#702735 (C++17) 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	2021-09-25 03:11:48
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	5,112 ms / 8,000 ms
コード長	11,369 bytes
コンパイル時間	1,932 ms
コンパイル使用メモリ	139,060 KB
実行使用メモリ	14,476 KB
最終ジャッジ日時	2023-10-09 22:50:02
合計ジャッジ時間	248,740 ms
ジャッジサーバーID （参考情報）	judge11 / judge12

このコードへのチャレンジ
（要ログイン）

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 4,356 KB
testcase_01	AC	1 ms 4,352 KB
testcase_02	AC	3 ms 4,352 KB
testcase_03	AC	6 ms 4,352 KB
testcase_04	AC	3 ms 4,348 KB
testcase_05	AC	5 ms 4,352 KB
testcase_06	AC	2 ms 4,348 KB
testcase_07	AC	12 ms 4,352 KB
testcase_08	AC	2 ms 4,352 KB
testcase_09	AC	2 ms 4,352 KB
testcase_10	AC	1 ms 4,348 KB
testcase_11	AC	17 ms 4,348 KB
testcase_12	AC	2,824 ms 11,636 KB
testcase_13	AC	1,561 ms 10,320 KB
testcase_14	AC	115 ms 4,352 KB
testcase_15	AC	1,190 ms 9,124 KB
testcase_16	AC	428 ms 5,564 KB
testcase_17	AC	22 ms 4,352 KB
testcase_18	AC	1,407 ms 9,928 KB
testcase_19	AC	49 ms 4,460 KB
testcase_20	AC	119 ms 4,544 KB
testcase_21	AC	71 ms 4,372 KB
testcase_22	AC	4,735 ms 14,044 KB
testcase_23	AC	4,744 ms 14,080 KB
testcase_24	AC	4,865 ms 13,964 KB
testcase_25	AC	4,726 ms 14,028 KB
testcase_26	AC	4,849 ms 14,200 KB
testcase_27	AC	4,833 ms 14,124 KB
testcase_28	AC	4,842 ms 13,868 KB
testcase_29	AC	5,043 ms 13,972 KB
testcase_30	AC	4,880 ms 14,044 KB
testcase_31	AC	4,748 ms 13,984 KB
testcase_32	AC	4,757 ms 13,996 KB
testcase_33	AC	4,792 ms 14,220 KB
testcase_34	AC	4,764 ms 14,332 KB
testcase_35	AC	4,725 ms 14,032 KB
testcase_36	AC	4,578 ms 13,892 KB
testcase_37	AC	4,942 ms 14,228 KB
testcase_38	AC	4,752 ms 14,092 KB
testcase_39	AC	4,835 ms 14,108 KB
testcase_40	AC	4,910 ms 14,024 KB
testcase_41	AC	4,798 ms 14,188 KB
testcase_42	AC	4,939 ms 14,100 KB
testcase_43	AC	4,792 ms 14,040 KB
testcase_44	AC	4,902 ms 14,096 KB
testcase_45	AC	4,847 ms 14,088 KB
testcase_46	AC	4,763 ms 13,984 KB
testcase_47	AC	4,827 ms 14,044 KB
testcase_48	AC	4,795 ms 14,260 KB
testcase_49	AC	4,754 ms 14,104 KB
testcase_50	AC	4,835 ms 14,252 KB
testcase_51	AC	4,954 ms 14,104 KB
testcase_52	AC	4,955 ms 14,192 KB
testcase_53	AC	5,004 ms 14,028 KB
testcase_54	AC	4,984 ms 13,980 KB
testcase_55	AC	4,965 ms 14,292 KB
testcase_56	AC	5,003 ms 14,088 KB
testcase_57	AC	4,975 ms 14,196 KB
testcase_58	AC	4,990 ms 14,260 KB
testcase_59	AC	5,005 ms 14,260 KB
testcase_60	AC	5,065 ms 14,104 KB
testcase_61	AC	4,967 ms 14,028 KB
testcase_62	AC	4,890 ms 14,112 KB
testcase_63	AC	4,762 ms 14,260 KB
testcase_64	AC	4,651 ms 13,948 KB
testcase_65	AC	4,795 ms 14,032 KB
testcase_66	AC	5,102 ms 14,028 KB
testcase_67	AC	4,936 ms 14,032 KB
testcase_68	AC	5,096 ms 14,296 KB
testcase_69	AC	5,106 ms 14,036 KB
testcase_70	AC	4,945 ms 13,988 KB
testcase_71	AC	5,112 ms 14,104 KB
testcase_72	AC	5,101 ms 14,280 KB
testcase_73	AC	5,087 ms 14,072 KB
testcase_74	AC	5,108 ms 14,444 KB
testcase_75	AC	5,098 ms 14,444 KB
testcase_76	AC	4,988 ms 14,044 KB
testcase_77	AC	5,095 ms 14,096 KB
testcase_78	AC	5,097 ms 14,092 KB
testcase_79	AC	4,874 ms 13,796 KB
testcase_80	AC	5,100 ms 14,264 KB
testcase_81	AC	5,095 ms 14,296 KB
testcase_82	AC	4,965 ms 14,096 KB
testcase_83	AC	4,964 ms 14,292 KB
testcase_84	AC	4,876 ms 13,976 KB
testcase_85	AC	4,887 ms 13,876 KB
testcase_86	AC	4,906 ms 13,960 KB
testcase_87	AC	5,090 ms 14,476 KB
testcase_88	AC	4,977 ms 14,180 KB
testcase_89	AC	4,996 ms 13,976 KB
testcase_90	AC	5,060 ms 14,296 KB
testcase_91	AC	4,826 ms 14,024 KB
testcase_92	AC	4,955 ms 13,792 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

raw source code

#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';
}

yukicoder

結果

テストケース

ソースコード