hdu 1757 和1005差不多 (矩阵快速幂)

If x < 10 f(x) = x.
If x >= 10 f(x) = a0 * f(x-1) + a1 * f(x-2) + a2 * f(x-3) + …… + a9 * f(x-10);
And ai(0<=i<=9) can only be 0 or 1

求f（n）%MOD

Sample Input
10 9999 //n mod
1 1 1 1 1 1 1 1 1 1
20 500
1 0 1 0 1 0 1 0 1 0

Sample Output
45
104

 

# include <iostream>
# include <cstdio>
# include <cstring>
# include <algorithm>
# include <cmath>
using namespace std ;

int MOD ;

struct Matrix
{
    int mat[10][10];
};

Matrix mul(Matrix a,Matrix b) //矩阵乘法
{
    Matrix c;
    for(int i=0;i<10;i++)
        for(int j=0;j<10;j++)
        {
            c.mat[i][j]=0;
            for(int k=0;k<10;k++)
            {
                c.mat[i][j]=(c.mat[i][j] + a.mat[i][k]*b.mat[k][j])%MOD;
            }
        }
    return c;
}
Matrix pow_M(Matrix a,int k)  //矩阵快速幂
{
    Matrix ans;
    memset(ans.mat,0,sizeof(ans.mat));
    for (int i=0;i<10;i++)
        ans.mat[i][i]=1;
    Matrix temp=a;
    while(k)
    {
        if(k&1)ans=mul(ans,temp);
        temp=mul(temp,temp);
        k>>=1;
    }
    return ans;
}



int main ()
{
    //freopen("in.txt","r",stdin) ;
    int n  ;
    while(cin>>n>>MOD)
    {
        Matrix t ;
        int i , j ;
        for (i = 0 ; i < 10 ; i++)
            cin>>t.mat[0][i] ;
        if (n < 10)
        {
            cout<<n<<endl ;
            continue ;
        }
        for (i = 1 ; i < 10 ; i++)
            for (j = 0 ; j < 10 ; j++)
        {
            if (i ==(j+1))
                t.mat[i][j] = 1 ;
            else
                t.mat[i][j] = 0 ;
        }
        Matrix ans = pow_M(t,n-9) ;
        int sum = 0 ;
        for (i = 0 ; i < 10 ; i++)
        {
            sum = (sum + ans.mat[0][i]*(9-i))%MOD ;
        }
        cout<<sum<<endl ;


    }


    return 0 ;
}