矩阵模板

struct Matrix {
    i64 N;
    vector<vector<i64>> A;
    Matrix() { N = 0;}
    Matrix(int n) {
        N = n;
        A.resize(N + 1);
        for (int i = 0; i <= N; i ++)
            A[i].resize(N + 1, 0);
    }
    void init(vector<vector<i64>> a, int n) {
        A = a;
        N = n;
    }

    Matrix operator*(const Matrix &b) const {
        Matrix res(b.N);

        for (int i = 1; i <= b.N; ++i)
            for (int j = 1; j <= b.N; ++j)
                for (int k = 1; k <= b.N; ++k)
                    res.A[i][j] = (res.A[i][j] + A[i][k] * b.A[k][j]);
        return res;
    }
    Matrix qpow(i64 k) {
        Matrix res(N);

        //斐波那契数列初始化
        //res.A[1][1] = res.A[1][2] = 1;
        //A[1][1] = A[1][2] = A[2][1] = 1;

        //单位矩阵
        for (int i = 0; i <= N; i ++)
            res.A[i][i] = 1;

        while (k) {
            if (k & 1) res = res * (*this);
            (*this) = (*this) * (*this);
            k >>= 1;
        }
        return res;
    }
    //求行列式
    i64 det() {
        return DET(A, N);
    }

    i64 DET(vector<vector<i64>> arr1, int n) {
        i64 sum = 0;
        //i是第一行的列指标，M是余子式的值，sum是行列式的计算值
        if (n == 1)//一阶行列式直接得出结果
            return arr1[0][0];
        else if (n > 1) {
            for (int i = 0; i < n; i++) {
                //按照第一行展开
                i64 M = Minor(arr1, i, n);
                sum += pow(-1, i + 2) * arr1[0][i] * M;
            }
        }
        return sum;
    }
    i64 Minor(vector<vector<i64>> arr1, int i, int n) {
        vector arr2(n + 1, vector<i64>(n + 1));

        //以下为构造余子式的过程。
        for (int j = 0; j < n - 1; j++) {
            for (int k = 0; k < n - 1; k++) {
                if (k < i)
                    arr2[j][k] = arr1[j + 1][k];
                else if (k >= i)
                    arr2[j][k] = arr1[j + 1][k + 1];
            }
        }

        return DET(arr2, n - 1);
        //构造完后，余子式是一个新的行列式，返回DET函数进行计算。
    }
};