Fibonacci数列计算的三种方法

以下分别用递归，迭代，动态规划求解Fibonacci数列：

#include <iostream>
#include <ctime>
using namespace std;

int Fibonacci_R(int n)
{
if((n == 1)||(n == 2))
return 1;
else
return Fibonacci_R(n-1) + Fibonacci_R(n-2);
}

int Fibonacci_I(int n)
{
int A = 1;
int B = 1;
int C = 2;
int index;
if((n == 1)||(n == 2))
return 1;
for(index = 3; index <= n; ++index)
{
C = A + B;
A = B;
B = C;
}
return C;
}

int Fibonacci_D(int n)
{
int * pCache = new int
; //avoid stack overflow
pCache[0] = 1;
pCache[1] = 1;
for(int i = 2; i<n; ++i)
{
pCache[i] = pCache[i-1] + pCache[i-2];
}
int result = pCache[n-1];
delete [] pCache;
return result;
}

int main()
{
int n = 30;
clock_t begin, end;

begin = clock();
cout<<"Fibonacci_R "<<n<<" = "<<Fibonacci_R(n);
end = clock();
cout<<" time cost is "<<(end-begin)<<" ms"<<endl;

begin = clock();
cout<<"Fibonacci_I "<<n<<" = "<<Fibonacci_I(n);
end = clock();
cout<<" time cost is "<<(end-begin)<<" ms"<<endl;

begin = clock();
cout<<"Fibonacci_D "<<n<<" = "<<Fibonacci_D(n);
end = clock();
cout<<" time cost is "<<(end-begin)<<" ms"<<endl;

return 0;
}

　　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：

#include <iostream>
#include <map>
#include <ctime>

using namespace std;

int Fibonacci_R(int n)
{
if((n == 1)||(n == 2))
return 1;
else
return Fibonacci_R(n-1) + Fibonacci_R(n-2);
}

int Fibonacci_I(int n)
{
int A = 1;
int B = 1;
int C = 2;
int index;
if((n == 1)||(n == 2))
return 1;
for(index = 3; index <= n; ++index)
{
C = A + B;
A = B;
B = C;
}
return C;
}

//int Fibonacci_D(int n)
//{
//    int * pCache = new int
;
//    pCache[0] = 1;
//    pCache[1] = 1;
//    for(int i = 2; i<n; ++i)
//    {
//        pCache[i] = pCache[i-1] + pCache[i-2];
//    }
//    int result = pCache[n-1];
//    delete [] pCache;
//    return result;
//}

int Fibonacci_D(int n, map<int, int> & Cache)
{
map<int, int>::const_iterator iLocator = Cache.find(n);
if(iLocator != Cache.end())
return iLocator->second;
else
Cache.insert(make_pair(n, Fibonacci_D(n - 1, Cache) + Fibonacci_D(n - 2, Cache) ));
iLocator = Cache.find(n);
return iLocator->second;
}

int main()
{
int n = 30;
clock_t begin, end;
map<int, int> Fibonacci_Cache;
Fibonacci_Cache.insert(make_pair(1, 1));
Fibonacci_Cache.insert(make_pair(2, 1));

begin = clock();
cout<<"Fibonacci_R "<<n<<" = "<<Fibonacci_R(n);
end = clock();
cout<<" time cost is "<<(end-begin)<<" ms"<<endl;

begin = clock();
cout<<"Fibonacci_I "<<n<<" = "<<Fibonacci_I(n);
end = clock();
cout<<" time cost is "<<(end-begin)<<" ms"<<endl;

begin = clock();
cout<<"Fibonacci_D "<<n<<" = "<<Fibonacci_D(n, Fibonacci_Cache);
end = clock();
cout<<" time cost is "<<(end-begin)<<" ms"<<endl;

return 0;
}

　　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。