test/yosupo_det.test.cpp

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• Last update: 2023-07-16 21:56:51+09:00
• Problem: https://judge.yosupo.jp/problem/matrix_det

Depends on

• template.hpp
• type/Matrix.hpp
• type/modint.hpp

Code

#define PROBLEM "https://judge.yosupo.jp/problem/matrix_det"

#include "../template.hpp"

#include "../type/modint.hpp"
using mint=ModInt<998244353>;

#include "../type/Matrix.hpp"

signed main(){
    int n;cin>>n;
    Matrix<mint> mat(n);
    rep(i,n)rep(j,n) cin>>mat[i][j];
    cout<<mat.det()<<endl;
    return 0;
}

#line 1 "test/yosupo_det.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/matrix_det"

#line 1 "template.hpp"
#include<bits/stdc++.h>
using namespace std;
#define ALL(x) begin(x),end(x)
#define rep(i,n) for(int i=0;i<(n);i++)
#define debug(v) cout<<#v<<":";for(auto x:v){cout<<x<<' ';}cout<<endl;
#define mod 1000000007
using ll=long long;
const int INF=1000000000;
const ll LINF=1001002003004005006ll;
int dx[]={1,0,-1,0},dy[]={0,1,0,-1};
// ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
template<class T>bool chmax(T &a,const T &b){if(a<b){a=b;return true;}return false;}
template<class T>bool chmin(T &a,const T &b){if(b<a){a=b;return true;}return false;}

struct IOSetup{
    IOSetup(){
        cin.tie(0);
        ios::sync_with_stdio(0);
        cout<<fixed<<setprecision(12);
    }
} iosetup;
 
template<typename T>
ostream &operator<<(ostream &os,const vector<T>&v){
    for(int i=0;i<(int)v.size();i++) os<<v[i]<<(i+1==(int)v.size()?"":" ");
    return os;
}
template<typename T>
istream &operator>>(istream &is,vector<T>&v){
    for(T &x:v)is>>x;
    return is;
}

#line 4 "test/yosupo_det.test.cpp"

#line 1 "type/modint.hpp"
template<int Mod>
struct ModInt{
    int x;
    ModInt():x(0){}
    ModInt(int y): x (y >= 0 ? y % Mod : (Mod - (-y) % Mod) % Mod){}
    ModInt(long long y){
        if (y >= 0)
        {
            x = (int)(y % (ll)(Mod));
        }
        else
        {
            int tmp = (int)((-y) % (ll)Mod);
            x = (Mod - tmp) % Mod;
        }
    }
    ModInt &operator+=(const ModInt &p){
        if((x += p.x) >= Mod) x -= Mod;
        return *this;
    }
    ModInt &operator-=(const ModInt &p){
        if((x += Mod - p.x) >= Mod) x -= Mod;
        return *this;
    }
    ModInt &operator*=(const ModInt &p){
        x = (int)(1ll * x * p.x % Mod);
        return *this;
    }
    ModInt &operator/=(const ModInt &p){
        (*this) *= p.inverse();
        return *this;
    }
    ModInt operator-()const{return ModInt(-x);}
    ModInt operator+(const ModInt &p)const{return ModInt(*this)+=p;}
    ModInt operator-(const ModInt &p)const{return ModInt(*this)-=p;}
    ModInt operator*(const ModInt &p)const{return ModInt(*this)*=p;}
    ModInt operator/(const ModInt &p)const{return ModInt(*this)/=p;}
    bool operator==(const ModInt &p)const{return x==p.x;}
    bool operator!=(const ModInt &p)const{return x!=p.x;}
    ModInt inverse()const{
        int a = x, b = Mod ,u = 1, v = 0, t;
        while(b>0){
            t=a/b;
            swap(a-=t*b,b);swap(u-=t*v,v);
        }
        return ModInt(u);
    }
    ModInt pow(long long n)const{
        ModInt ret(1),mul(x);
        while(n>0){
            if(n&1) ret*=mul;
            mul*=mul;n>>=1;
        }
        return ret;
    }
    friend ostream &operator<<(ostream &os,const ModInt &p){return os<<p.x;}
    friend istream &operator>>(istream &is,ModInt &a){long long t;is>>t;a=ModInt<Mod>(t);return (is);}
    static int get_mod(){return Mod;}
};
#line 6 "test/yosupo_det.test.cpp"
using mint=ModInt<998244353>;

#line 1 "type/Matrix.hpp"
template<typename T>
struct Matrix{

private:
    vector<vector<T>> a;

    Matrix matMulImpl(const Matrix &lhs, const Matrix &rhs)
    {
        Matrix ret(lhs.h(), rhs.w());
        for (int i = 0; i < lhs.h(); i++)
        {
            for (int j = 0; j < lhs.w(); j++)
            {
                for (int k = 0; k < rhs.w(); k++)
                {
                    ret[i][k] += lhs[i][j] * rhs[j][k];
                }
            }
        }
        return ret;
    }

public:
    Matrix(){}
    Matrix(int n):a(n,vector<T>(n,0)){}
    Matrix(int h,int w):a(h,vector<T>(w,0)){}

    int h()const{return (int)a.size();}
    int w()const{return (int)a[0].size();}

    const vector<T> &operator[](int k)const{
        return a.at(k);// reference   
    }
    vector<T> &operator[](int k){
        return a.at(k);
    }

    Matrix id(int n){
        Matrix ret(n);
        for(int i=0;i<n;i++) ret[i][i]=1;
        return ret;
    }

    Matrix &operator+=(const Matrix &rhs){
        assert(h()==rhs.h() and w()==rhs.w());
        for(int i=0;i<h();i++)for(int j=0;j<w();j++) (*this)[i][j]+=rhs[i][j];
        return (*this);
    }
    Matrix &operator-=(const Matrix &rhs){
        assert(h()==rhs.h() and w()==rhs.w());
        for(int i=0;i<h();i++)for(int j=0;j<w();j++) (*this)[i][j]-=rhs[i][j];
        return (*this);
    }
    Matrix &operator*=(const Matrix &rhs){
        assert(w()==rhs.h());
        Matrix res = matMulImpl(*this, rhs);
        swap(a, res.a);
        return (*this);
    }
    Matrix operator+(const Matrix &rhs)const{return Matrix(*this)+=rhs;}
    Matrix operator-(const Matrix &rhs)const{return Matrix(*this)-=rhs;}
    Matrix operator*(const Matrix &rhs)const{return Matrix(*this)*=rhs;}

    Matrix pow(long long k){
        Matrix ret=Matrix::id(h());
        Matrix b=Matrix(*this);
        while(k){
            if(k&1) ret*=b;
            b*=b;
            k>>=1;
        }
        return ret;
    }

    T det(){
        assert(h()==w());
        Matrix x(*this);
        T ret=1;
        for(int i=0;i<w();i++){
            int idx=-1;
            for(int j=i;j<w();j++)if(x[j][i]!=0) idx=j;
            if(idx==-1) return 0;// 三角行列の対角成分の1つが0
            if(i!=idx){
                ret*=-1;
                swap(x[i],x[idx]);
            }
            T b=x[i][i];
            ret*=b;
            for(int j=0;j<w();j++) x[i][j]/=b;
            for(int j=i+1;j<w();j++){
                T t=x[j][i];
                for(int k=0;k<w();k++) x[j][k]-=x[i][k]*t;
            }
        }
        return ret;
    }
};
#line 9 "test/yosupo_det.test.cpp"

signed main(){
    int n;cin>>n;
    Matrix<mint> mat(n);
    rep(i,n)rep(j,n) cin>>mat[i][j];
    cout<<mat.det()<<endl;
    return 0;
}

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