矩陣快速冪模板

矩陣快速冪其實跟普通快速冪一樣，只是把數換成矩陣而已。

模板，兩種寫法，親測可用：

//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)  //第二種寫法,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;
}

 

 另一種：

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;
}

 

 對元素0較多的矩陣取快速冪時可在Mul函數中加一個小優化：

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;
}