fzoj--1683--矩阵快速幂

 1 #include <iostream>
 2 #include <cstring>
 3 using namespace std;
 4 
 5 const int mod = 2009;
 6 
 7 struct data
 8 {
 9     int m[4][4];
10 }base,result;
11 
12 void init( )
13 {
14     memset( base.m , 0 , sizeof(base.m) );
15     base.m[0][1] = base.m[1][2] = base.m[3][0] = base.m[3][3] = 1;
16     base.m[2][0] = 7;
17     base.m[2][1] = 2;
18     base.m[2][2] = 3;
19     
20     memset( result.m , 0 , sizeof(result.m) );
21     result.m[0][0] = 1;
22     result.m[1][0] = 3;
23     result.m[2][0] = 5;
24     result.m[3][0] = 0;
25 }
26 
27 data multi( data& p , data& q )//p--base q--result
28 {
29     data temp;
30     for( int i = 0 ; i<4 ; i++ )
31     {
32         for( int j = 0 ; j<4 ; j++ )
33         {
34             temp.m[i][j] = 0;
35             for( int k = 0 ; k<4 ; k++ )
36             {
37                 temp.m[i][j] = ( temp.m[i][j] + p.m[i][k]*q.m[k][j] ) %mod;
38             }
39         }
40     }
41     return temp;
42 }
43 
44 int fastMod( int n )
45 {
46     while( n )
47     {
48         if( n&1 )
49         {
50             result = multi( base , result );
51         }
52         base = multi( base , base );
53         n >>= 1;
54     }
55     return result.m[3][0];
56 }
57 
58 int main()
59 {
60     int t , n;
61     while( cin >> t )
62     {
63         for( int i = 1 ; i<=t ; i++ )
64         {
65             init();
66             cin >> n;
67             cout << "Case " << i << ": " << fastMod(n+1) << endl;
68         }
69     }
70     return 0;
71 }

 1 #include <iostream>
 2 #include <cstring>
 3 using namespace std;
 4 
 5 const int mod = 2009;
 6 
 7 struct data
 8 {
 9     int m[4][4];
10     int mat[4][1];
11 }base,result;
12 
13 void init( )
14 {
15     memset( base.m , 0 , sizeof(base.m) );
16     base.m[0][1] = base.m[1][2] = base.m[3][0] = base.m[3][3] = 1;
17     base.m[2][0] = 7;
18     base.m[2][1] = 2;
19     base.m[2][2] = 3;
20     
21     result.mat[0][0] = 1;
22     result.mat[1][0] = 3;
23     result.mat[2][0] = 5;
24     result.mat[3][0] = 0;
25 }
26 
27 data multi( data& p , data& q )//p--base q--result
28 {
29     data temp;
30     for( int i = 0 ; i<4 ; i++ )
31     {
32         for( int j = 0 ; j<1 ; j++ )
33         {
34             temp.mat[i][j] = 0;
35             for( int k = 0 ; k<4 ; k++ )
36             {
37                 temp.mat[i][j] = ( temp.mat[i][j] + p.m[i][k]*q.mat[k][j] ) %mod;
38             }
39         }
40     }
41     return temp;
42 }
43 
44 data mul( data& p , data& q )//p--base q--base
45 {
46     data t;
47     for( int i = 0 ; i<4 ; i++ )
48     {
49         for( int j = 0 ; j<4 ; j++ )
50         {
51             t.m[i][j] = 0;
52             for( int k = 0 ; k<4 ; k++ )
53             {
54                 t.m[i][j] = ( t.m[i][j] + p.m[i][k]*q.m[k][j] ) %mod;
55             }
56         }
57     }
58     return t;
59 }
60 
61 int fastMod( int n )
62 {
63     while( n )
64     {
65         if( n&1 )
66         {
67             result = multi( base , result );
68         }
69         base = mul( base , base );
70         n >>= 1;
71     }
72     return result.mat[3][0];
73 }
74 
75 int main()
76 {
77     int t , n;
78     while( cin >> t )
79     {
80         for( int i = 1 ; i<=t ; i++ )
81         {
82             init();
83             cin >> n;
84             cout << "Case " << i << ": " << fastMod(n+1) << endl;
85         }
86     }
87     return 0;
88 }