Fibonacci数列计算的三种方法
2011-08-22 21:38 Daniel Zheng 阅读(2749) 评论(0) 编辑 收藏 举报以下分别用递归，迭代，动态规划求解Fibonacci数列：
1 #include <iostream>
2 #include <ctime>
3 using namespace std;
4
5 int Fibonacci_R(int n)
6 {
7 if((n == 1)||(n == 2))
8 return 1;
9 else
10 return Fibonacci_R(n-1) + Fibonacci_R(n-2);
11 }
12
13 int Fibonacci_I(int n)
14 {
15 int A = 1;
16 int B = 1;
17 int C = 2;
18 int index;
19 if((n == 1)||(n == 2))
20 return 1;
21 for(index = 3; index <= n; ++index)
22 {
23 C = A + B;
24 A = B;
25 B = C;
26 }
27 return C;
28 }
29
30 int Fibonacci_D(int n)
31 {
32 int * pCache = new int[n]; //avoid stack overflow
33 pCache[0] = 1;
34 pCache[1] = 1;
35 for(int i = 2; i<n; ++i)
36 {
37 pCache[i] = pCache[i-1] + pCache[i-2];
38 }
39 int result = pCache[n-1];
40 delete [] pCache;
41 return result;
42 }
43
44 int main()
45 {
46 int n = 30;
47 clock_t begin, end;
48
49 begin = clock();
50 cout<<"Fibonacci_R "<<n<<" = "<<Fibonacci_R(n);
51 end = clock();
52 cout<<" time cost is "<<(end-begin)<<" ms"<<endl;
53
54 begin = clock();
55 cout<<"Fibonacci_I "<<n<<" = "<<Fibonacci_I(n);
56 end = clock();
57 cout<<" time cost is "<<(end-begin)<<" ms"<<endl;
58
59 begin = clock();
60 cout<<"Fibonacci_D "<<n<<" = "<<Fibonacci_D(n);
61 end = clock();
62 cout<<" time cost is "<<(end-begin)<<" ms"<<endl;
63
64 return 0;
65 }
后来想想，使用数组的方法跟迭代没什么区别，算不上动态规划，修改如下：
1 #include <iostream>
2 #include <map>
3 #include <ctime>
4
5 using namespace std;
6
7 int Fibonacci_R(int n)
8 {
9 if((n == 1)||(n == 2))
10 return 1;
11 else
12 return Fibonacci_R(n-1) + Fibonacci_R(n-2);
13 }
14
15 int Fibonacci_I(int n)
16 {
17 int A = 1;
18 int B = 1;
19 int C = 2;
20 int index;
21 if((n == 1)||(n == 2))
22 return 1;
23 for(index = 3; index <= n; ++index)
24 {
25 C = A + B;
26 A = B;
27 B = C;
28 }
29 return C;
30 }
31
32 //int Fibonacci_D(int n)
33 //{
34 // int * pCache = new int[n];
35 // pCache[0] = 1;
36 // pCache[1] = 1;
37 // for(int i = 2; i<n; ++i)
38 // {
39 // pCache[i] = pCache[i-1] + pCache[i-2];
40 // }
41 // int result = pCache[n-1];
42 // delete [] pCache;
43 // return result;
44 //}
45
46
47 int Fibonacci_D(int n, map<int, int> & Cache)
48 {
49 map<int, int>::const_iterator iLocator = Cache.find(n);
50 if(iLocator != Cache.end())
51 return iLocator->second;
52 else
53 Cache.insert(make_pair(n, Fibonacci_D(n - 1, Cache) + Fibonacci_D(n - 2, Cache) ));
54 iLocator = Cache.find(n);
55 return iLocator->second;
56 }
57
58
59 int main()
60 {
61 int n = 30;
62 clock_t begin, end;
63 map<int, int> Fibonacci_Cache;
64 Fibonacci_Cache.insert(make_pair(1, 1));
65 Fibonacci_Cache.insert(make_pair(2, 1));
66
67 begin = clock();
68 cout<<"Fibonacci_R "<<n<<" = "<<Fibonacci_R(n);
69 end = clock();
70 cout<<" time cost is "<<(end-begin)<<" ms"<<endl;
71
72 begin = clock();
73 cout<<"Fibonacci_I "<<n<<" = "<<Fibonacci_I(n);
74 end = clock();
75 cout<<" time cost is "<<(end-begin)<<" ms"<<endl;
76
77 begin = clock();
78 cout<<"Fibonacci_D "<<n<<" = "<<Fibonacci_D(n, Fibonacci_Cache);
79 end = clock();
80 cout<<" time cost is "<<(end-begin)<<" ms"<<endl;
81
82 return 0;
83 }
当计算数字很大时，迭代速度 > 动态规划（map操作耗费的时间？） >>> 递归。
