#include<iostream>
#include<algorithm>
#include<ctime>using namespace std;int F1(int n)
{if (n == 1)return 1;if (n == 2)return 1;return F1(n - 1) + F1(n - 2);
}int main()
{int n;cout << "请输入n的值：";while (cin >> n){time_t time1, time2;time1 = clock();long long result = F1(n);time2 = clock();cout << "F(n) = " << result << "\t耗时：" << (double)(time2 - time1) / CLOCKS_PER_SEC << endl;}cout << __DATE__ << "  " << __TIME__ << endl;system("pause");return 0;
}

请输入n的值：10
F(n) = 55       耗时：0
15
F(n) = 610      耗时：0
20
F(n) = 6765     耗时：0
30
F(n) = 832040   耗时：0.08
35
F(n) = 9227465  耗时：0.424
40
F(n) = 102334155        耗时：4.33
41
F(n) = 165580141        耗时：6.989
^Z
Aug 24 2016  13:17:07
请按任意键继续. . .

从计算结果中我们可以看到，没有备忘录模式的自顶向下的计算方法是非常耗时的，因为每一次的递归都会有大量的重复计算的过程！

方法二：

#include<iostream>
#include<algorithm>
#include<ctime>using namespace std;int F2(int n, int *f)
{if (f[n] != -1)return f[n];if (n == 1)return 1;if (n == 2)return 1;f[n] = F2(n - 1, f) + F2(n - 2, f);return f[n];
}int main()
{int n;cout << "请输入n的值：";while (cin >> n){int *f = new int[n + 1];memset(f, -1, sizeof(int)*(n + 1));time_t time1, time2;time1 = clock();long long result = F2(n, f);time2 = clock();cout << "F(n) = " << result << "\t耗时：" << (double)(time2 - time1) / CLOCKS_PER_SEC << endl;free(f);}cout << __DATE__ << "  " << __TIME__ << endl;system("pause");return 0;
}

请输入n的值：10
F(n) = 55       耗时：0
15
F(n) = 610      耗时：020
F(n) = 6765     耗时：0
30
F(n) = 832040   耗时：0
40
F(n) = 102334155        耗时：0
41
F(n) = 165580141        耗时：0
^Z
Aug 24 2016  13:19:43
请按任意键继续. . .

带有备忘的自定向下的方法可以节省大量的时间，因为没有子问题的重复计算！

#include<iostream>
#include<algorithm>
#include<ctime>using namespace std;int F3(int n, int *f)
{f[1] = 1;f[2] = 1;for (int i = 3; i <= n; i++)f[i] = f[i - 1] + f[i - 2];return f[n];
}int main()
{int n;cout << "请输入n的值：";while (cin >> n){int *f = new int[n + 1];memset(f, -1, sizeof(int)*(n + 1));time_t time1, time2;time1 = clock();long long result = F3(n, f);time2 = clock();cout << "F(n) = " << result << "\t耗时：" << (double)(time2 - time1) / CLOCKS_PER_SEC << endl;free(f);}cout << __DATE__ << "  " << __TIME__ << endl;system("pause");return 0;
}

运行结果：

请输入n的值：10
F(n) = 55       耗时：0
15
F(n) = 610      耗时：0
20
F(n) = 6765     耗时：0
25
F(n) = 75025    耗时：0
30
F(n) = 832040   耗时：0
35
F(n) = 9227465  耗时：0
40
F(n) = 102334155        耗时：0
41
F(n) = 165580141        耗时：0
^Z
Aug 24 2016  13:23:16
请按任意键继续. . .