hdu 1005 根据递推公式构造矩阵 ( 矩阵快速幂)

f(1) = 1, f(2) = 1, f(n) = (A * f(n - 1) + B * f(n - 2)) mod 7.

Sample Input
1 1 3 //a b n
1 2 10
0 0 0

Sample Output
2
5

矩阵A  * 矩阵B  = 矩阵C 

a b        f(n-1)     f(n)

1 0        f(n-2)    f(n-1)

# include <iostream>
# include <cstdio>
# include <algorithm>
# include <map>
# include <cmath>
# define LL long long
using namespace std ;

const int MOD = 7 ;

struct Matrix
{
    int mat[2][2];
};

Matrix mul(Matrix a,Matrix b) //矩阵乘法
{
    Matrix c;
    for(int i=0;i<2;i++)
        for(int j=0;j<2;j++)
        {
            c.mat[i][j]=0;
            for(int k=0;k<2;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<2;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 a,b,n;
    while(scanf("%d%d%d" , &a,&b,&n) != EOF)
    {
        if (a==0 && b==0 && n==0)
            break ;
        if (n <= 2)
        {
            printf("1
") ;
            continue ;
        }
        Matrix t ;
        t.mat[0][0] = a ;
        t.mat[0][1] = b ;
        t.mat[1][0] = 1 ;
        t.mat[1][1] = 0 ;
        Matrix ans = pow_M(t,n-2) ;
        printf("%d
" , (ans.mat[0][0] + ans.mat[0][1])%MOD) ;

    }


    return 0 ;
}