結果
問題 | No.1774 Love Triangle (Hard) |
ユーザー |
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提出日時 | 2021-10-08 01:15:55 |
言語 | C++17(clang) (17.0.6 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 3,645 ms / 8,000 ms |
コード長 | 5,330 bytes |
コンパイル時間 | 4,669 ms |
コンパイル使用メモリ | 150,260 KB |
実行使用メモリ | 10,368 KB |
最終ジャッジ日時 | 2024-12-16 03:57:49 |
合計ジャッジ時間 | 257,333 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge1 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 90 |
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 // using mint = atcoder::modint1000000007; std::mt19937 mt(159376); 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::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); } return linear_matroid_parity<mint>(vs); } 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'; }