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 =  ;
 
 struct Matrix
 {
     int mat[][];
 };
 
 Matrix mul(Matrix a,Matrix b) //矩阵乘法
 {
     Matrix c;
     for(int i=;i<;i++)
         for(int j=;j<;j++)
         {
             c.mat[i][j]=;
             for(int k=;k<;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,,sizeof(ans.mat));
     for (int i=;i<;i++)
         ans.mat[i][i]=;
     Matrix temp=a;
     while(k)
     {
         if(k&)ans=mul(ans,temp);
         temp=mul(temp,temp);
         k>>=;
     }
     return ans;
 }
 
 int main ()
 {
    // freopen("in.txt","r",stdin) ;
     int a,b,n;
     while(scanf("%d%d%d" , &a,&b,&n) != EOF)
     {
         if (a== && b== && n==)
             break ;
         if (n <= )
         {
             printf("1\n") ;
             continue ;
         }
         Matrix t ;
         t.mat[][] = a ;
         t.mat[][] = b ;
         t.mat[][] =  ;
         t.mat[][] =  ;
         Matrix ans = pow_M(t,n-) ;
         printf("%d\n" , (ans.mat[][] + ans.mat[][])%MOD) ;
 
     }
 
     return  ;
 }