verify/library_checker/linear_algebra/rank_of_matrix.test.cpp

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• Last update: 2024-11-09 02:30:41+09:00
• Problem: https://judge.yosupo.jp/problem/matrix_rank

Depends on

• gauss_elimination (src/matrix/gauss_elimination.hpp)
• Matrix (src/matrix/matrix.hpp)
• StaticModint (src/template/static_modint.hpp)
• template (src/template/template.hpp)

Code

#define PROBLEM "https://judge.yosupo.jp/problem/matrix_rank"
#include "../../../src/template/template.hpp"
#include "../../../src/template/static_modint.hpp"
#include "../../../src/matrix/gauss_elimination.hpp"
using mint = modint998244353;
int main(void) {
    int n, m;
    cin >> n >> m;
    Matrix<mint> a(n, m);
    rep(i, 0, n) {
        rep(j, 0, m) {
            cin >> a[i][j];
        }
    }
    auto [rank, det] = gauss_elimination(a);
    cout << rank << '\n';
}

#line 1 "verify/library_checker/linear_algebra/rank_of_matrix.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/matrix_rank"
#line 2 "src/template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using P = pair<long long, long long>;
#define rep(i, a, b) for(long long i = (a); i < (b); ++i)
#define rrep(i, a, b) for(long long i = (a); i >= (b); --i)
constexpr long long inf = 4e18;
struct SetupIO {
    SetupIO() {
        ios::sync_with_stdio(0);
        cin.tie(0);
        cout << fixed << setprecision(30);
    }
} setup_io;
#line 3 "src/template/static_modint.hpp"
template <uint32_t m>
struct StaticModint {
    using mint = StaticModint;
    static constexpr uint32_t mod() {
        return m;
    }
    static constexpr mint raw(const uint32_t v) {
        mint a;
        a._v = v;
        return a;
    }
    constexpr StaticModint()
        : _v(0) {}
    template <class T>
    constexpr StaticModint(const T& v) {
        static_assert(is_integral_v<T>);
        if constexpr(is_signed_v<T>) {
            int64_t x = int64_t(v % int64_t(m));
            if(x < 0) x += m;
            _v = uint32_t(x);
        } else _v = uint32_t(v % m);
    }
    constexpr uint32_t val() const {
        return _v;
    }
    constexpr mint& operator++() {
        return *this += 1;
    }
    constexpr mint& operator--() {
        return *this -= 1;
    }
    constexpr mint operator++(int) {
        mint res = *this;
        ++*this;
        return res;
    }
    constexpr mint operator--(int) {
        mint res = *this;
        --*this;
        return res;
    }
    constexpr mint& operator+=(mint rhs) {
        if(_v >= m - rhs._v) _v -= m;
        _v += rhs._v;
        return *this;
    }
    constexpr mint& operator-=(mint rhs) {
        if(_v < rhs._v) _v += m;
        _v -= rhs._v;
        return *this;
    }
    constexpr mint& operator*=(mint rhs) {
        return *this = *this * rhs;
    }
    constexpr mint& operator/=(mint rhs) {
        return *this *= rhs.inv();
    }
    constexpr mint operator+() const {
        return *this;
    }
    constexpr mint operator-() const {
        return mint{} - *this;
    }
    constexpr mint pow(long long n) const {
        assert(0 <= n);
        if(n == 0) return 1;
        mint x = *this, r = 1;
        while(1) {
            if(n & 1) r *= x;
            n >>= 1;
            if(n == 0) return r;
            x *= x;
        }
    }
    constexpr mint inv() const {
        if constexpr(prime) {
            assert(_v);
            return pow(m - 2);
        } else {
            const auto eg = inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }
    friend constexpr mint operator+(mint lhs, mint rhs) {
        return lhs += rhs;
    }
    friend constexpr mint operator-(mint lhs, mint rhs) {
        return lhs -= rhs;
    }
    friend constexpr mint operator*(mint lhs, mint rhs) {
        return uint64_t(lhs._v) * rhs._v;
    }
    friend constexpr mint operator/(mint lhs, mint rhs) {
        return lhs /= rhs;
    }
    friend constexpr bool operator==(mint lhs, mint rhs) {
        return lhs._v == rhs._v;
    }
    friend constexpr bool operator!=(mint lhs, mint rhs) {
        return lhs._v != rhs._v;
    }
    friend istream& operator>>(istream& in, mint& x) {
        long long a;
        in >> a;
        x = a;
        return in;
    }
    friend ostream& operator<<(ostream& out, const mint& x) {
        return out << x.val();
    }

   private:
    uint32_t _v = 0;
    static constexpr bool prime = []() -> bool {
        if(m == 1) return 0;
        if(m == 2 or m == 7 or m == 61) return 1;
        if(m % 2 == 0) return 0;
        uint32_t d = m - 1;
        while(d % 2 == 0) d /= 2;
        for(uint32_t a : {2, 7, 61}) {
            uint32_t t = d;
            mint y = mint(a).pow(t);
            while(t != m - 1 && y != 1 && y != m - 1) {
                y *= y;
                t <<= 1;
            }
            if(y != m - 1 && t % 2 == 0) return 0;
        }
        return 1;
    }();
    static constexpr pair<int32_t, int32_t> inv_gcd(const int32_t a, const int32_t b) {
        if(a == 0) return {b, 0};
        int32_t s = b, t = a, m0 = 0, m1 = 1;
        while(t) {
            const int32_t u = s / t;
            s -= t * u;
            m0 -= m1 * u;
            swap(s, t);
            swap(m0, m1);
        }
        if(m0 < 0) m0 += b / s;
        return {s, m0};
    }
};
using modint998244353 = StaticModint<998244353>;
using modint1000000007 = StaticModint<1000000007>;
#line 3 "src/matrix/matrix.hpp"
template <typename T>
struct Matrix {
    Matrix(const int h, const int w, const T& val = 0)
        : h(h), w(w), A(h, vector<T>(w, val)) {}
    int H() const {
        return h;
    }
    int W() const {
        return w;
    }
    const vector<T>& operator[](const int i) const {
        assert(0 <= i and i < h);
        return A[i];
    }
    vector<T>& operator[](const int i) {
        assert(0 <= i and i < h);
        return A[i];
    }
    static Matrix I(const int n) {
        Matrix mat(n, n);
        for(int i = 0; i < n; ++i) mat[i][i] = 1;
        return mat;
    }
    Matrix& operator+=(const Matrix& B) {
        assert(h == B.h and w == B.w);
        for(int i = 0; i < h; ++i) {
            for(int j = 0; j < w; ++j) {
                (*this)[i][j] += B[i][j];
            }
        }
        return (*this);
    }
    Matrix& operator-=(const Matrix& B) {
        assert(h == B.h and w == B.w);
        for(int i = 0; i < h; ++i) {
            for(int j = 0; j < w; ++j) {
                (*this)[i][j] -= B[i][j];
            }
        }
        return (*this);
    }
    Matrix& operator*=(const Matrix& B) {
        assert(w == B.h);
        vector<vector<T>> C(h, vector<T>(B.w, 0));
        for(int i = 0; i < h; ++i) {
            for(int k = 0; k < w; ++k) {
                for(int j = 0; j < B.w; ++j) {
                    C[i][j] += (*this)[i][k] * B[k][j];
                }
            }
        }
        A.swap(C);
        return (*this);
    }
    Matrix& pow(long long t) {
        assert(h == w);
        assert(t >= 0);
        Matrix B = Matrix::I(h);
        while(t > 0) {
            if(t & 1ll) B *= (*this);
            (*this) *= (*this);
            t >>= 1ll;
        }
        A.swap(B.A);
        return (*this);
    }
    Matrix operator+(const Matrix& B) const {
        return (Matrix(*this) += B);
    }
    Matrix operator-(const Matrix& B) const {
        return (Matrix(*this) -= B);
    }
    Matrix operator*(const Matrix& B) const {
        return (Matrix(*this) *= B);
    }
    bool operator==(const Matrix& B) const {
        assert(h == B.H() and w == B.W());
        for(int i = 0; i < h; ++i) {
            for(int j = 0; j < w; ++j) {
                if(A[i][j] != B[i][j]) return false;
            }
        }
        return true;
    }
    bool operator!=(const Matrix& B) const {
        assert(h == B.H() and w == B.W());
        for(int i = 0; i < h; ++i) {
            for(int j = 0; j < w; ++j) {
                if(A[i][j] != B[i][j]) return true;
            }
        }
        return false;
    }

   private:
    int h, w;
    vector<vector<T>> A;
};
#line 4 "src/matrix/gauss_elimination.hpp"
template <typename T>
pair<int, T> gauss_elimination(Matrix<T>& a, int pivot_end = -1) {
    const int h = a.H(), w = a.W();
    int rank = 0;
    assert(-1 <= pivot_end and pivot_end <= w);
    if(pivot_end == -1) pivot_end = w;
    T det = 1;
    for(int j = 0; j < pivot_end; ++j) {
        int idx = -1;
        for(int i = rank; i < h; ++i) {
            if(a[i][j] != T(0)) {
                idx = i;
                break;
            }
        }
        if(idx == -1) {
            det = 0;
            continue;
        }
        if(rank != idx) det = -det, swap(a[rank], a[idx]);
        det *= a[rank][j];
        if(a[rank][j] != T(1)) {
            const T coeff = T(1) / a[rank][j];
            for(int k = j; k < w; ++k) a[rank][k] *= coeff;
        }
        for(int i = 0; i < h; ++i) {
            if(i == rank) continue;
            if(a[i][j] != T(0)) {
                const T coeff = a[i][j] / a[rank][j];
                for(int k = j; k < w; ++k) a[i][k] -= a[rank][k] * coeff;
            }
        }
        ++rank;
    }
    return {rank, det};
}
#line 5 "verify/library_checker/linear_algebra/rank_of_matrix.test.cpp"
using mint = modint998244353;
int main(void) {
    int n, m;
    cin >> n >> m;
    Matrix<mint> a(n, m);
    rep(i, 0, n) {
        rep(j, 0, m) {
            cin >> a[i][j];
        }
    }
    auto [rank, det] = gauss_elimination(a);
    cout << rank << '\n';
}

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