結果

問題 No.1774 Love Triangle (Hard)
ユーザー 👑 hitonanodehitonanode
提出日時 2021-10-08 01:15:55
言語 C++17(clang)
(17.0.6 + boost 1.83.0)
結果
AC  
実行時間 3,714 ms / 8,000 ms
コード長 5,330 bytes
コンパイル時間 3,246 ms
コンパイル使用メモリ 116,024 KB
実行使用メモリ 10,352 KB
最終ジャッジ日時 2023-08-22 08:16:53
合計ジャッジ時間 274,344 ms
ジャッジサーバーID
（参考情報） 		judge13 / judge11
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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
4,388 KB
testcase_01 AC 2 ms
4,380 KB
testcase_02 AC 3 ms
4,380 KB
testcase_03 AC 5 ms
4,384 KB
testcase_04 AC 3 ms
4,380 KB
testcase_05 AC 4 ms
4,380 KB
testcase_06 AC 2 ms
4,384 KB
testcase_07 AC 10 ms
4,380 KB
testcase_08 AC 2 ms
4,384 KB
testcase_09 AC 2 ms
4,384 KB
testcase_10 AC 1 ms
4,384 KB
testcase_11 AC 14 ms
4,380 KB
testcase_12 AC 2,128 ms
7,912 KB
testcase_13 AC 1,200 ms
6,580 KB
testcase_14 AC 85 ms
4,380 KB
testcase_15 AC 906 ms
6,032 KB
testcase_16 AC 316 ms
5,116 KB
testcase_17 AC 17 ms
4,384 KB
testcase_18 AC 1,097 ms
6,368 KB
testcase_19 AC 38 ms
4,380 KB
testcase_20 AC 92 ms
4,380 KB
testcase_21 AC 54 ms
4,380 KB
testcase_22 AC 3,530 ms
10,036 KB
testcase_23 AC 3,628 ms
10,120 KB
testcase_24 AC 3,657 ms
10,148 KB
testcase_25 AC 3,612 ms
10,080 KB
testcase_26 AC 3,635 ms
10,192 KB
testcase_27 AC 3,603 ms
10,056 KB
testcase_28 AC 3,597 ms
10,064 KB
testcase_29 AC 3,660 ms
10,112 KB
testcase_30 AC 3,705 ms
10,264 KB
testcase_31 AC 3,621 ms
10,172 KB
testcase_32 AC 3,624 ms
10,196 KB
testcase_33 AC 3,670 ms
10,256 KB
testcase_34 AC 3,660 ms
10,104 KB
testcase_35 AC 3,676 ms
10,132 KB
testcase_36 AC 3,536 ms
10,040 KB
testcase_37 AC 3,669 ms
10,120 KB
testcase_38 AC 3,608 ms
10,132 KB
testcase_39 AC 3,591 ms
10,092 KB
testcase_40 AC 3,651 ms
10,132 KB
testcase_41 AC 3,657 ms
10,104 KB
testcase_42 AC 3,706 ms
10,284 KB
testcase_43 AC 3,707 ms
10,236 KB
testcase_44 AC 3,705 ms
10,224 KB
testcase_45 AC 3,702 ms
10,272 KB
testcase_46 AC 3,697 ms
10,280 KB
testcase_47 AC 3,694 ms
10,228 KB
testcase_48 AC 3,692 ms
10,212 KB
testcase_49 AC 3,705 ms
10,320 KB
testcase_50 AC 3,694 ms
10,220 KB
testcase_51 AC 3,703 ms
10,256 KB
testcase_52 AC 3,709 ms
10,220 KB
testcase_53 AC 3,696 ms
10,228 KB
testcase_54 AC 3,706 ms
10,288 KB
testcase_55 AC 3,702 ms
10,320 KB
testcase_56 AC 3,704 ms
10,240 KB
testcase_57 AC 3,699 ms
10,260 KB
testcase_58 AC 3,702 ms
10,352 KB
testcase_59 AC 3,696 ms
10,212 KB
testcase_60 AC 3,707 ms
10,248 KB
testcase_61 AC 3,706 ms
10,280 KB
testcase_62 AC 3,709 ms
10,300 KB
testcase_63 AC 3,710 ms
10,304 KB
testcase_64 AC 3,600 ms
10,056 KB
testcase_65 AC 3,703 ms
10,276 KB
testcase_66 AC 3,698 ms
10,232 KB
testcase_67 AC 3,579 ms
10,120 KB
testcase_68 AC 3,708 ms
10,248 KB
testcase_69 AC 3,700 ms
10,240 KB
testcase_70 AC 3,602 ms
10,068 KB
testcase_71 AC 3,703 ms
10,208 KB
testcase_72 AC 3,702 ms
10,252 KB
testcase_73 AC 3,682 ms
10,280 KB
testcase_74 AC 3,708 ms
10,292 KB
testcase_75 AC 3,707 ms
10,240 KB
testcase_76 AC 3,628 ms
10,104 KB
testcase_77 AC 3,714 ms
10,236 KB
testcase_78 AC 3,709 ms
10,292 KB
testcase_79 AC 3,547 ms
10,056 KB
testcase_80 AC 3,704 ms
10,280 KB
testcase_81 AC 3,693 ms
10,312 KB
testcase_82 AC 3,609 ms
10,136 KB
testcase_83 AC 3,631 ms
10,036 KB
testcase_84 AC 3,542 ms
10,084 KB
testcase_85 AC 3,608 ms
10,056 KB
testcase_86 AC 3,626 ms
10,036 KB
testcase_87 AC 3,701 ms
10,232 KB
testcase_88 AC 3,603 ms
10,124 KB
testcase_89 AC 3,623 ms
10,144 KB
testcase_90 AC 3,666 ms
10,300 KB
testcase_91 AC 3,487 ms
9,988 KB
testcase_92 AC 3,506 ms
9,964 KB
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ソースコード

diff # 

#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';
}
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