test/math/Matrix-det.test.cpp

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• Last update: 2023-05-30 04:49:31+09:00
• Problem: https://judge.yosupo.jp/problem/matrix_det

Depends on

• ModInt (lib/00-util/ModInt.cpp)
• Matrix - 行列演算 (lib/30-math/Matrix.cpp)

Code

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

#include <vector>
#include <iostream>
#include <array>
#include <cassert>
using namespace std;
#include "../../lib/00-util/ModInt.cpp"
#include "../../lib/30-math/Matrix.cpp"
constexpr long long MOD = 998'244'353;

int main(void){
    using modint = ModInt<MOD>;
    Matrix<modint,500> m=Matrix<modint,500>::E();
    int N; cin >> N;
    for(int i = 0; i < N; ++i) {
        for(int j = 0; j < N; ++j) {
            cin >> m[i][j];
        }
    }
    cout << m.determinant() << endl;
	return 0;
}

#line 1 "test/math/Matrix-det.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/matrix_det"

#include <vector>
#include <iostream>
#include <array>
#include <cassert>
using namespace std;
#line 1 "lib/00-util/ModInt.cpp"
/*
 * @title ModInt
 * @docs md/util/ModInt.md
 */
template<long long mod> class ModInt {
public:
    long long x;
    constexpr ModInt():x(0) {}
    constexpr ModInt(long long y) : x(y>=0?(y%mod): (mod - (-y)%mod)%mod) {}
    constexpr ModInt &operator+=(const ModInt &p) {if((x += p.x) >= mod) x -= mod;return *this;}
    constexpr ModInt &operator+=(const long long y) {ModInt p(y);if((x += p.x) >= mod) x -= mod;return *this;}
    constexpr ModInt &operator+=(const int y) {ModInt p(y);if((x += p.x) >= mod) x -= mod;return *this;}
    constexpr ModInt &operator-=(const ModInt &p) {if((x += mod - p.x) >= mod) x -= mod;return *this;}
    constexpr ModInt &operator-=(const long long y) {ModInt p(y);if((x += mod - p.x) >= mod) x -= mod;return *this;}
    constexpr ModInt &operator-=(const int y) {ModInt p(y);if((x += mod - p.x) >= mod) x -= mod;return *this;}
    constexpr ModInt &operator*=(const ModInt &p) {x = (x * p.x % mod);return *this;}
    constexpr ModInt &operator*=(const long long y) {ModInt p(y);x = (x * p.x % mod);return *this;}
    constexpr ModInt &operator*=(const int y) {ModInt p(y);x = (x * p.x % mod);return *this;}
    constexpr ModInt &operator^=(const ModInt &p) {x = (x ^ p.x) % mod;return *this;}
    constexpr ModInt &operator^=(const long long y) {ModInt p(y);x = (x ^ p.x) % mod;return *this;}
    constexpr ModInt &operator^=(const int y) {ModInt p(y);x = (x ^ p.x) % mod;return *this;}
    constexpr ModInt &operator/=(const ModInt &p) {*this *= p.inv();return *this;}
    constexpr ModInt &operator/=(const long long y) {ModInt p(y);*this *= p.inv();return *this;}
    constexpr ModInt &operator/=(const int y) {ModInt p(y);*this *= p.inv();return *this;}
    constexpr ModInt operator=(const int y) {ModInt p(y);*this = p;return *this;}
    constexpr ModInt operator=(const long long y) {ModInt p(y);*this = p;return *this;}
    constexpr ModInt operator-() const {return ModInt(-x); }
    constexpr ModInt operator++() {x++;if(x>=mod) x-=mod;return *this;}
    constexpr ModInt operator--() {x--;if(x<0) x+=mod;return *this;}
    constexpr ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
    constexpr ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
    constexpr ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
    constexpr ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
    constexpr ModInt operator^(const ModInt &p) const { return ModInt(*this) ^= p; }
    constexpr bool operator==(const ModInt &p) const { return x == p.x; }
    constexpr bool operator!=(const ModInt &p) const { return x != p.x; }
    // ModInt inv() 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);}
    constexpr ModInt inv() const {int a=x,b=mod,u=1,v=0,t=0,tmp=0;while(b > 0) {t = a / b;a-=t*b;tmp=a;a=b;b=tmp;u-=t*v;tmp=u;u=v;v=tmp;} return ModInt(u);}
    constexpr ModInt pow(long long n) const {ModInt ret(1), mul(x);for(;n > 0;mul *= mul,n >>= 1) if(n & 1) ret *= mul;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);}
};
constexpr long long MOD_998244353 = 998244353;
constexpr long long MOD_1000000007 = 1'000'000'000LL + 7; //'
#line 1 "lib/30-math/Matrix.cpp"
/*
 * @title Matrix - 行列演算
 * @docs md/math/Matrix.md
 */
template <class T, int H, int W = H> class Matrix {
public:
    int h,w;
    array<array<T,W>,H> a;
    Matrix():h(H),w(W){
        // do nothing
    }
    Matrix(const vector<vector<T>>& vec):h(H),w(W) {
        assert(vec.size()==H && vec.front().size()==W);
        for(int i = 0; i < H; ++i) for(int j = 0; j < W; ++j) a[i][j]=vec[i][j];
    }
    static Matrix E() {
        assert(H==W);
        Matrix res = Matrix();
        for(int i = 0; i < H; ++i) res[i][i]=1;
        return res;
    }
    Matrix &operator+=(const Matrix &r) {
        assert(H==r.h&&W==r.w);
        for(int i = 0; i < H; ++i) for(int j = 0; j < W; ++j) a[i][j]+=r[i][j];
        return *this;
    }
    Matrix &operator-=(const Matrix &r) {
        assert(H==r.h&&W==r.w);
        for(int i = 0; i < H; ++i) for(int j = 0; j < W; ++j) a[i][j]-=r[i][j];
        return *this;
    }
    Matrix &operator*=(const Matrix &r) {
        assert(W==r.h);
        Matrix res = Matrix();
        for(int i = 0; i < H; ++i) for(int j = 0; j < r.w; ++j) for(int k = 0; k < W; ++k) res[i][j]+=(a[i][k])*(r[k][j]);
        a.swap(res.a);
        return *this;
    }
    Matrix operator+(const Matrix& r) const {
        return Matrix(*this) += r;
    }
    Matrix operator-(const Matrix& r) const {
        return Matrix(*this) -= r;
    }
    Matrix operator*(const Matrix& r) const {
        return Matrix(*this) *= r;
    }
    inline array<T,W> &operator[](int i) {
        return a[i];
    }
    inline const array<T,W> &operator[](int i) const {
        return a[i];
    }
    Matrix pow(long long K) const {
        assert(H == W);
        Matrix x(*this);
        Matrix res = this->E();
        for (; K > 0; K /= 2) {
            if (K & 1) res *= x;
            x *= x;
        }
        return res;
    }
    T determinant(void) const {
        assert(H==W);
        Matrix x(*this);
        T res = 1;
        for(int i = 0; i < H; i++) {
            int idx = -1;
            for(int j = i; j < W; j++) if(x[j][i] != 0) idx = j;
            if(idx == -1) return 0;
            if(i != idx) {
                res *= -1;
                swap(x[i], x[idx]);
            }
            res *= x[i][i];
            T tmp = x[i][i];
            for(int j = 0; j < W; ++j) x[i][j] /= tmp;
            for(int j = i + 1; j < H; j++) {
                tmp = x[j][i];
                for(int k = 0; k < W; k++) x[j][k] -= x[i][k]*tmp;
            }
        }
        return res;
    }
};
#line 10 "test/math/Matrix-det.test.cpp"
constexpr long long MOD = 998'244'353;

int main(void){
    using modint = ModInt<MOD>;
    Matrix<modint,500> m=Matrix<modint,500>::E();
    int N; cin >> N;
    for(int i = 0; i < N; ++i) {
        for(int j = 0; j < N; ++j) {
            cin >> m[i][j];
        }
    }
    cout << m.determinant() << endl;
	return 0;
}

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