hBits.push_back(move(bits)); | |
| for (auto &row : hDiff) row.push_back(0); | |
| hDiff.emplace_back(hBits.size(), 0); | |
| for (int hi = 0; hi < id; ++hi) { | |
| int common = 0; | |
| for (int col : adj[r]) { | |
| if ( (hBits[hi][col >> 6] >> (col & 63)) & 1ULL ) ++common; | |
| } | |
| hDiff[id][hi] = deg[r] - common; // r \ h | |
| hDiff[hi][id] = deg[heavyRows[hi]] - common; // h \ r | |
| } | |
| heavyRows.push_back(r); | |
| } | |
| void addHeavyEdge(int r, int c) { | |
| int id = hId[r]; | |
| for (int hi = 0; hi < (int)hBits.size(); ++hi) { | |
| if (hi == id) continue; | |
| if ( (hBits[hi][c >> 6] >> (c & 63)) & 1ULL ) { | |
| --hDiff[hi][id]; // hi had c, r did not, now it does | |
| } else { | |
| ++hDiff[id][hi]; // r gains c which hi lacks | |
| } | |
| } | |
| hBits[id][c >> 6] |= 1ULL << (c & 63); | |
| } | |
| void addEdge(int r, int c) { | |
| adj[r].push_back(c); | |
| ++deg[r]; | |
| if (isHeavy[r]) { | |
| addHeavyEdge(r, c); | |
| } else if (deg[r] > B) { | |
| makeHeavy(r); | |
| } | |
| } | |
| string answerQuery(int r, int c) { | |
| // 1) remove r from the degree order, updating the counter | |
| auto it = ord.find({deg[r], r}); | |
| int oldL = -1, oldR = -1; | |
| if (it != ord.begin()) { | |
| auto it2 = it; --it2; | |
| oldL = it2->second; | |
| } | |
| auto itNxt = next(it); | |
| if (itNxt != ord.end()) oldR = itNxt->second; | |
| if (oldL != -1 && !comp(oldL, r)) --bad; | |
| if (oldR != -1 && !comp(r, oldR)) --bad; | |
| if (oldL != -1 && oldR != -1 && !comp(oldL, oldR)) ++bad; | |
| ord.erase(it); | |
| // 2) actually color the cell black | |
| addEdge(r, c); | |
| // 3) insert r with its new degree and update the counter | |
| auto ret = ord.insert({deg[r], r}); | |
| auto it2 = ret.first; | |
| int newL = -1, newR = -1; | |
| if (it2 != ord.begin()) { | |
| auto it3 = it2; --it3; | |
| newL = it3->second; | |
| } | |
| auto it4 = next(it2); | |
| if (it4 != ord.end()) newR = it4->second; | |
| if (newL != -1 && newR != -1 && !comp(newL, newR)) --bad; | |
| if (newL != -1 && !comp(newL, r)) ++bad; | |
| if (newR != -1 && !comp(r, newR)) ++bad; | |
| return bad == 0 ? "YES" : "NO"; | |
| } | |
| }; | |
| int main() { | |
| ios::sync_with_stdio(false); | |
| cin.tie(nullptr); | |
| int T; | |
| if (!(cin >> T)) return 0; | |
| while (T--) { | |
| int n, q; | |
| cin >> n >> q; | |
| Solver solver(n, q); | |
| for (int i = 0; i < q; ++i) { | |
| int r, c; | |
| cin >> r >> c; | |
| --r; --c; | |
| cout << solver.answerQuery(r, c) << '\n'; | |
| } | |
| } | |
| return 0; | |
| } |