poj3070 Fibonacci 斐波那契数列的第n项的矩阵求法

对于满足（F0 = 0, F1 = 1, and Fn = Fn − 1 + Fn − 2 for n ≥ 2）的斐波那契数列，第n项可由矩阵求出公式如下：

 1 ///2014.2.24
 2 ///poj3070
 3 
 4 #include <iostream>
 5 #include <vector>
 6 #include <cstdio>
 7 using namespace std;
 8 
 9 #define MOD 10000
10 //定义二阶矩阵
11 struct MATRIX
12 {
13     long long f11;
14     long long f12;
15     long long f21;
16     long long f22;
17 };
18 
19 //定义二阶矩阵乘法函数
20 MATRIX matMulti(MATRIX mat1, MATRIX mat2)
21 {
22     MATRIX matrix;
23     matrix.f11 = (mat1.f11*mat2.f11 + mat1.f12*mat2.f21)%MOD;
24     matrix.f12 = (mat1.f11*mat2.f12 + mat1.f12*mat2.f22)%MOD;
25     matrix.f21 = (mat1.f21*mat2.f11 + mat1.f22*mat2.f21)%MOD;
26     matrix.f22 = (mat1.f21*mat2.f12 + mat1.f22*mat2.f22)%MOD;
27 
28     return matrix;
29 }
30 
31 MATRIX Fibo(int m)
32 {
33     MATRIX unitMat,retMat;
34     unitMat.f11 = (long long)1;
35     unitMat.f12 = (long long)1;
36     unitMat.f21 = (long long)1;
37     unitMat.f22 = (long long)0;
38 
39     if(m==1)
40     {
41         retMat.f11 = (long long)1;
42         retMat.f12 = (long long)1;
43         retMat.f21 = (long long)1;
44         retMat.f22 = (long long)0;
45     }
46     else if(m%2 == 0)
47     {
48         retMat = Fibo(m/2);
49         retMat = matMulti(retMat,retMat);
50     }
51     else if(m%2 == 1)
52     {
53         retMat = Fibo((m-1)/2);
54         retMat = matMulti(retMat,retMat);
55         retMat = matMulti(retMat,unitMat);
56     }
57 
58     return retMat;
59 }
60 
61 int main()
62 {
63 //    freopen("in","r",stdin);
64 //    freopen("out","w",stdout);
65 
66     int m;
67     vector<int> output;
68     MATRIX retMatrix;
69 
70     while( cin>>m && m!=-1)
71     {
72         if(m==0)
73         {
74             output.push_back(0);
75         }
76         else
77         {
78             retMatrix = Fibo(m);
79             output.push_back( retMatrix.f12 % 10000 );
80         }
81     }
82 
83     for(vector<int>::size_type i=0; i<output.size(); i++)
84         cout<<output[i]<<endl;
85     return 0;
86 }
code for poj3070 in C++ (g++)

 

posted @ 2014-02-24 19:45  basement_boy  阅读(508)  评论(0)  编辑  收藏  举报