UVA 11149.Power of Matrix-矩阵快速幂倍增

Power of Matrix

UVA - 11149

代码:

 1 #include <cstdio>
 2 #include <cstring>
 3 #include <iostream>
 4 #include <algorithm>
 5 using namespace std;
 6 #define maxn 44
 7 #define mod 10
 8 int n;
 9 struct matrix{
10     int f[maxn][maxn];
11 };
12 matrix sum(matrix a,matrix b){
13     int i,j;
14     matrix s;
15     for(i=0;i<n;i++)
16         for(j=0;j<n;j++)
17             s.f[i][j]=(a.f[i][j]+b.f[i][j])%mod;
18     return s;
19 }
20 matrix mul(matrix a,matrix b){
21     int i,j,k;
22     matrix s;
23     memset(s.f,0,sizeof(s.f));
24     for(i=0;i<n;i++)
25         for(j=0;j<n;j++)
26             for(k=0;k<n;k++)
27             s.f[i][j]=(s.f[i][j]+a.f[i][k]*b.f[k][j])%mod;
28     return s;
29 }
30 matrix pows(matrix e,int b){
31     matrix s,a;
32     int i,j,k;
33     a=e;
34     for(i=0;i<n;i++)
35         for(j=0;j<n;j++)
36         if(i==j)s.f[i][j]=1;
37         else s.f[i][j]=0;
38     while(b){
39         if(b&1)
40             s=mul(s,a);
41         a=mul(a,a);
42         b=b>>1;
43     }
44     return s;
45 }
46 matrix work(matrix e,int k){
47     matrix s,a,b;
48     if(k==1)
49         return e;
50     a=work(e,k/2);
51     s=sum(a,mul(a,pows(e,k/2)));
52     if(k&1)
53         s=sum(s,pows(e,k));
54     return s;
55 }
56 int main(){
57     int k;
58     while( cin>>n>>k){
59         if(n==0)
60             break;
61         int i,j,a;
62         matrix e;
63         for(i=0;i<n;i++)
64         {
65             for(j=0;j<n;j++)
66             {
67                 cin>>a;
68                 e.f[i][j]=a%10;
69             }
70         }
71         e=work(e,k);
72         for(i=0;i<n;i++)
73         {
74             cout<<e.f[i][0];
75             for(j=1;j<n;j++)
76                 cout<<" "<<e.f[i][j];
77             cout<<endl;
78         }
79         cout<<endl;
80     }
81     return 0;
82 }