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再谈 斐波拉契数

Posted on 2011-06-24 13:19  ForXiXi  阅读(239)  评论(0编辑  收藏  举报

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Diagnostics;
 
namespace Phabe
{
    class Program
    {
 
        private static long[] Values;
        private static List<long> Values2;
 
        static void Main(string[] args)
        {
            Values = new long[200000];
            Values[1] = 1;
            Values[2] = 1;
 
            Values2 = new List<long>();
            Values2.Add(1);
            Values2.Add(1);
 
            for(int i=0;i<2000;i++)
            {
                Console.WriteLine("请输入项:");
                int index = int.Parse(Console.ReadLine());
 
                var bt = new Stopwatch();
                bt.Start();
                var ret = GetNumber(index);
                bt.Stop();
                Console.WriteLine("第{0}种计算结果:{1},耗时{2}毫秒", 1,ret, bt.ElapsedMilliseconds);
 
 
                var bt2 = new Stopwatch();
                bt2.Start();
                var ret2 = GetNumber2(index);
                bt2.Stop();
                Console.WriteLine("第{0}种计算结果:{1},耗时{2}毫秒", 2, ret2, bt2.ElapsedMilliseconds);
 
                var bt3 = new Stopwatch();
                bt3.Start();
                var ret3 = GetNumber3(index);
                bt3.Stop();
                Console.WriteLine("第{0}种计算结果:{1},耗时{2}毫秒", 3, ret3, bt3.ElapsedMilliseconds);
 
                var bt4 = new Stopwatch();
                bt4.Start();
                var ret4 = GetNumber4(index-1);
                bt4.Stop();
                Console.WriteLine("第{0}种计算结果:{1},耗时{2}毫秒", 4, ret4, bt4.ElapsedMilliseconds);
 
 
                var bt5 = new Stopwatch();
                bt5.Start();
                var ret5 = GetNumber5(index);
                bt5.Stop();
                Console.WriteLine("第{0}种计算结果:{1},耗时{2}毫秒", 5, ret5, bt5.ElapsedMilliseconds);
 
            }           
        }
 
        private static long GetNumber(int index)
        {
            long a = 1;
            long b = 1;
            long c = 1;
            for (int i = 2; i < index; i++)
            {
                c = a + b;
                a = b;
                b = c;
            }
            return c;
        }
 
        private static long GetNumber2(int index)
        {
            long a = 1;
            long b = 0;
            for (int i = 2; i < index; i++)
            {
                a += b;
                b = a - b;
            }
            return a + b;
        }
 
        private static long GetNumber3(int index)
        {
            long ret = Values[index];
            if (ret == 0)
            {
                ret = GetNumber3(index - 1) + GetNumber3(index - 2);
                Values[index] = ret;
            }
            return ret;
        }
 
 
        private static long GetNumber4(int index)
        {
             
            while (Values2.Count <= index)
            {
                int count = Values2.Count;               
                long temp = Values2[count - 1] + Values2[count - 2];
                Values2.Add(temp);
            }
 
            return Values2[index];
        }
 
        private static double GetNumber5(int n)
        {
            //直接利用其通项公式 (1/√5)*{[(1+√5)/2]^n - [(1-√5)/2]^n} 
            return (1.0 / Math.Sqrt(5.0)) * (Math.Pow((1 + Math.Sqrt(5.0)) / 2.0, n) - Math.Pow((1 - Math.Sqrt(5.0)) / 2.0, n));
        } 
    }
}

 单纯比较1和2二种方案,哪个更优?为什么?

单纯比较3和4二种方案,哪个更优?为什么?

希望有人能帮我解释一下。