math/gauss_jordan_mint.cpp

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• Last update: 2021-06-21 15:24:20+09:00

Depends on

• modint(固定MOD) (util/modint.cpp)

Code

#include "../util/modint.cpp"

int gauss_jordan(vector<vector<mint>> &A, bool is_extended = false) {
    int m = A.size(), n = A[0].size();
    int rank = 0;
    for (int col = 0; col < n; ++col) {
        if (is_extended && col == n-1) break;
        int pivot = -1;
        for (int row = rank; row < m; ++row) {
            if (A[row][col].val) {
                pivot = row;
                break;
            }
        }
        if (pivot == -1) continue;
        swap(A[pivot], A[rank]);
        auto d = A[rank][col].inv();
        for (int col2 = 0; col2 < n; ++col2) A[rank][col2] *= d;
        for (int row = 0; row < m; ++row) {
            if (row != rank && A[row][col].val) {
                auto fac = A[row][col];
                for (int col2 = 0; col2 < n; ++col2) {
                    A[row][col2] -= A[rank][col2] * fac;
                }
            }
        }
        ++rank;
    }
    return rank;
}

#line 1 "util/modint.cpp"
template <uint M>
struct modint {
    uint val;
public:
    static modint raw(int v) { modint x; x.val = v; return x; }
    modint() : val(0) {}
    template <class T>
    modint(T v) { ll x = (ll)(v%(ll)(M)); if (x < 0) x += M; val = uint(x); }
    modint(bool v) { val = ((unsigned int)(v) % M); }
    modint& operator++() { val++; if (val == M) val = 0; return *this; }
    modint& operator--() { if (val == 0) val = M; val--; return *this; }
    modint operator++(int) { modint result = *this; ++*this; return result; }
    modint operator--(int) { modint result = *this; --*this; return result; }
    modint& operator+=(const modint& b) { val += b.val; if (val >= M) val -= M; return *this; }
    modint& operator-=(const modint& b) { val -= b.val; if (val >= M) val += M; return *this; }
    modint& operator*=(const modint& b) { ull z = val; z *= b.val; val = (uint)(z % M); return *this; }
    modint& operator/=(const modint& b) { return *this = *this * b.inv(); }
    modint operator+() const { return *this; }
    modint operator-() const { return modint() - *this; }
    modint pow(long long n) const { modint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; }
    modint inv() const { return pow(M-2); }
    friend modint operator+(const modint& a, const modint& b) { return modint(a) += b; }
    friend modint operator-(const modint& a, const modint& b) { return modint(a) -= b; }
    friend modint operator*(const modint& a, const modint& b) { return modint(a) *= b; }
    friend modint operator/(const modint& a, const modint& b) { return modint(a) /= b; }
    friend bool operator==(const modint& a, const modint& b) { return a.val == b.val; }
    friend bool operator!=(const modint& a, const modint& b) { return a.val != b.val; }
};
using mint = modint<MOD>;

/**
 * @brief modint(固定MOD)
 * @docs _md/modint.md
 */
#line 2 "math/gauss_jordan_mint.cpp"

int gauss_jordan(vector<vector<mint>> &A, bool is_extended = false) {
    int m = A.size(), n = A[0].size();
    int rank = 0;
    for (int col = 0; col < n; ++col) {
        if (is_extended && col == n-1) break;
        int pivot = -1;
        for (int row = rank; row < m; ++row) {
            if (A[row][col].val) {
                pivot = row;
                break;
            }
        }
        if (pivot == -1) continue;
        swap(A[pivot], A[rank]);
        auto d = A[rank][col].inv();
        for (int col2 = 0; col2 < n; ++col2) A[rank][col2] *= d;
        for (int row = 0; row < m; ++row) {
            if (row != rank && A[row][col].val) {
                auto fac = A[row][col];
                for (int col2 = 0; col2 < n; ++col2) {
                    A[row][col2] -= A[rank][col2] * fac;
                }
            }
        }
        ++rank;
    }
    return rank;
}

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