#905293 (C++17) No.2435 Order All Company

• 問題: No.2435 Order All Company
• ユーザー: Forested
• 提出日時: 2023-08-18 21:43:32
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 22 ms / 2,000 ms
• コード長: 13,039 bytes
• コンパイル時間: 1,678 ms
• コンパイル使用メモリ: 141,496 KB
• 最終ジャッジ日時: 2025-02-16 09:49:06
• ジャッジサーバーID （参考情報）: judge4 / judge4

ファイルパターン	結果
other	AC * 36

ソースコード

#ifndef LOCAL
#define FAST_IO
#endif

// ============
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i)
#define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER(i, n) for (i32 i = (i32)(n) - 1; i >= 0; --i)
#define ALL(x) begin(x), end(x)

using namespace std;

using u32 = unsigned int;
using u64 = unsigned long long;
using i32 = signed int;
using i64 = signed long long;
using f64 = double;
using f80 = long double;

template <typename T>
using Vec = vector<T>;

template <typename T>
bool chmin(T &x, const T &y) {
    if (x > y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
    if (x < y) {
        x = y;
        return true;
    }
    return false;
}

#ifdef INT128

using u128 = __uint128_t;
using i128 = __int128_t;

istream &operator>>(istream &is, i128 &x) {
    i64 v;
    is >> v;
    x = v;
    return is;
}
ostream &operator<<(ostream &os, i128 x) {
    os << (i64)x;
    return os;
}
istream &operator>>(istream &is, u128 &x) {
    u64 v;
    is >> v;
    x = v;
    return is;
}
ostream &operator<<(ostream &os, u128 x) {
    os << (u64)x;
    return os;
}

#endif

[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct SetUpIO {
    SetUpIO() {
#ifdef FAST_IO
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
#endif
        cout << fixed << setprecision(15);
    }
} set_up_io;
// ============

#ifdef DEBUGF
#else
#define DBG(x) (void)0
#endif

// ============

#include <cassert>
#include <iostream>
#include <type_traits>

// ============

constexpr bool is_prime(unsigned n) {
    if (n == 0 || n == 1) {
        return false;
    }
    for (unsigned i = 2; i * i <= n; ++i) {
        if (n % i == 0) {
            return false;
        }
    }
    return true;
}

constexpr unsigned mod_pow(unsigned x, unsigned y, unsigned mod) {
    unsigned ret = 1, self = x;
    while (y != 0) {
        if (y & 1) {
            ret = (unsigned) ((unsigned long long) ret * self % mod);
        }
        self = (unsigned) ((unsigned long long) self * self % mod);
        y /= 2;
    }
    return ret;
}

template <unsigned mod>
constexpr unsigned primitive_root() {
    static_assert(is_prime(mod), "`mod` must be a prime number.");
    if (mod == 2) {
        return 1;
    }

    unsigned primes[32] = {};
    int it = 0;
    {
        unsigned m = mod - 1;
        for (unsigned i = 2; i * i <= m; ++i) {
            if (m % i == 0) {
                primes[it++] = i;
                while (m % i == 0) {
                    m /= i;
                }
            }
        }
        if (m != 1) {
            primes[it++] = m;
        }
    }
    for (unsigned i = 2; i < mod; ++i) {
        bool ok = true;
        for (int j = 0; j < it; ++j) {
            if (mod_pow(i, (mod - 1) / primes[j], mod) == 1) {
                ok = false;
                break;
            }
        }
        if (ok)
            return i;
    }
    return 0;
}

// y >= 1
template <typename T>
constexpr T safe_mod(T x, T y) {
    x %= y;
    if (x < 0) {
        x += y;
    }
    return x;
}

// y != 0
template <typename T>
constexpr T floor_div(T x, T y) {
    if (y < 0) {
        x *= -1;
        y *= -1;
    }
    if (x >= 0) {
        return x / y;
    } else {
        return -((-x + y - 1) / y);
    }
}

// y != 0
template <typename T>
constexpr T ceil_div(T x, T y) {
    if (y < 0) {
        x *= -1;
        y *= -1;
    }
    if (x >= 0) {
        return (x + y - 1) / y;
    } else {
        return -(-x / y);
    }
}
// ============

template <unsigned mod>
class ModInt {
    static_assert(mod != 0, "`mod` must not be equal to 0.");
    static_assert(
        mod < (1u << 31),
        "`mod` must be less than (1u << 31) = 2147483648.");

    unsigned val;

public:
    static constexpr unsigned get_mod() {
        return mod;
    }
    
    constexpr ModInt() : val(0) {}
    template <typename T, std::enable_if_t<std::is_signed_v<T>> * = nullptr>
    constexpr ModInt(T x) : val((unsigned) ((long long) x % (long long) mod + (x < 0 ? mod : 0))) {}
    template <typename T, std::enable_if_t<std::is_unsigned_v<T>> * = nullptr>
    constexpr ModInt(T x) : val((unsigned) (x % mod)) {}

    static constexpr ModInt raw(unsigned x) {
        ModInt<mod> ret;
        ret.val = x;
        return ret;
    }

    constexpr unsigned get_val() const {
        return val;
    }

    constexpr ModInt operator+() const {
        return *this;
    }
    constexpr ModInt operator-() const {
        return ModInt<mod>(0u) - *this;
    }

    constexpr ModInt &operator+=(const ModInt &rhs) {
        val += rhs.val;
        if (val >= mod)
            val -= mod;
        return *this;
    }
    constexpr ModInt &operator-=(const ModInt &rhs) {
        val -= rhs.val;
        if (val >= mod)
            val += mod;
        return *this;
    }
    constexpr ModInt &operator*=(const ModInt &rhs) {
        val = (unsigned long long)val * rhs.val % mod;
        return *this;
    }
    constexpr ModInt &operator/=(const ModInt &rhs) {
        val = (unsigned long long)val * rhs.inv().val % mod;
        return *this;
    }

    friend constexpr ModInt operator+(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) += rhs;
    }
    friend constexpr ModInt operator-(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) -= rhs;
    }
    friend constexpr ModInt operator*(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) *= rhs;
    }
    friend constexpr ModInt operator/(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) /= rhs;
    }

    constexpr ModInt pow(unsigned long long x) const {
        ModInt<mod> ret = ModInt<mod>::raw(1);
        ModInt<mod> self = *this;
        while (x != 0) {
            if (x & 1)
                ret *= self;
            self *= self;
            x >>= 1;
        }
        return ret;
    }
    constexpr ModInt inv() const {
        static_assert(is_prime(mod), "`mod` must be a prime number.");
        assert(val != 0);
        return this->pow(mod - 2);
    }

    friend std::istream &operator>>(std::istream &is, ModInt<mod> &x) {
        long long val;
        is >> val;
        x.val = val % mod + (val < 0 ? mod : 0);
        return is;
    }

    friend std::ostream &operator<<(std::ostream &os, const ModInt<mod> &x) {
        os << x.val;
        return os;
    }

    friend bool operator==(const ModInt &lhs, const ModInt &rhs) {
        return lhs.val == rhs.val;
    }
    
    friend bool operator!=(const ModInt &lhs, const ModInt &rhs) {
        return lhs.val != rhs.val;
    }
};

[[maybe_unused]] constexpr unsigned mod998244353 = 998244353;
[[maybe_unused]] constexpr unsigned mod1000000007 = 1000000007;

// ============
// ============

#include <cassert>
#include <utility>
#include <vector>

template <typename T>
class Matrix {
    std::vector<std::vector<T>> data;
    
public:
    Matrix(int n) : data(n, std::vector<T>(n, T(0))) {}
    Matrix(int h, int w) : data(h, std::vector<T>(w, T(0))) {}
    // must be rectangular
    Matrix(std::vector<std::vector<T>> a) : data(std::move(a)) {}
    
    int height() const {
        return data.size();
    }
    int width() const {
        return data.empty() ? 0 : data[0].size();
    }
    bool is_square() const {
        return height() == width();
    }
    
    const T &operator()(int i, int j) const {
        return data[i][j];
    }
    T &operator()(int i, int j) {
        return data[i][j];
    }
    
    Matrix<T> trans() const {
        const int h = height(), w = width();
        Matrix<T> ret(w, h);
        for (int i = 0; i < h; ++i) {
            for (int j = 0; j < w; ++j) {
                ret.data[j][i] = data[i][j];
            }
        }
        return ret;
    }
    
    Matrix<T> operator+() const {
        return *this;
    }
    Matrix<T> operator-() const {
        const int h = height(), w = width();
        Matrix<T> ret = *this;
        for (int i = 0; i < h; ++i) {
            for (int j = 0; j < w; ++j) {
                ret.data[i][j] = -ret.data[i][j];
            }
        }
        return ret;
    }
    
    Matrix<T> &operator+=(const Matrix<T> &rhs) {
        assert(height() == rhs.height() && width() == rhs.width());
        const int h = height(), w = width();
        for (int i = 0; i < h; ++i) {
            for (int j = 0; j < w; ++j) {
                data[i][j] += rhs.data[i][j];
            }
        }
        return *this;
    }
    Matrix<T> &operator-=(const Matrix<T> &rhs) {
        assert(height() == rhs.height() && width() == rhs.width());
        const int h = height(), w = width();
        for (int i = 0; i < h; ++i) {
            for (int j = 0; j < w; ++j) {
                data[i][j] -= rhs.data[i][j];
            }
        }
        return *this;
    }
    friend Matrix<T> operator+(const Matrix<T> &lhs, const Matrix<T> &rhs) {
        return lhs += rhs;
    }
    friend Matrix<T> operator-(const Matrix<T> &lhs, const Matrix<T> &rhs) {
        return lhs -= rhs;
    }
    
    friend Matrix<T> operator*(const Matrix<T> &lhs, const Matrix<T> &rhs) {
        assert(lhs.width() == rhs.height());
        const int n = lhs.height(), m = rhs.height(), k = rhs.width();
        Matrix<T> ret(n, k);
        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < k; ++j) {
                for (int l = 0; l < m; ++l) {
                    ret.data[i][j] += lhs.data[i][l] * rhs.data[l][j];
                }
            }
        }
        return ret;
    }
    Matrix<T> &operator*=(const Matrix<T> &rhs) {
        return *this = *this * rhs;
    }
    
    static Matrix<T> e(int n) {
        Matrix<T> mat(n);
        for (int i = 0; i < n; ++i) {
            mat.data[i][i] = T(1);
        }
        return mat;
    }
    
    Matrix<T> pow(unsigned long long t) {
        assert(height() == width());
        Matrix<T> ret = Matrix::e(height());
        Matrix<T> self = *this;
        while (t > 0) {
            if (t % 2 == 1) {
                ret = ret * self;
            }
            self = self * self;
            t /= 2;
        }
        return ret;
    }
    
    T det() const {
        assert(is_square());
        const int n = height();
        std::vector<std::vector<T>> a = data;
        T ans(1);
        for (int i = 0; i < n; ++i) {
            int nonzero = -1;
            for (int j = i; j < n; ++j) {
                if (a[j][i] != T(0)) {
                    nonzero = j;
                    break;
                }
            }
            if (nonzero == -1) {
                return T(0);
            }
            if (nonzero != i) {
                std::swap(a[i], a[nonzero]);
                ans = -ans;
            }
            ans *= a[i][i];
            {
                const T inv = T(1) / T(a[i][i]);
                for (int j = i; j < n; ++j) {
                    a[i][j] *= inv;
                }
            }
            for (int j = i + 1; j < n; ++j) {
                const T tmp = a[j][i];
                for (int k = i; k < n; ++k) {
                    a[j][k] -= tmp * a[i][k];
                }
            }
        }
        return ans;
    }
};
// ============

using Mint = ModInt<mod998244353>;

Mint spanning(i32 n, const Vec<Vec<i32>> &edge) {
    Vec<i32> deg(n, 0);
    REP(i, n) REP(j, i) {
        deg[i] += edge[i][j];
        deg[j] += edge[i][j];
    }
    Matrix<Mint> mat(n - 1, n - 1);
    REP(i, n - 1) REP(j, n - 1) {
        if (i == j) {
            mat(i, j) = Mint(deg[i]);
        } else {
            mat(i, j) = -Mint(edge[i][j]);
        }
    }
    return mat.det();
}

int main() {
    i32 n, k;
    cin >> n >> k;
    Vec<Vec<pair<i32, i32>>> edges(k);
    REP(i, k) {
        i32 t;
        cin >> t;
        edges[i].reserve(t);
        while (t--) {
            i32 a, b;
            cin >> a >> b;
            --a;
            --b;
            edges[i].emplace_back(a, b);
        }
    }
    Mint ans;
    REP(st, 1, 1 << k) {
        Vec<Vec<i32>> edge(n, Vec<i32>(n, 0));
        REP(i, k) {
            if (st & (1 << i)) {
                for (auto [a, b] : edges[i]) {
                    ++edge[a][b];
                    ++edge[b][a];
                }
            }
        }
        Mint cnt = spanning(n, edge);
        if (__builtin_parity(((1 << k) - 1) ^ st)) {
            ans -= cnt;
        } else {
            ans += cnt;
        }
    }
    cout << ans << '\n';
}