結果

問題 No.1773 Love Triangle
ユーザー Sumitacchan
提出日時 2021-12-04 05:40:50
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 15,234 bytes
コンパイル時間 2,663 ms
コンパイル使用メモリ 218,304 KB
最終ジャッジ日時 2025-01-26 03:32:26
ジャッジサーバーID
（参考情報） 		judge4 / judge5
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ファイルパターン 結果
sample AC * 2 WA * 1
other AC * 38 WA * 49 TLE * 3
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ソースコード

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プレゼンテーションモードにする

#include <bits/stdc++.h>
//cplib-cpp
//https://hitonanode.github.io/cplib-cpp/graph/test/general_matching.test.cpp
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]; }
    operator std::vector<std::vector<T>>() 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;
    }
    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; for (auto &x : ret.elem) x /= v; 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);
        if (n == 0) return ret;
        for (int i = 63 - __builtin_clzll(n); i >= 0; i--) {
            ret *= ret;
            if ((n >> i) & 1) ret *= (*this);
        }
        return ret;
    }
    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)
    matrix gauss_jordan() const {
        int c = 0;
        matrix mtr(*this);
        for (int h = 0; h < H; h++) {
            if (c == W) break;
            int piv = -1;
            for (int j = h; j < H; j++) if (mtr.get(j, c)) {
                piv = j;
                break;
            }
            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
                }
            }
            for (int hh = 0; hh < H; hh++) if (hh != h) {
                T coeff = mtr.at(hh, c) * mtr.at(h, c).inv();
                for (int w = W - 1; w >= c; w--) {
                    mtr.at(hh, w) -= mtr.at(h, w) * coeff;
                }
            }
            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;
    }
    T determinant_of_upper_triangle() const {
        T ret = 1;
        for (int i = 0; i < H; i++) ret *= get(i, i);
        return ret;
    }
    int inverse() {
        assert(H == W);
        std::vector<std::vector<T>> tmp = Identity(H), A = *this;
        std::vector<int> col(H);
        std::iota(col.begin(), col.end(), 0);
        for (int i = 0; i < H; i++) {
            int r = -1, c = -1;
            [&]() {
                for (int j = i; j < H; j++) {
                    for (int k = i; k < H; k++) {
                        if (A[j][k]) {
                            r = j, c = k;
                            return;
                        }
                    }
                }
            }();
            if (r < 0) {
                return i;
            }
            A[i].swap(A[r]), tmp[i].swap(tmp[r]);
            for (int j = 0; j < H; j++) {
                std::swap(A[j][i], A[j][c]), std::swap(tmp[j][i], tmp[j][c]);
            }
            std::swap(col[i], col[c]);
            T v = A[i][i].inv();
            for (int j = i + 1; j < H; j++) {
                T f = A[j][i] * v;
                A[j][i] = 0;
                for (int k = i + 1; k < H; k++) {
                    A[j][k] -= f * A[i][k];
                }
                for (int k = 0; k < H; k++) {
                    tmp[j][k] -= f * tmp[i][k];
                }
            }
            for (int j = i + 1; j < H; j++) {
                A[i][j] *= v;
            }
            for (int j = 0; j < H; j++) {
                tmp[i][j] *= v;
            }
            A[i][i] = 1;
        }
        for (int i = H - 1; i > 0; --i) {
            for (int j = 0; j < i; j++) {
                T v = A[j][i];
                for (int k = 0; k < H; k++) {
                    tmp[j][k] -= v * tmp[i][k];
                }
            }
        }
        for (int i = 0; i < H; i++) {
            for (int j = 0; j < H; j++) {
                (*this)[col[i]][col[j]] = tmp[i][j];
            }
        }
        return H;
    }
    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;
    }
    friend std::ostream &operator<<(std::ostream &os, const matrix &x) {
        os << "[(" << x.H << " * " << x.W << " matrix)";
        os << "\n[column sums: ";
        for (int j = 0; j < x.W; j++) {
            T s = 0;
            for (int i = 0; i < x.H; i++) s += x.get(i, j);
            os << s << ",";
        }
        os << "]";
        for (int i = 0; i < x.H; i++) {
            os << "\n[";
            for (int j = 0; j < x.W; j++) os << x.get(i, j) << ",";
            os << "]";
        }
        os << "]\n";
        return os;
    }
    friend std::istream &operator>>(std::istream &is, matrix &x) {
        for (auto &v : x.elem) is >> v;
        return is;
    }
};
template <typename MODINT>
std::vector<std::pair<int, int>> generalMatching(int N, const std::vector<std::pair<int, int>>& ed)
{
    std::mt19937 mt(std::chrono::steady_clock::now().time_since_epoch().count());
    std::uniform_int_distribution<int> d(MODINT::get_mod());
    std::vector<std::vector<MODINT>> mat(N, std::vector<MODINT>(N));
    for (auto p : ed) {
        int a = p.first, b = p.second;
        if (a == b) continue;
        mat[a][b] = d(mt), mat[b][a] = -mat[a][b];
    }
    matrix<MODINT> A = mat;
    const int rank = A.inverse(), M = 2 * N - rank;
    if (M != N) {
        do {
            mat.resize(M, std::vector<MODINT>(M));
            for (int i = 0; i < N; i++) {
                mat[i].resize(M);
                for (int j = N; j < M; j++) {
                    mat[i][j] = d(mt), mat[j][i] = -mat[i][j];
                }
            }
            A = mat;
        } while (A.inverse() != M);
    }
    std::vector<int> has(M, 1);
    std::vector<std::pair<int, int>> ret;
    int fi = -1, fj = -1;
    for (int it = 0; it < M / 2; it++) {
        [&]() {
            for (int i = 0; i < M; i++) {
                if (has[i]) {
                    for (int j = i + 1; j < M; j++) {
                        if (A[i][j] and mat[i][j]) {
                            fi = i, fj = j;
                            return;
                        }
                    }
                }
            }
        }();
        if (fj < N) {
            ret.emplace_back(fi, fj);
        }
        has[fi] = has[fj] = 0;
        for (int sw = 0; sw < 2; sw++) {
            MODINT a = A[fi][fj].inv();
            for (int i = 0; i < M; i++) {
                if (has[i] and A[i][fj]) {
                    MODINT b = A[i][fj] * a;
                    for (int j = 0; j < M; j++) {
                        A[i][j] -= A[fi][j] * b;
                    }
                }
            }
            std::swap(fi, fj);
        }
    }
    return ret;
}
template <int mod>
struct ModInt
{
    using lint = long long;
    static int get_mod() { return mod; }
    static int get_primitive_root() {
        static int primitive_root = 0;
        if (!primitive_root) {
            primitive_root = [&](){
                std::set<int> fac;
                int v = mod - 1;
                for (lint i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i;
                if (v > 1) fac.insert(v);
                for (int g = 1; g < mod; g++) {
                    bool ok = true;
                    for (auto i : fac) if (ModInt(g).power((mod - 1) / i) == 1) { ok = false; break; }
                    if (ok) return g;
                }
                return -1;
            }();
        }
        return primitive_root;
    }
    int val;
    constexpr ModInt() : val(0) {}
    constexpr ModInt &_setval(lint v) { val = (v >= mod ? v - mod : v); return *this; }
    constexpr ModInt(lint v) { _setval(v % mod + mod); }
    explicit operator bool() const { return val != 0; }
    constexpr ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); }
    constexpr ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + mod); }
    constexpr ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % mod); }
    constexpr ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % mod); }
    constexpr ModInt operator-() const { return ModInt()._setval(mod - val); }
    constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; }
    constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; }
    constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; }
    constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; }
    friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % mod + x.val); }
    friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % mod - x.val + mod); }
    friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.val % mod); }
    friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.inv() % mod); }
    constexpr bool operator==(const ModInt &x) const { return val == x.val; }
    constexpr bool operator!=(const ModInt &x) const { return val != x.val; }
    bool operator<(const ModInt &x) const { return val < x.val; }  // To use std::map<ModInt, T>
    friend std::istream &operator>>(std::istream &is, ModInt &x) { lint t; is >> t; x = ModInt(t); return is; }
    friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { os << x.val;  return os; }
    constexpr lint power(lint n) const {
        lint ans = 1, tmp = this->val;
        while (n) {
            if (n & 1) ans = ans * tmp % mod;
            tmp = tmp * tmp % mod;
            n /= 2;
        }
        return ans;
    }
    constexpr lint inv() const { return this->power(mod - 2); }
    constexpr ModInt operator^(lint n) const { return ModInt(this->power(n)); }
    constexpr ModInt &operator^=(lint n) { return *this = *this ^ n; }
    inline ModInt fac() const {
        static std::vector<ModInt> facs;
        int l0 = facs.size();
        if (l0 > this->val) return facs[this->val];
        facs.resize(this->val + 1);
        for (int i = l0; i <= this->val; i++) facs[i] = (i == 0 ? ModInt(1) : facs[i - 1] * ModInt(i));
        return facs[this->val];
    }
    ModInt doublefac() const {
        lint k = (this->val + 1) / 2;
        if (this->val & 1) return ModInt(k * 2).fac() / ModInt(2).power(k) / ModInt(k).fac();
        else return ModInt(k).fac() * ModInt(2).power(k);
    }
    ModInt nCr(const ModInt &r) const {
        if (this->val < r.val) return ModInt(0);
        return this->fac() / ((*this - r).fac() * r.fac());
    }
    ModInt sqrt() const {
        if (val == 0) return 0;
        if (mod == 2) return val;
        if (power((mod - 1) / 2) != 1) return 0;
        ModInt b = 1;
        while (b.power((mod - 1) / 2) == 1) b += 1;
        int e = 0, m = mod - 1;
        while (m % 2 == 0) m >>= 1, e++;
        ModInt x = power((m - 1) / 2), y = (*this) * x * x;
        x *= (*this);
        ModInt z = b.power(m);
        while (y != 1) {
            int j = 0;
            ModInt t = y;
            while (t != 1) j++, t *= t;
            z = z.power(1LL << (e - j - 1));
            x *= z, z *= z, y *= z;
            e = j;
        }
        return ModInt(std::min(x.val, mod - x.val));
    }
};
#define PROBLEM "https://judge.yosupo.jp/problem/general_matching"
using namespace std;
int main()
{
    //それぞれの三角形につき、(u->v,u->w),(v->u,v->w),(w->u,w->v)の3択のいずれかを貼ると解釈
    //できる有向グラフが根付き木にできることが必要十分条件？
    //(u->v,u->w)の代わりに(v<->w)に貼る、みたいなことを考えると、一般マッチングになっていることが必要条件
    //ただしそれだけだと最初の有向グラフに戻したときになもりになることがある、情助
    cin.tie(NULL), ios::sync_with_stdio(false);
    int N, M;
    cin >> N >> M;
    vector<pair<int, int>> edges;
    for(int i = 0; i < M; i++) {
        int u, v, w;
        cin >> u >> v >> w;
        u--; v--; w--;
        edges.emplace_back(u, v);
        edges.emplace_back(v, w);
        edges.emplace_back(w, u);
    }
    vector<pair<int, int>> ret = generalMatching<ModInt<1000000007>>(N, edges);
    cout << ret.size() << '\n';
}
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