[luoguP1962] 斐波那契数列（矩阵快速幂）

传送门

解析详见julao博客连接 http://worldframe.top/2017/05/10/清单-数学方法-——-矩阵/

——代码

 1 #include <cstdio>
 2 #include <cstring>
 3 #define LL long long
 4
 5 LL n;
 6 const int p = 1e9 + 7;
 7
 8 struct Matrix
 9 {
10     LL a[2][2];
11     Matrix()
12     {
13         memset(a, 0, sizeof(a));
14     }
15 };
16
17 inline Matrix operator * (const Matrix x, const Matrix y)
18 {
19     Matrix ans;
20     int i, j, k;
21     for(i = 0; i < 2; i++)
22         for(j = 0; j < 2; j++)
23             for(k = 0; k < 2; k++)
24                 ans.a[i][j] = (ans.a[i][j] + x.a[i][k] * y.a[k][j]) % p;
25     return ans;
26 }
27
28 inline int pow(LL x)
29 {
30     Matrix ans, trs;
31     ans.a[0][0] = ans.a[1][1] = 1;
32     trs.a[0][0] = trs.a[1][0] = trs.a[0][1] = 1;
33     while(x)
34     {
35         if(x & 1) ans = ans * trs;
36         trs = trs * trs;
37         x >>= 1;
38     }
39     return ans.a[0][0];
40 }
41
42 int main()
43 {
44     scanf("%lld", &n);
45     printf("%d\n", pow(n - 1));
46     return 0;
47 }