結果

問題 No.1774 Love Triangle (Hard)
ユーザー hitonanodehitonanode
提出日時 2021-09-25 03:11:48
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 5,140 ms / 8,000 ms
コード長 11,369 bytes
コンパイル時間 2,227 ms
コンパイル使用メモリ 140,424 KB
実行使用メモリ 14,484 KB
最終ジャッジ日時 2024-07-26 21:17:53
合計ジャッジ時間 370,002 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge1
このコードへのチャレンジ
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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
6,812 KB
testcase_01 AC 2 ms
6,940 KB
testcase_02 AC 3 ms
6,940 KB
testcase_03 AC 6 ms
6,940 KB
testcase_04 AC 3 ms
6,940 KB
testcase_05 AC 6 ms
6,940 KB
testcase_06 AC 2 ms
6,944 KB
testcase_07 AC 12 ms
6,940 KB
testcase_08 AC 2 ms
6,940 KB
testcase_09 AC 2 ms
6,944 KB
testcase_10 AC 2 ms
6,940 KB
testcase_11 AC 18 ms
6,944 KB
testcase_12 AC 2,890 ms
11,960 KB
testcase_13 AC 1,580 ms
10,632 KB
testcase_14 AC 118 ms
6,944 KB
testcase_15 AC 1,208 ms
9,460 KB
testcase_16 AC 445 ms
6,940 KB
testcase_17 AC 22 ms
6,940 KB
testcase_18 AC 1,443 ms
10,064 KB
testcase_19 AC 48 ms
6,940 KB
testcase_20 AC 121 ms
6,940 KB
testcase_21 AC 72 ms
6,940 KB
testcase_22 AC 4,909 ms
14,104 KB
testcase_23 AC 4,936 ms
14,176 KB
testcase_24 AC 5,103 ms
14,268 KB
testcase_25 AC 4,902 ms
14,172 KB
testcase_26 AC 5,038 ms
14,260 KB
testcase_27 AC 4,958 ms
14,324 KB
testcase_28 AC 4,949 ms
14,188 KB
testcase_29 AC 5,047 ms
14,276 KB
testcase_30 AC 5,092 ms
14,348 KB
testcase_31 AC 5,008 ms
14,252 KB
testcase_32 AC 5,036 ms
14,252 KB
testcase_33 AC 5,047 ms
14,280 KB
testcase_34 AC 5,044 ms
14,340 KB
testcase_35 AC 5,040 ms
14,152 KB
testcase_36 AC 4,866 ms
14,104 KB
testcase_37 AC 5,060 ms
14,288 KB
testcase_38 AC 4,908 ms
14,164 KB
testcase_39 AC 4,968 ms
14,204 KB
testcase_40 AC 5,040 ms
14,272 KB
testcase_41 AC 5,050 ms
14,288 KB
testcase_42 AC 5,112 ms
14,356 KB
testcase_43 AC 5,100 ms
14,352 KB
testcase_44 AC 5,100 ms
14,352 KB
testcase_45 AC 5,096 ms
14,352 KB
testcase_46 AC 5,099 ms
14,356 KB
testcase_47 AC 5,104 ms
14,352 KB
testcase_48 AC 5,088 ms
14,228 KB
testcase_49 AC 5,094 ms
14,356 KB
testcase_50 AC 5,099 ms
14,356 KB
testcase_51 AC 5,098 ms
14,352 KB
testcase_52 AC 5,140 ms
14,484 KB
testcase_53 AC 5,105 ms
14,352 KB
testcase_54 AC 5,097 ms
14,480 KB
testcase_55 AC 5,103 ms
14,352 KB
testcase_56 AC 5,102 ms
14,352 KB
testcase_57 AC 5,101 ms
14,356 KB
testcase_58 AC 5,096 ms
14,356 KB
testcase_59 AC 5,092 ms
14,352 KB
testcase_60 AC 5,096 ms
14,352 KB
testcase_61 AC 5,099 ms
14,484 KB
testcase_62 AC 5,100 ms
14,356 KB
testcase_63 AC 5,106 ms
14,224 KB
testcase_64 AC 4,948 ms
14,188 KB
testcase_65 AC 5,092 ms
14,224 KB
testcase_66 AC 5,095 ms
14,356 KB
testcase_67 AC 4,936 ms
14,160 KB
testcase_68 AC 5,098 ms
14,352 KB
testcase_69 AC 5,090 ms
14,224 KB
testcase_70 AC 4,948 ms
14,184 KB
testcase_71 AC 5,098 ms
14,352 KB
testcase_72 AC 5,103 ms
14,228 KB
testcase_73 AC 5,072 ms
14,332 KB
testcase_74 AC 5,089 ms
14,352 KB
testcase_75 AC 5,098 ms
14,356 KB
testcase_76 AC 5,026 ms
14,236 KB
testcase_77 AC 5,089 ms
14,352 KB
testcase_78 AC 5,094 ms
14,352 KB
testcase_79 AC 4,882 ms
14,116 KB
testcase_80 AC 5,100 ms
14,356 KB
testcase_81 AC 5,097 ms
14,356 KB
testcase_82 AC 4,967 ms
14,232 KB
testcase_83 AC 4,907 ms
14,168 KB
testcase_84 AC 4,866 ms
14,108 KB
testcase_85 AC 4,903 ms
14,148 KB
testcase_86 AC 4,994 ms
14,172 KB
testcase_87 AC 5,102 ms
14,356 KB
testcase_88 AC 4,982 ms
14,236 KB
testcase_89 AC 4,988 ms
14,244 KB
testcase_90 AC 5,057 ms
14,352 KB
testcase_91 AC 4,825 ms
14,096 KB
testcase_92 AC 4,828 ms
14,112 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <algorithm>
#include <cassert>
#include <chrono>
#include <iostream>
#include <numeric>
#include <queue>
#include <random>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define REP(i, n) FOR(i,0,n)

#include <atcoder/modint>
// using mint = atcoder::modint1000000007;
using mint = atcoder::static_modint<1000000009>;


template <typename T> struct matrix {
    int H, W;
    std::vector<T> elem;
    typename std::vector<T>::iterator operator[](int i) { return elem.begin() + i * W; }
    inline T &at(int i, int j) { return elem[i * W + j]; }
    inline T get(int i, int j) const { return elem[i * W + j]; }
    int height() const { return H; }
    int width() const { return W; }
    std::vector<std::vector<T>> vecvec() const {
        std::vector<std::vector<T>> ret(H);
        for (int i = 0; i < H; i++) {
            std::copy(elem.begin() + i * W, elem.begin() + (i + 1) * W, std::back_inserter(ret[i]));
        }
        return ret;
    }
    operator std::vector<std::vector<T>>() const { return vecvec(); }
    matrix() = default;
    matrix(int H, int W) : H(H), W(W), elem(H * W) {}
    matrix(const std::vector<std::vector<T>> &d) : H(d.size()), W(d.size() ? d[0].size() : 0) {
        for (auto &raw : d) std::copy(raw.begin(), raw.end(), std::back_inserter(elem));
    }

    static matrix Identity(int N) {
        matrix ret(N, N);
        for (int i = 0; i < N; i++) ret.at(i, i) = 1;
        return ret;
    }

    matrix operator-() const {
        matrix ret(H, W);
        for (int i = 0; i < H * W; i++) ret.elem[i] = -elem[i];
        return ret;
    }
    matrix operator*(const T &v) const {
        matrix ret = *this;
        for (auto &x : ret.elem) x *= v;
        return ret;
    }
    matrix operator/(const T &v) const {
        matrix ret = *this;
        const T vinv = T(1) / v;
        for (auto &x : ret.elem) x *= vinv;
        return ret;
    }
    matrix operator+(const matrix &r) const {
        matrix ret = *this;
        for (int i = 0; i < H * W; i++) ret.elem[i] += r.elem[i];
        return ret;
    }
    matrix operator-(const matrix &r) const {
        matrix ret = *this;
        for (int i = 0; i < H * W; i++) ret.elem[i] -= r.elem[i];
        return ret;
    }
    matrix operator*(const matrix &r) const {
        matrix ret(H, r.W);
        for (int i = 0; i < H; i++) {
            for (int k = 0; k < W; k++) {
                for (int j = 0; j < r.W; j++) ret.at(i, j) += this->get(i, k) * r.get(k, j);
            }
        }
        return ret;
    }
    matrix &operator*=(const T &v) { return *this = *this * v; }
    matrix &operator/=(const T &v) { return *this = *this / v; }
    matrix &operator+=(const matrix &r) { return *this = *this + r; }
    matrix &operator-=(const matrix &r) { return *this = *this - r; }
    matrix &operator*=(const matrix &r) { return *this = *this * r; }
    bool operator==(const matrix &r) const { return H == r.H and W == r.W and elem == r.elem; }
    bool operator!=(const matrix &r) const { return H != r.H or W != r.W or elem != r.elem; }
    bool operator<(const matrix &r) const { return elem < r.elem; }
    matrix pow(int64_t n) const {
        matrix ret = Identity(H);
        bool ret_is_id = true;
        if (n == 0) return ret;
        for (int i = 63 - __builtin_clzll(n); i >= 0; i--) {
            if (!ret_is_id) ret *= ret;
            if ((n >> i) & 1) ret *= (*this), ret_is_id = false;
        }
        return ret;
    }
    std::vector<T> pow_vec(int64_t n, std::vector<T> vec) const {
        matrix x = *this;
        while (n) {
            if (n & 1) vec = x * vec;
            x *= x;
            n >>= 1;
        }
        return vec;
    };
    matrix transpose() const {
        matrix ret(W, H);
        for (int i = 0; i < H; i++) {
            for (int j = 0; j < W; j++) ret.at(j, i) = this->get(i, j);
        }
        return ret;
    }
    // Gauss-Jordan elimination
    // - Require inverse for every non-zero element
    // - Complexity: O(H^2 W)
    template <typename T2, typename std::enable_if<std::is_floating_point<T2>::value>::type * = nullptr>
    static int choose_pivot(const matrix<T2> &mtr, int h, int c) noexcept {
        int piv = -1;
        for (int j = h; j < mtr.H; j++) {
            if (mtr.get(j, c) and (piv < 0 or std::abs(mtr.get(j, c)) > std::abs(mtr.get(piv, c)))) piv = j;
        }
        return piv;
    }
    template <typename T2, typename std::enable_if<!std::is_floating_point<T2>::value>::type * = nullptr>
    static int choose_pivot(const matrix<T2> &mtr, int h, int c) noexcept {
        for (int j = h; j < mtr.H; j++) {
            if (mtr.get(j, c)) return j;
        }
        return -1;
    }
    matrix gauss_jordan() const {
        int c = 0;
        matrix mtr(*this);
        std::vector<int> ws;
        ws.reserve(W);
        for (int h = 0; h < H; h++) {
            if (c == W) break;
            int piv = choose_pivot(mtr, h, c);
            if (piv == -1) {
                c++;
                h--;
                continue;
            }
            if (h != piv) {
                for (int w = 0; w < W; w++) {
                    std::swap(mtr[piv][w], mtr[h][w]);
                    mtr.at(piv, w) *= -1; // To preserve sign of determinant
                }
            }
            ws.clear();
            for (int w = c; w < W; w++) {
                if (mtr.at(h, w) != 0) ws.emplace_back(w);
            }
            const T hcinv = T(1) / mtr.at(h, c);
            for (int hh = 0; hh < H; hh++)
                if (hh != h) {
                    const T coeff = mtr.at(hh, c) * hcinv;
                    for (auto w : ws) mtr.at(hh, w) -= mtr.at(h, w) * coeff;
                    mtr.at(hh, c) = 0;
                }
            c++;
        }
        return mtr;
    }
    int rank_of_gauss_jordan() const {
        for (int i = H * W - 1; i >= 0; i--) {
            if (elem[i]) return i / W + 1;
        }
        return 0;
    }
    int inverse() {
        assert(H == W);
        std::vector<std::vector<T>> ret = Identity(H), tmp = *this;
        int rank = 0;
        for (int i = 0; i < H; i++) {
            int ti = i;
            while (ti < H and tmp[ti][i] == 0) ti++;
            if (ti == H) {
                continue;
            } else {
                rank++;
            }
            ret[i].swap(ret[ti]), tmp[i].swap(tmp[ti]);
            T inv = T(1) / tmp[i][i];
            for (int j = 0; j < W; j++) ret[i][j] *= inv;
            for (int j = i + 1; j < W; j++) tmp[i][j] *= inv;
            for (int h = 0; h < H; h++) {
                if (i == h) continue;
                const T c = -tmp[h][i];
                for (int j = 0; j < W; j++) ret[h][j] += ret[i][j] * c;
                for (int j = i + 1; j < W; j++) tmp[h][j] += tmp[i][j] * c;
            }
        }
        *this = ret;
        return rank;
    }
    friend std::vector<T> operator*(const matrix &m, const std::vector<T> &v) {
        assert(m.W == int(v.size()));
        std::vector<T> ret(m.H);
        for (int i = 0; i < m.H; i++) {
            for (int j = 0; j < m.W; j++) ret[i] += m.get(i, j) * v[j];
        }
        return ret;
    }
    friend std::vector<T> operator*(const std::vector<T> &v, const matrix &m) {
        assert(int(v.size()) == m.H);
        std::vector<T> ret(m.W);
        for (int i = 0; i < m.H; i++) {
            for (int j = 0; j < m.W; j++) ret[j] += v[i] * m.get(i, j);
        }
        return ret;
    }
};


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);

    matrix<ModInt> Y, Yinv; // r2 * r2 matrices
    int rankY = -1;
    while (rankY < r2 * 2) {
        Y = matrix<ModInt>(r2 * 2, r2 * 2);
        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++) Y[j][k] += b[j] * c[k] - c[j] * b[k];
            }
        }
        Yinv = Y;
        rankY = Yinv.inverse();
    }

    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 = Yinv * b, Yic = Yinv * c;
            ModInt bYic = std::inner_product(b.begin(), b.end(), Yic.begin(), ModInt(0));
            ModInt v = 1 + x[i] * bYic;

            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 = Yinv * b, Yic = 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<pint, pint>> 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 ret1 = linear_matroid_parity<mint>(vs);
    // auto ret2 = linear_matroid_parity<mint>(vs);
    // for (int i = 0; i < int(ret1.size()); i++) ret1[i] = max(ret1[i], ret2[i]);
    return ret1;
}

int main() {
    int N, M;
    cin >> N >> M;
    vector<pair<pint, pint>> 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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