矩阵快速幂模板

矩阵快速幂其实跟普通快速幂一样，只是把数换成矩阵而已。

模板，两种写法，亲测可用：

//made by whatbeg

//2014.6.15

struct Matrix

{

    int m[3][3];

};



Matrix Mul(Matrix a,Matrix b)

{

    Matrix c;

    memset(c.m,0,sizeof(c.m));

    for(int i=0;i<3;i++)

        for(int j=0;j<3;j++)

            for(int k=0;k<3;k++)

                c.m[i][j] += ((a.m[i][k]*b.m[k][j])%SMod + SMod)%SMod;

    return c;

}



Matrix fastm(Matrix a,int n) 

{

    Matrix res;

    memset(res.m,0,sizeof(res.m));

    res.m[0][0] = res.m[1][1] = res.m[2][2] = 1;

    while(n)

    {

        if(n&1)

            res = Mul(res,a);

        n>>=1;

        a = Mul(a,a);

    }

    return res;

}



Matrix MPow(Matrix a,int n)  //第二种写法,慎用,易RE

{

    if(n == 1)

        return a;

    Matrix res = fastm(a,n/2);

    res = Mul(res,res);

    if(n&1)

        res = Mul(res,a);

    return res;

}

 

 另一种：

struct Matrix

{

    lll m[13][13];

    Matrix()

    {

        memset(m,0,sizeof(m));

        for(int i=1;i<=n+2;i++)

            m[i][i] = 1LL;

    }

};



Matrix Mul(Matrix a,Matrix b)

{

    Matrix res;

    int i,j,k;

    for(i=1;i<=n+2;i++)

    {

        for(j=1;j<=n+2;j++)

        {

            res.m[i][j] = 0;

            for(k=1;k<=n+2;k++)

                res.m[i][j] = (res.m[i][j]+(a.m[i][k]*b.m[k][j])%SMod + SMod)%SMod;

        }

    }

    return res;

}



Matrix fastm(Matrix a,int b)

{

    Matrix res;

    while(b)

    {

        if(b&1)

            res = Mul(res,a);

        a = Mul(a,a);

        b >>= 1;

    }

    return res;

}

 

 对元素0较多的矩阵取快速幂时可在Mul函数中加一个小优化：

Matrix Mul(Matrix a,Matrix b)

{

    Matrix res;

    int i,j,k;

    memset(res.m,0,sizeof(res.m));

    for(k=1;k<=n+2;k++)

    {

        for(i=1;i<=n+2;i++)

        {

            if(a.m[i][k])

            {

                for(j=1;j<=n+2;j++)

                    res.m[i][j] = (res.m[i][j]+(a.m[i][k]*b.m[k][j])%SMod + SMod)%SMod;

            }

        }

    }

    return res;

}