結果
問題 | No.1774 Love Triangle (Hard) |
ユーザー | 👑 hitonanode |
提出日時 | 2021-10-11 23:25:58 |
言語 | C++17(clang) (17.0.6 + boost 1.83.0) |
結果 |
TLE
(最新)
AC
(最初)
|
実行時間 | - |
コード長 | 5,490 bytes |
コンパイル時間 | 6,749 ms |
コンパイル使用メモリ | 141,444 KB |
実行使用メモリ | 14,752 KB |
最終ジャッジ日時 | 2023-10-17 09:19:57 |
合計ジャッジ時間 | 451,907 ms |
ジャッジサーバーID (参考情報) |
judge15 / judge14 |
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テストケース
テストケース表示入力 | 結果 | 実行時間 実行使用メモリ |
---|---|---|
testcase_00 | AC | 1 ms
4,348 KB |
testcase_01 | AC | 1 ms
4,348 KB |
testcase_02 | AC | 4 ms
4,348 KB |
testcase_03 | AC | 8 ms
4,348 KB |
testcase_04 | AC | 3 ms
4,348 KB |
testcase_05 | AC | 7 ms
4,348 KB |
testcase_06 | AC | 2 ms
4,348 KB |
testcase_07 | AC | 16 ms
4,348 KB |
testcase_08 | AC | 2 ms
4,348 KB |
testcase_09 | AC | 2 ms
4,348 KB |
testcase_10 | AC | 1 ms
4,348 KB |
testcase_11 | AC | 24 ms
4,348 KB |
testcase_12 | AC | 4,262 ms
8,020 KB |
testcase_13 | AC | 2,404 ms
6,828 KB |
testcase_14 | AC | 169 ms
4,348 KB |
testcase_15 | AC | 1,819 ms
6,172 KB |
testcase_16 | AC | 629 ms
5,088 KB |
testcase_17 | AC | 34 ms
4,348 KB |
testcase_18 | AC | 2,182 ms
6,604 KB |
testcase_19 | AC | 76 ms
4,348 KB |
testcase_20 | AC | 182 ms
4,348 KB |
testcase_21 | AC | 107 ms
4,348 KB |
testcase_22 | AC | 7,055 ms
10,176 KB |
testcase_23 | AC | 7,253 ms
10,232 KB |
testcase_24 | AC | 7,309 ms
10,288 KB |
testcase_25 | AC | 7,311 ms
10,220 KB |
testcase_26 | AC | 7,241 ms
10,296 KB |
testcase_27 | AC | 7,181 ms
10,240 KB |
testcase_28 | AC | 7,184 ms
10,228 KB |
testcase_29 | AC | 7,310 ms
10,296 KB |
testcase_30 | AC | 7,413 ms
10,396 KB |
testcase_31 | AC | 7,251 ms
10,288 KB |
testcase_32 | AC | 7,256 ms
10,288 KB |
testcase_33 | AC | 7,308 ms
10,300 KB |
testcase_34 | AC | 7,358 ms
10,296 KB |
testcase_35 | AC | 7,316 ms
10,300 KB |
testcase_36 | AC | 7,050 ms
10,168 KB |
testcase_37 | AC | 7,330 ms
10,308 KB |
testcase_38 | AC | 7,223 ms
10,224 KB |
testcase_39 | AC | 7,198 ms
10,244 KB |
testcase_40 | AC | 7,279 ms
10,288 KB |
testcase_41 | AC | 7,307 ms
10,304 KB |
testcase_42 | AC | 7,398 ms
10,396 KB |
testcase_43 | AC | 7,393 ms
10,396 KB |
testcase_44 | AC | 7,385 ms
10,396 KB |
testcase_45 | AC | 7,388 ms
10,396 KB |
testcase_46 | AC | 7,385 ms
10,396 KB |
testcase_47 | AC | 7,403 ms
10,396 KB |
testcase_48 | AC | 7,438 ms
10,396 KB |
testcase_49 | AC | 7,397 ms
10,396 KB |
testcase_50 | AC | 7,398 ms
10,396 KB |
testcase_51 | AC | 7,394 ms
10,396 KB |
testcase_52 | AC | 7,409 ms
10,396 KB |
testcase_53 | AC | 7,387 ms
10,396 KB |
testcase_54 | AC | 7,394 ms
10,396 KB |
testcase_55 | AC | 7,388 ms
10,396 KB |
testcase_56 | AC | 7,394 ms
10,396 KB |
testcase_57 | AC | 7,391 ms
10,396 KB |
testcase_58 | AC | 7,386 ms
10,396 KB |
testcase_59 | AC | 7,396 ms
10,396 KB |
testcase_60 | AC | 7,390 ms
10,396 KB |
testcase_61 | AC | 7,389 ms
10,396 KB |
testcase_62 | AC | 7,393 ms
10,396 KB |
testcase_63 | AC | 7,394 ms
10,396 KB |
testcase_64 | AC | 7,192 ms
10,232 KB |
testcase_65 | AC | 7,423 ms
10,396 KB |
testcase_66 | AC | 7,391 ms
10,396 KB |
testcase_67 | AC | 7,140 ms
10,208 KB |
testcase_68 | AC | 7,388 ms
10,396 KB |
testcase_69 | AC | 7,387 ms
10,396 KB |
testcase_70 | AC | 7,163 ms
10,224 KB |
testcase_71 | AC | 7,382 ms
10,396 KB |
testcase_72 | AC | 7,384 ms
10,396 KB |
testcase_73 | AC | 7,360 ms
10,396 KB |
testcase_74 | AC | 7,397 ms
10,396 KB |
testcase_75 | AC | 7,399 ms
10,396 KB |
testcase_76 | AC | 7,214 ms
10,272 KB |
testcase_77 | AC | 7,391 ms
10,396 KB |
testcase_78 | AC | 7,387 ms
10,396 KB |
testcase_79 | AC | 7,064 ms
10,192 KB |
testcase_80 | TLE | - |
testcase_81 | -- | - |
testcase_82 | -- | - |
testcase_83 | -- | - |
testcase_84 | -- | - |
testcase_85 | -- | - |
testcase_86 | -- | - |
testcase_87 | -- | - |
testcase_88 | -- | - |
testcase_89 | -- | - |
testcase_90 | -- | - |
testcase_91 | -- | - |
testcase_92 | -- | - |
ソースコード
#include <algorithm> #include <cassert> #include <chrono> #include <iostream> #include <numeric> #include <random> #include <utility> #include <vector> using namespace std; #include <atcoder/modint> using mint = atcoder::static_modint<(1 << 30) + 3>; // prime template <class T> std::vector<T> mat_vec_mul(const std::vector<std::vector<T>> &mat, const std::vector<T> &vec) { int H = mat.size(), W = mat[0].size(); assert(W == int(vec.size())); std::vector<T> ret(H); for (int i = 0; i < H; ++i) { for (int j = 0; j < W; ++j) ret[i] += mat[i][j] * vec[j]; } return ret; } // Try to calculate inverse of M and return rank of M (destructive) template <class T> int inverse_matrix(std::vector<std::vector<T>> &M) { const int N = M.size(); assert(N and M[0].size() == M.size()); std::vector<std::vector<T>> ret(N, std::vector<T>(N)); for (int i = 0; i < N; ++i) ret[i][i] = 1; int rank = 0; for (int i = 0; i < N; ++i) { int ti = i; while (ti < N and M[ti][i] == 0) ti++; if (ti == N) { continue; } ++rank; ret[i].swap(ret[ti]), M[i].swap(M[ti]); T inv = T(1) / M[i][i]; for (int j = 0; j < N; ++j) ret[i][j] *= inv; for (int j = i + 1; j < N; ++j) M[i][j] *= inv; for (int h = 0; h < N; ++h) { if (i == h) continue; const T c = -M[h][i]; for (int j = 0; j < N; ++j) ret[h][j] += ret[i][j] * c; for (int j = i + 1; j < N; ++j) M[h][j] += M[i][j] * c; } } M = ret; return rank; } template <class ModInt> std::vector<int> linear_matroid_parity(const std::vector<std::pair<std::vector<ModInt>, std::vector<ModInt>>> &bcs) { if (bcs.empty()) return {}; const int r = bcs[0].first.size(), m = bcs.size(), r2 = (r + 1) / 2; std::mt19937 mt(std::chrono::steady_clock::now().time_since_epoch().count()); std::uniform_int_distribution<int> d(0, ModInt::mod() - 1); auto gen_random_vector = [&]() -> std::vector<ModInt> { std::vector<ModInt> v(r2 * 2); for (int i = 0; i < r2 * 2; i++) v[i] = d(mt); return v; }; std::vector<ModInt> x(m); std::vector<std::pair<vector<ModInt>, vector<ModInt>>> bcadd(r2); std::vector<std::vector<ModInt>> Yinv; // r2 * r2 matrices int rankY = -1; while (rankY < r2 * 2) { Yinv.assign(r2 * 2, std::vector<ModInt>(r2 * 2, 0)); for (auto &[b, c] : bcadd) { b = gen_random_vector(), c = gen_random_vector(); for (int j = 0; j < r2 * 2; j++) { for (int k = 0; k < r2 * 2; k++) Yinv[j][k] += b[j] * c[k] - c[j] * b[k]; } } rankY = inverse_matrix(Yinv); } std::vector<std::vector<ModInt>> tmpmat(r2 * 2, std::vector<ModInt>(r2 * 2)); std::vector<int> ret(m, -1); int additional_dim = bcadd.size(); for (int i = 0; i < m; i++) { { x[i] = d(mt); auto b = bcs[i].first, c = bcs[i].second; b.resize(r2 * 2, 0), c.resize(r2 * 2, 0); std::vector<ModInt> Yib = mat_vec_mul(Yinv, b), Yic = mat_vec_mul(Yinv, c); ModInt bYic = std::inner_product(b.begin(), b.end(), Yic.begin(), ModInt(0)); ModInt v = 1 + x[i] * bYic; if (v == 0) break; // failed const auto coeff = x[i] / v; for (int j = 0; j < r2 * 2; j++) { for (int k = 0; k < r2 * 2; k++) { tmpmat[j][k] = Yib[j] * Yic[k] - Yic[j] * Yib[k]; } } for (int j = 0; j < r2 * 2; j++) { for (int k = 0; k < r2 * 2; k++) Yinv[j][k] -= tmpmat[j][k] * coeff; } } if (additional_dim) { const auto &[b, c] = bcadd[additional_dim - 1]; std::vector<ModInt> Yib = mat_vec_mul(Yinv, b), Yic = mat_vec_mul(Yinv, c); ModInt bYic = std::inner_product(b.begin(), b.end(), Yic.begin(), ModInt(0)); const ModInt v = 1 + bYic; if (v != 0) { // 消しても正則 additional_dim--; const auto coeff = 1 / v; for (int j = 0; j < r2 * 2; j++) { for (int k = 0; k < r2 * 2; k++) tmpmat[j][k] = Yib[j] * Yic[k] - Yic[j] * Yib[k]; } for (int j = 0; j < r2 * 2; j++) { for (int k = 0; k < r2 * 2; k++) Yinv[j][k] -= tmpmat[j][k] * coeff; } } } ret[i] = r2 - additional_dim; } return ret; } vector<int> solve(int N, vector<pair<pair<int, int>, pair<int, int>>> bcs) { vector<pair<vector<mint>, vector<mint>>> vs; for (auto [ab, cd] : bcs) { auto [a, b] = ab; auto [c, d] = cd; vector<mint> B(N), C(N); B.at(a) += 1; B.at(b) -= 1; C.at(c) += 1; C.at(d) -= 1; vs.emplace_back(B, C); } auto ret = linear_matroid_parity<mint>(vs); auto ret2 = linear_matroid_parity<mint>(vs); for (int i = 0; i < int(ret.size()); i++) ret[i] = max(ret[i], ret2[i]); return ret; } int main() { int N, M; cin >> N >> M; vector<pair<pair<int, int>, pair<int, int>>> edges; while (M--) { int u, v, w; cin >> u >> v >> w; u--, v--, w--; edges.push_back({{u, w}, {v, w}}); } auto ret = solve(N, edges); for (auto x : ret) cout << x << '\n'; }