#706841 (C++17(clang)) No.1774 Love Triangle (Hard)

提出ソース

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	AC
実行時間	7,192 ms / 8,000 ms
コード長	5,490 bytes
コンパイル時間	4,189 ms
コンパイル使用メモリ	152,992 KB
実行使用メモリ	10,412 KB
最終ジャッジ日時	2024-09-17 07:48:04
合計ジャッジ時間	493,667 ms
ジャッジサーバーID （参考情報）	judge3 / judge5

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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	2 ms 5,248 KB
testcase_01	AC	1 ms 5,248 KB
testcase_02	AC	4 ms 5,376 KB
testcase_03	AC	7 ms 5,376 KB
testcase_04	AC	3 ms 5,376 KB
testcase_05	AC	7 ms 5,376 KB
testcase_06	AC	3 ms 5,376 KB
testcase_07	AC	14 ms 5,376 KB
testcase_08	AC	2 ms 5,376 KB
testcase_09	AC	2 ms 5,376 KB
testcase_10	AC	1 ms 5,376 KB
testcase_11	AC	22 ms 5,376 KB
testcase_12	AC	4,076 ms 8,064 KB
testcase_13	AC	2,231 ms 6,876 KB
testcase_14	AC	160 ms 5,376 KB
testcase_15	AC	1,702 ms 6,272 KB
testcase_16	AC	574 ms 5,376 KB
testcase_17	AC	31 ms 5,376 KB
testcase_18	AC	2,061 ms 6,532 KB
testcase_19	AC	71 ms 5,376 KB
testcase_20	AC	169 ms 5,376 KB
testcase_21	AC	99 ms 5,376 KB
testcase_22	AC	6,461 ms 10,076 KB
testcase_23	AC	6,617 ms 10,112 KB
testcase_24	AC	6,745 ms 10,128 KB
testcase_25	AC	6,644 ms 10,112 KB
testcase_26	AC	6,645 ms 10,268 KB
testcase_27	AC	6,575 ms 10,240 KB
testcase_28	AC	6,515 ms 10,240 KB
testcase_29	AC	6,769 ms 10,264 KB
testcase_30	AC	6,707 ms 10,240 KB
testcase_31	AC	6,587 ms 10,144 KB
testcase_32	AC	6,630 ms 10,132 KB
testcase_33	AC	6,601 ms 10,140 KB
testcase_34	AC	6,697 ms 10,144 KB
testcase_35	AC	6,602 ms 10,168 KB
testcase_36	AC	6,422 ms 10,012 KB
testcase_37	AC	6,611 ms 10,280 KB
testcase_38	AC	6,577 ms 10,112 KB
testcase_39	AC	6,434 ms 10,112 KB
testcase_40	AC	6,533 ms 10,128 KB
testcase_41	AC	6,540 ms 10,272 KB
testcase_42	AC	6,584 ms 10,368 KB
testcase_43	AC	6,673 ms 10,240 KB
testcase_44	AC	6,609 ms 10,368 KB
testcase_45	AC	6,595 ms 10,332 KB
testcase_46	AC	6,644 ms 10,240 KB
testcase_47	AC	6,676 ms 10,336 KB
testcase_48	AC	6,684 ms 10,240 KB
testcase_49	AC	6,642 ms 10,336 KB
testcase_50	AC	6,767 ms 10,240 KB
testcase_51	AC	6,943 ms 10,240 KB
testcase_52	AC	6,762 ms 10,240 KB
testcase_53	AC	7,192 ms 10,240 KB
testcase_54	AC	6,870 ms 10,240 KB
testcase_55	AC	6,688 ms 10,240 KB
testcase_56	AC	6,755 ms 10,240 KB
testcase_57	AC	6,666 ms 10,240 KB
testcase_58	AC	6,607 ms 10,332 KB
testcase_59	AC	6,664 ms 10,240 KB
testcase_60	AC	6,668 ms 10,240 KB
testcase_61	AC	6,919 ms 10,240 KB
testcase_62	AC	6,909 ms 10,240 KB
testcase_63	AC	6,872 ms 10,368 KB
testcase_64	AC	6,654 ms 10,112 KB
testcase_65	AC	6,989 ms 10,240 KB
testcase_66	AC	6,904 ms 10,240 KB
testcase_67	AC	6,581 ms 10,048 KB
testcase_68	AC	6,835 ms 10,412 KB
testcase_69	AC	6,948 ms 10,240 KB
testcase_70	AC	6,799 ms 10,240 KB
testcase_71	AC	6,889 ms 10,368 KB
testcase_72	AC	6,838 ms 10,240 KB
testcase_73	AC	6,785 ms 10,368 KB
testcase_74	AC	6,863 ms 10,240 KB
testcase_75	AC	6,939 ms 10,240 KB
testcase_76	AC	6,713 ms 10,112 KB
testcase_77	AC	6,926 ms 10,240 KB
testcase_78	AC	6,842 ms 10,368 KB
testcase_79	AC	6,573 ms 10,028 KB
testcase_80	AC	6,827 ms 10,240 KB
testcase_81	AC	6,728 ms 10,240 KB
testcase_82	AC	6,627 ms 10,112 KB
testcase_83	AC	6,635 ms 10,112 KB
testcase_84	AC	6,593 ms 10,020 KB
testcase_85	AC	6,586 ms 10,180 KB
testcase_86	AC	6,634 ms 10,112 KB
testcase_87	AC	6,967 ms 10,240 KB
testcase_88	AC	6,638 ms 10,244 KB
testcase_89	AC	6,677 ms 10,120 KB
testcase_90	AC	6,810 ms 10,240 KB
testcase_91	AC	6,365 ms 10,000 KB
testcase_92	AC	6,408 ms 10,028 KB

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ソースコード

raw source code

#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';
}

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結果

テストケース

ソースコード