51Nod 1126 求递推序列的第N项（矩阵快速幂） 

 1 #include <iostream>
 2 #include <algorithm>
 3 #include <cmath>
 4 #define MOD 7 
 5 #define N 2
 6 using namespace std;
 7 
 8 struct Matrix
 9 {
10     long long v[N][N];
11 };
12 
13 //矩阵间的乘法%m
14 Matrix matrix_mul(Matrix A, Matrix B, long long m)
15 {
16     Matrix ans;
17 
18     for (int i = 0; i < N; i++)
19     {
20         for (int j = 0; j < N; j++)
21         {
22             ans.v[i][j] = 0;
23             for (int k = 0; k < N; k++)
24             {
25                 ans.v[i][j] += (A.v[i][k] * B.v[k][j]) % m;
26             }
27             ans.v[i][j] %= m;
28         }
29     }
30     return ans;
31 }
32 
33 //矩阵快速幂c^n%m
34 Matrix matrix_pow(Matrix C, long long n, long long m)
35 {
36     Matrix ans = { 1, 0, 0, 1 };//e
37     while (n)
38     {
39         if (n & 1)
40             ans = matrix_mul(ans, C, m);
41         C = matrix_mul(C, C, m);
42         n >>= 1;
43     }
44     return ans;
45 }
46 
47 int main()
48 {
49     long long n;
50     int a, b;
51     cin >> a >> b >> n;
52     Matrix temp1 = { (a%MOD + MOD) % MOD, (b%MOD + MOD) % MOD, 1, 0 };
53     Matrix temp2 = { 1, 0, 1, 0 }; // temp2{f[2],0,f[1],0}!!!!!
54 
55     if (n < 2)
56     {
57         cout << 1 << endl;
58         return 0;
59     }
60     Matrix res = matrix_pow(temp1, n - 2, MOD);
61     res = matrix_mul(res, temp2, MOD);
62     cout << res.v[0][0] << endl;
63     return 0;
64 }

 

posted @ 2018-04-06 14:20  ouyang_wsgwz  阅读(146)  评论(0)    收藏  举报