結果

問題 No.3105 Parallel Connection and Spanning Trees
ユーザー hint908
提出日時 2025-04-11 23:09:11
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 315 ms / 5,000 ms
コード長 11,210 bytes
コンパイル時間 3,470 ms
コンパイル使用メモリ 289,408 KB
実行使用メモリ 7,844 KB
最終ジャッジ日時 2025-04-11 23:09:34
合計ジャッジ時間 6,662 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
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ファイルパターン 結果
sample AC * 2
other AC * 32
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ソースコード

diff # 

//https://drken1215.hatenablog.com/entry/2024/01/08/195300

#include <bits/stdc++.h>
using namespace std;

// matrix
template<class mint> struct MintMatrix {
    // inner value
    vector<vector<mint>> val;
    
    // constructors
    MintMatrix(int H, int W, mint x = 0) : val(H, vector<mint>(W, x)) {}
    MintMatrix(const MintMatrix &mat) : val(mat.val) {}
    void init(int H, int W, mint x = 0) {
        val.assign(H, vector<mint>(W, x));
    }
    void resize(int H, int W) {
        val.resize(H);
        for (int i = 0; i < H; ++i) val[i].resize(W);
    }
    
    // getter and debugger
    constexpr int height() const { return (int)val.size(); }
    constexpr int width() const { return (int)val[0].size(); }
    vector<mint>& operator [] (int i) { return val[i]; }
    constexpr vector<mint>& operator [] (int i) const { return val[i]; }
    friend constexpr ostream& operator << (ostream &os, const MintMatrix<mint> &mat) {
        os << endl;
        for (int i = 0; i < mat.height(); ++i) {
            for (int j = 0; j < mat.width(); ++j) {
                if (j) os << ", ";
                os << mat.val[i][j];
            }
            os << endl;
        }
        return os;
    }
    
    // comparison operators
    constexpr bool operator == (const MintMatrix &r) const {
        return this->val == r.val;
    }
    constexpr bool operator != (const MintMatrix &r) const {
        return this->val != r.val;
    }
    
    // arithmetic operators
    constexpr MintMatrix& operator += (const MintMatrix &r) {
        assert(height() == r.height());
        assert(width() == r.width());
        for (int i = 0; i < height(); ++i) {
            for (int j = 0; j < width(); ++j) {
                val[i][j] += r[i][j];
            }
        }
        return *this;
    }
    constexpr MintMatrix& operator -= (const MintMatrix &r) {
        assert(height() == r.height());
        assert(width() == r.width());
        for (int i = 0; i < height(); ++i) {
            for (int j = 0; j < width(); ++j) {
                val[i][j] -= r[i][j];
            }
        }
        return *this;
    }
    constexpr MintMatrix& operator *= (const mint &v) {
        for (int i = 0; i < height(); ++i)
            for (int j = 0; j < width(); ++j)
                val[i][j] *= v;
        return *this;
    }
    constexpr MintMatrix& operator *= (const MintMatrix &r) {
        assert(width() == r.height());
        MintMatrix<mint> res(height(), r.width());
        for (int i = 0; i < height(); ++i)
            for (int j = 0; j < r.width(); ++j)
                for (int k = 0; k < width(); ++k)
                    res[i][j] += val[i][k] * r[k][j];
        return (*this) = res;
    }
    constexpr MintMatrix operator + () const { return MintMatrix(*this); }
    constexpr MintMatrix operator - () const { return MintMatrix(*this) *= mint(-1); }
    constexpr MintMatrix operator + (const MintMatrix &r) const { return MintMatrix(*this) += r; }
    constexpr MintMatrix operator - (const MintMatrix &r) const { return MintMatrix(*this) -= r; }
    constexpr MintMatrix operator * (const mint &v) const { return MintMatrix(*this) *= v; }
    constexpr MintMatrix operator * (const MintMatrix &r) const { return MintMatrix(*this) *= r; }
    
    // pow
    constexpr MintMatrix pow(long long n) const {
        assert(height() == width());
        MintMatrix<mint> res(height(), width()),  mul(*this);
        while (n > 0) {
            if (n & 1) res *= mul;
            mul *= mul;
            n >>= 1;
        }
        return res;
    }
    friend constexpr MintMatrix<mint> pow(const MintMatrix<mint> &mat, long long n) {
        return mat.pow(n);
    }
    
    // gauss-jordan
    constexpr int find_pivot(int cur_rank, int col) const {
        int pivot = -1;
        for (int row = cur_rank; row < height(); ++row) {
            if (val[row][col] != 0) {
                pivot = row;
                break;
            }
        }
        return pivot;
    }
    constexpr void sweep(int cur_rank, int col, int pivot) {
        swap(val[pivot], val[cur_rank]);
        auto ifac = val[cur_rank][col].inv();
        for (int col2 = 0; col2 < width(); ++col2) {
            val[cur_rank][col2] *= ifac;
        }
        for (int row = 0; row < height(); ++row) {
            if (row != cur_rank && val[row][col] != 0) {
                auto fac = val[row][col];
                for (int col2 = 0; col2 < width(); ++col2) {
                    val[row][col2] -= val[cur_rank][col2] * fac;
                }
            }
        }
    }
    constexpr int gauss_jordan(int not_sweep_width = 0) {
        int rank = 0;
        for (int col = 0; col < width(); ++col) {
            if (col == width() - not_sweep_width) break;
            int pivot = find_pivot(rank, col);
            if (pivot == -1) continue;
            sweep(rank++, col, pivot);
        }
        return rank;
    }
    friend constexpr int gauss_jordan(MintMatrix<mint> &mat, int not_sweep_width = 0) {
        return mat.gauss_jordan(not_sweep_width);
    }
    friend constexpr int linear_equation
    (const MintMatrix<mint> &mat, const vector<mint> &b, vector<mint> &res) {
        // extend
        MintMatrix<mint> A(mat.height(), mat.width() + 1);
        for (int i = 0; i < mat.height(); ++i) {
            for (int j = 0; j < mat.width(); ++j) A[i][j] = mat.val[i][j];
            A[i].back() = b[i];
        }
        int rank = A.gauss_jordan(1);
        
        // check if it has no solution
        for (int row = rank; row < mat.height(); ++row) if (A[row].back() != 0) return -1;

        // answer
        res.assign(mat.width(), 0);
        for (int i = 0; i < rank; ++i) res[i] = A[i].back();
        return rank;
    }
    friend constexpr int linear_equation(const MintMatrix<mint> &mat, const vector<mint> &b) {
        vector<mint> res;
        return linear_equation(mat, b, res);
    }
    
    // determinant
    constexpr mint det() const {
        MintMatrix<mint> A(*this);
        int rank = 0;
        mint res = 1;
        for (int col = 0; col < width(); ++col) {
            int pivot = A.find_pivot(rank, col);
            if (pivot == -1) return mint(0);
            res *= A[pivot][rank];
            A.sweep(rank++, col, pivot);
        }
        return res;
    }
    friend constexpr mint det(const MintMatrix<mint> &mat) {
        return mat.det();
    }
};

// modint
template<int MOD> struct Fp {
    // inner value
    long long val;
    
    // constructor
    constexpr Fp() : val(0) { }
    constexpr Fp(long long v) : val(v % MOD) {
        if (val < 0) val += MOD;
    }
    constexpr Fp(const Fp &v) : val(v.get()) { }
    constexpr long long get() const { return val; }
    constexpr int get_mod() const { return MOD; }
    
    // arithmetic operators
    constexpr Fp operator + () const { return Fp(*this); }
    constexpr Fp operator - () const { return Fp(0) - Fp(*this); }
    constexpr Fp operator + (const Fp &r) const { return Fp(*this) += r; }
    constexpr Fp operator - (const Fp &r) const { return Fp(*this) -= r; }
    constexpr Fp operator * (const Fp &r) const { return Fp(*this) *= r; }
    constexpr Fp operator / (const Fp &r) const { return Fp(*this) /= r; }
    constexpr Fp& operator += (const Fp &r) {
        val += r.val;
        if (val >= MOD) val -= MOD;
        return *this;
    }
    constexpr Fp& operator -= (const Fp &r) {
        val -= r.val;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr Fp& operator *= (const Fp &r) {
        val = val * r.val % MOD;
        return *this;
    }
    constexpr Fp& operator /= (const Fp &r) {
        long long a = r.val, b = MOD, u = 1, v = 0;
        while (b) {
            long long t = a / b;
            a -= t * b, swap(a, b);
            u -= t * v, swap(u, v);
        }
        val = val * u % MOD;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr Fp pow(long long n) const {
        Fp res(1), mul(*this);
        while (n > 0) {
            if (n & 1) res *= mul;
            mul *= mul;
            n >>= 1;
        }
        return res;
    }
    constexpr Fp inv() const {
        Fp res(1), div(*this);
        return res / div;
    }

    // other operators
    constexpr bool operator == (const Fp &r) const {
        return this->val == r.val;
    }
    constexpr bool operator != (const Fp &r) const {
        return this->val != r.val;
    }
    constexpr Fp& operator ++ () {
        ++val;
        if (val >= MOD) val -= MOD;
        return *this;
    }
    constexpr Fp& operator -- () {
        if (val == 0) val += MOD;
        --val;
        return *this;
    }
    constexpr Fp operator ++ (int) const {
        Fp res = *this;
        ++*this;
        return res;
    }
    constexpr Fp operator -- (int) const {
        Fp res = *this;
        --*this;
        return res;
    }
    friend constexpr istream& operator >> (istream &is, Fp<MOD> &x) {
        is >> x.val;
        x.val %= MOD;
        if (x.val < 0) x.val += MOD;
        return is;
    }
    friend constexpr ostream& operator << (ostream &os, const Fp<MOD> &x) {
        return os << x.val;
    }
    friend constexpr Fp<MOD> pow(const Fp<MOD> &r, long long n) {
        return r.pow(n);
    }
    friend constexpr Fp<MOD> inv(const Fp<MOD> &r) {
        return r.inv();
    }
};


// AOJ 3369 Namori Counting (OUPC 2023 day2-D)
int f(vector<vector<int>> G){
    int N = G.size();
    vector<int> deg(N, 0);
    for(int i=0;i<N;i++) for(int j=0;j<N;j++) deg[i] += G[i][j];
    
    const int MOD = 998244353;
    using mint = Fp<MOD>;
    
    // ラプラシアン行列の余因子を求めるため、行・列の末尾を削る
    MintMatrix<mint> L(N - 1, N - 1, 0);
    for (int i = 0; i < N - 1; ++i) {
        for (int j = 0; j < N - 1; ++j) {
            if (i == j) L[i][j] = deg[i];
            else L[i][j] = -G[i][j];
        }
    }
    return det(L).val;
}

#include<atcoder/modint>
using namespace atcoder;
using mint = modint998244353;


void solve(){
    int k;
    cin >> k;
    mint a = 1, b = 0;
    for(int _=0;_<k;_++){
        int n,m;
        cin >> n >> m;
        vector<int> u(m), v(m);
        for(int i=0;i<m;i++){
            cin >> u[i] >> v[i];
            u[i]--;
            v[i]--;
        }
        int x,y;
        {
            vector G(n, vector<int>(n, 0));
            for(int i=0;i<m;i++){
                G[u[i]][v[i]] = 1;
                G[v[i]][u[i]] = 1;
            }
            x = f(G);
        }
        {
            vector G(n-1, vector<int>(n-1, 0));
            for(int i=0;i<m;i++){
                if(u[i]) u[i]--;
                if(v[i]) v[i]--;
                G[u[i]][v[i]] += 1;
                G[v[i]][u[i]] += 1;
            }
            G[0][0] = 0;
            if(n > 2) y = f(G);
            else y = 1;
        }
        
        // cout << x << " " << y << endl;
        mint na = 0, nb = 0;
        na += a * y;
        na += a * x * 2;
        nb += b * y;
        nb += b * x * 2;
        nb += a * x;
        a = na;
        b = nb;
        // cout << a.val() << " " << b.val() << endl;
    }
    cout << b.val() << endl;
}

int main() {
    solve();
}
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