矩阵运算板子

用法

声明一个矩阵: matrix a;

支持 + , - , * , % , 下标访问和快速幂.

注意：为了方便debug，在不满足运算法则进行运算时会直接退出程序并输出 Matrix error!

默认矩阵大小为 Xsize , Ysize ，可自行修改
我也写了构造函数，可以用 matrix a(10,10) 来手动规定矩形的长和宽.

默认情况下矩阵内全为0，可以通过下标访问修改矩阵内元素的值.

默认情况下矩阵内元素类型为 int ，可以修改 #define type int 来修改元素类型.

默认情况下矩阵自动对 INT_MAX 取模，你也可以修改这个自动模数，在 const type mod = INT_MAX 处可以修改.

为了debug方便你可以直接 print(matrix) 来输出一个矩阵.

我内部是用一个 vector<vector<type>> 实现的矩阵(二维数组太不灵活了)，常数有点大请见谅，但是我找不到更好的写法来实现矩阵了，如果有速度更快的办法可以私信我，我尽量更新( .

code

namespace Matrix
{
    #define type int
    const int Xsize = 80;
    const int Ysize = 80;
    const type mod = INT_MAX;    
    struct matrix
    {
        vector<vector<type>> a;
        int xlen, ylen;
        matrix(int x=Xsize, int y=Ysize)
        {
            xlen = x, ylen = y;
            a.resize(x+1);
            for(int i = 1; i <= x; i++)
            {
                a[i].resize(y+1);
                a[i].assign(y+1, 0);
            }
        }
        vector<type>& operator [] (int x)
        {
            return a[x];
        }
    };
    void throw_error()
    {
        cout << "Matrix error!";
        std::exit(0);
    }
    matrix operator + (matrix a, matrix b)
    {
        if(a.xlen != b.xlen or a.ylen != b.ylen)
            throw_error();
        for(int i = 1; i <= a.xlen; i++)
        for(int j = 1; j <= a.ylen; j++)
            (a[i][j] += b[i][j]) %= mod;
        return a;
    }
    matrix operator - (matrix a, matrix b)
    {
        if(a.xlen != b.xlen or a.ylen != b.ylen)
            throw_error();
        for(int i = 1; i <= a.xlen; i++)
        for(int j = 1; j <= a.ylen; j++)
            (a[i][j] -= b[i][j]) %= mod;
        return a;
    }
    matrix operator * (matrix a, matrix b)
    {
        if(a.ylen != b.xlen) throw_error();
        matrix ans(a.xlen, b.ylen);
        for(int i = 1; i <= a.xlen; i++)
        for(int j = 1; j <= b.ylen; j++)
        for(int k = 1; k <= a.ylen; k++)
            (ans[i][j] += a[i][k]*b[k][j]) %= mod;
        return ans;
    }
    matrix operator * (matrix a, type k)
    {
        for(int i = 1; i <= a.xlen; i++)
        for(int j = 1; j <= a.ylen; j++)
            (a[i][j] *= k) %= mod;
        return a;
    }
    matrix operator % (matrix a, type k)
    {
        for(int i = 1; i <= a.xlen; i++)
        for(int j = 1; j <= a.ylen; j++)
            a[i][j] %= k;
        return a;
    }
    matrix& operator += (matrix &a, matrix b){ return (a = a+b); }
    matrix& operator -= (matrix &a, matrix b){ return (a = a-b); }
    matrix& operator *= (matrix &a, matrix b){ return (a = a*b); }
    matrix& operator *= (matrix &a, type k){ return (a = a*k); }
    matrix& operator %= (matrix &a, type k){ return (a = a%k); }
    matrix pow(matrix a, long long p, type k=mod)
    {
        if(a.xlen != a.ylen) throw_error();
        matrix ans(a.xlen, a.ylen);
        for(int i = 1; i <= a.xlen; i++)
            ans[i][i] = 1;
        for(; p; p >>= 1, (a *= a) %= k)
            if(p&1) (ans *= a) %= k;
        return ans;
    }
    void print(matrix a)
    {
        for(int i = 1; i <= a.xlen; i++)
        {
            for(int j = 1; j <= a.ylen; j++)
                cout << a[i][j] << ' ';
            cout << endl;
        }
    }
}
using namespace Matrix;