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

 

 1 # include <iostream>
 2 # include <cstdio>
 3 # include <cstring>
 4 # include <algorithm>
 5 # include <cmath>
 6 using namespace std ;
 7 
 8 int MOD ;
 9 
10 struct Matrix
11 {
12     int mat[10][10];
13 };
14 
15 Matrix mul(Matrix a,Matrix b) //矩阵乘法
16 {
17     Matrix c;
18     for(int i=0;i<10;i++)
19         for(int j=0;j<10;j++)
20         {
21             c.mat[i][j]=0;
22             for(int k=0;k<10;k++)
23             {
24                 c.mat[i][j]=(c.mat[i][j] + a.mat[i][k]*b.mat[k][j])%MOD;
25             }
26         }
27     return c;
28 }
29 Matrix pow_M(Matrix a,int k)  //矩阵快速幂
30 {
31     Matrix ans;
32     memset(ans.mat,0,sizeof(ans.mat));
33     for (int i=0;i<10;i++)
34         ans.mat[i][i]=1;
35     Matrix temp=a;
36     while(k)
37     {
38         if(k&1)ans=mul(ans,temp);
39         temp=mul(temp,temp);
40         k>>=1;
41     }
42     return ans;
43 }
44 
45 
46 
47 int main ()
48 {
49     //freopen("in.txt","r",stdin) ;
50     int n  ;
51     while(cin>>n>>MOD)
52     {
53         Matrix t ;
54         int i , j ;
55         for (i = 0 ; i < 10 ; i++)
56             cin>>t.mat[0][i] ;
57         if (n < 10)
58         {
59             cout<<n<<endl ;
60             continue ;
61         }
62         for (i = 1 ; i < 10 ; i++)
63             for (j = 0 ; j < 10 ; j++)
64         {
65             if (i ==(j+1))
66                 t.mat[i][j] = 1 ;
67             else
68                 t.mat[i][j] = 0 ;
69         }
70         Matrix ans = pow_M(t,n-9) ;
71         int sum = 0 ;
72         for (i = 0 ; i < 10 ; i++)
73         {
74             sum = (sum + ans.mat[0][i]*(9-i))%MOD ;
75         }
76         cout<<sum<<endl ;
77 
78 
79     }
80 
81 
82     return 0 ;
83 }
View Code

 

posted @ 2015-05-28 23:59  __Meng  阅读(151)  评论(0)  编辑  收藏  举报