更高效的Fibonacci求解

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两种思想三种方式实现斐波那序列求解，一种是传统递归的思想，一种是动态规划的思想，动态规划又分为Top-down和Bottom-up两种方式。

// Fast_Fibonacci.cpp : 定义控制台应用程序的入口点。//#include "stdafx.h"#include <iostream>#include <time.h>//support for clock()using namespace std;int Fib1(int n)//传统递归方式实现--有每次重复计算值的缺点{if (n <= 0)return -1;if (n == 1 || n == 2)return 1;elsereturn Fib1(n - 1) + Fib1(n - 2);}int F[10] = { 0 };//暂存数组（每位均初始为0），用来判断F[n]是否已定义过int Fib2(int n)//动态规划思想--高效的Top-down方法--记忆化，不重复计算值{if (n <= 0)return -1;if (n == 1 || n == 2)return 1;if (F[n] != 0)//Indicate that F[n] is defined!return F[n];F[n] = Fib2(n-1) + Fib2(n-2);return F[n];}int Fib3(int n)//用动态规划的思想求解--Bottom up方法{if (n <= 0)return -1;if (n == 1 || n == 2)return 1;F[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 t1,t2,t3;t1 = Fib1(5);t2 = Fib2(5);t3 = Fib3(5);cout << t1 << endl << t2 << endl << t3 << endl;////int n = 100000;//clock_t start, finish, duration;//start = clock();//t1 = Fib1(5);////while (n--);//finish = clock();//duration = (double)(finish - start) / CLOCKS_PER_SEC;//cout << "方法1--传统方法，耗时秒数：" << duration << endl;//start = clock();//t2 = Fib2(5);//finish = clock();//duration = (double)(finish - start) / CLOCKS_PER_SEC;//cout << "方法2--Top-down方法，耗时秒数：" << duration << endl;    return 0;}

动态规划是个好东西也是个难点。是个非常重要的算法，需要好好学习。

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