結果

問題 No.2825 Sum of Scores of Sets of Specified Sections
コンテスト
ユーザー 👑 potato167
提出日時 2024-07-26 23:13:58
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 131 ms / 3,000 ms
コード長 5,391 bytes
コンパイル時間 2,105 ms
コンパイル使用メモリ 206,908 KB
最終ジャッジ日時 2025-02-23 18:54:19
ジャッジサーバーID
（参考情報） 		judge5 / judge2
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ファイルパターン 結果
sample AC * 1
other AC * 32
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 <bits/stdc++.h>
using namespace std;
using std::cout;
using std::cin;
using std::endl;
using ll=long long;
using ld=long double;
const ll ILL=2167167167167167167;
const int INF=2100000000;
const int mod=998244353;
#define rep(i,a,b) for (int i=(int)(a);i<(int)(b);i++)
#define all(p) p.begin(),p.end()
template<class T> using _pq = priority_queue<T, vector<T>, greater<T>>;
template<class T> ll LB(vector<T> &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();}
template<class T> ll UB(vector<T> &v,T a){return upper_bound(v.begin(),v.end(),a)-v.begin();}
template<class T> bool chmin(T &a,T b){if(a>b){a=b;return 1;}else return 0;}
template<class T> bool chmax(T &a,T b){if(a<b){a=b;return 1;}else return 0;}
template<class T> void So(vector<T> &v) {sort(v.begin(),v.end());}
template<class T> void Sore(vector<T> &v) {sort(v.begin(),v.end(),[](T x,T y){return x>y;});}
bool yneos(bool a,bool upp=0){if(a){cout<<(upp?"YES\n":"Yes\n");}else{cout<<(upp?"NO\n":"No\n");}return a;}
template<class T> void vec_out(vector<T> &p,int ty=0){
if(ty==2){cout<<'{';for(int i=0;i<(int)p.size();i++){if(i){cout<<",";}cout<<'"'<<p[i]<<'"';}cout<<"}\n";}
else{if(ty==1){cout<<p.size()<<"\n";}for(int i=0;i<(int)(p.size());i++){if(i) cout<<" ";cout<<p[i];}cout<<"\n";}}
template<class T> T vec_min(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmin(ans,x);return ans;}
template<class T> T vec_max(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmax(ans,x);return ans;}
template<class T> T vec_sum(vector<T> &a){T ans=T(0);for(auto &x:a) ans+=x;return ans;}
int pop_count(long long a){int res=0;while(a){res+=(a&1),a>>=1;}return res;}
template<class T> bool inside(T l,T x,T r){return l<=x&&x<r;}

#include <atcoder/modint>
using mint = atcoder::modint998244353;
// O(|M|^{3})
template<class T>
T det_matrix(std::vector<std::vector<T>> M){
    int N = M.size();
    if (N == 0) return 1;
    if (N == 1) return M[0][0];
    if (N == 2) return M[0][0] * M[1][1] - M[0][1] * M[1][0];

    T res = 1;
    for (int i = 0; i < N; i++){
        for (int  j = i; j < N; j++){
            if (M[j][i] != 0){
                if (j != i){
                    swap(M[i], M[j]);
                    res *= -1;
                }
                break;
            }
        }
        if (M[i][i] == 0) return 0;
        res *= M[i][i];
        if (i + 1 == N) break;
        T v = 1 / M[i][i];
        for (int j = i + 1; j < N; j++){
            T t = M[j][i] * v;
            for (int k = i; k < N; k++){
                M[j][k] -= M[i][k] * t;
            }
        }
    }
    return res;
}

template<class T>
pair<T, std::vector<std::vector<T>>> inv_matrix(std::vector<std::vector<T>> M){
    int N = M.size();
    auto B = M;
    rep(i, 0, N) rep(j, 0, N) B[i][j] = (i == j ? 1 : 0);
    T res = 1;
    for (int i = 0; i < N; i++){
        for (int  j = i; j < N; j++){
            if (M[j][i] != 0){
                if (j != i){
                    swap(M[i], M[j]);
                    swap(B[i], B[j]);
                    res *= -1;
                }
                break;
            }
        }
        if (M[i][i] == 0) return {0, B};
        res *= M[i][i];
        if (i + 1 == N) break;
        T v = 1 / M[i][i];
        for (int j = 0; j < N; j++){
            M[i][j] *= v;
            B[i][j] *= v;
        }
        for (int j = i + 1; j < N; j++){
            T t = M[j][i];
            for (int k = i; k < N; k++){
                M[j][k] -= M[i][k] * t;
                B[j][k] -= B[i][k] * t;
            }
        }
    }
    return {res, B};
}

void solve();
// CYAN / FREDERIC
int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    
    int t = 1;
    // cin >> t;
    rep(i, 0, t) solve();
}

void solve(){
    ll N, M;
    cin >> N >> M;
    vector A(N, vector<mint>(M));
    vector B(N, vector<mint>(M));
    srand(167);
    int mask = 100;
    //rep(i, 0, N) rep(j, 0, M) A[i][j] = rand() % mask;
    //rep(i, 0, N) rep(j, 0, M) B[i][j] = rand() % mask;
    
    rep(i, 0, N) rep(j, 0, M){
        int a;
        cin >> a;
        A[i][j] = a;
    }
    rep(i, 0, N) rep(j, 0, M){
        int a;
        cin >> a;
        B[i][j] = a;
    }
    auto f = [&](int a){
        mint base = -1;
        rep(i, 0, 1 << N) rep(j, 0, 1 << M){
            if (pop_count(i) != pop_count(j)) continue;
            vector<int> p, q;
            int tmp = i;
            rep(k, 0, N) if (tmp & (1 << k)) p.push_back(k);
            tmp = j;
            rep(k, 0, M) if (tmp & (1 << k)) q.push_back(k);
            int X = p.size();
            vector Y(X, vector<mint>(X));
            rep(a, 0, X) rep(b, 0, X) Y[a][b] = A[p[a]][q[b]];
            mint val = det_matrix(Y);
            if (a == 0){
                if (i != j) continue;
                base += val;
                continue;
            }
            rep(a, 0, X) rep(b, 0, X) Y[a][b] = B[p[a]][q[b]];
            val *= det_matrix(Y);
            base += val;
        }
        cout << base.val() << "\n";
    };
    if (false){
        f(1);
    }
    vector<vector<mint>> C(N, vector<mint>(N));
    rep(i, 0, N) rep(j, 0, M) rep(k, 0, N){
        C[i][k] += A[i][j] * B[k][j];
    }
    mint ans = 0;
    if (true){
        rep(i, 0, N) C[i][i] += 1;
        cout << (det_matrix(C) - 1).val() << "\n";
    }
    // cout << ((N - 1) * ans + det_matrix(C)).val() << "\n";
}
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