f(n) = n的优化（二）

对程序做了进一步优化，目前总耗时1分20秒。

代码如下：

///jailusd@hotmail.com
///2006-09-11
///
/*
 * 题目：;Consider a function which, for a given whole number n, returns the number of ones required when writing out all numbers between 0 and n. 

For example, f(13)=6. Notice that f(1)=1. What is the next largest n such that f(n)=n?

翻译过来大体是这样：
有一个整数n,写一个函数f(n),返回0到n之间出现的"1"的个数。比如f(13)=6,现在f(1)=1,问下一个最大的f(n)=n的n是什么？

为什么f(13)=6, 因为1,2,3,4,5,6,7,8,9,10,11,12,13.数数1的个数，正好是6.

请大家写出自己的算法，并统计一些在你机器上计算出1111111110的时间。为了不影响大家的思路，我最后贴上我的程序。

语言不限，随便了。
 */

using System;
using System.Collections.Generic;
using System.Text;

namespace ping4210_1
{
    class Program
    {
        static void Main(string[] args)
        {
            Count();

            Console.ReadLine();
        }

        static void Count()
        {
            DateTime dtStart = DateTime.Now;
            DateTime dtEnd;

            TimeSpan ts;
            double count;

            int N = 1;          //自然数N
            bool bl = true;
            int intCount = 0;     //1的总个数

            int intTemp = 0;      //当前数字含1的个数
            int a,b;

            Console.WriteLine("满足f(n) = n的n值列表：");

            //核心代码
            while (bl)
            {
                if (N % 10 == 1)
                {
                    intCount++;
                    intCount += intTemp;
                }
                else if (N % 10 == 0)
                {
                    intTemp = 0;    //统计1的个数

                    b = N;
                    while (b > 0)
                    {
                        a = b % 10;
                        if (a == 1)
                        {
                            intTemp++;
                        }
                        b = (b - a) / 10;
                    }
                    intCount += intTemp;
                }
                else if (N % 10 == 2)
                {
                    intCount += intTemp;
                    if ((intCount >= N) && (intCount <= (N + 8)))
                    {
                    }
                    else
                    {
                        N += 7;
                        intCount += (7 * intTemp);
                    }
                }
                else
                {
                    intCount += intTemp;
                }

                //intCount += intTemp;

                //判断N值是否与1的个数相等
                if (intCount == N)
                {
                    Console.WriteLine(N.ToString());

                    //显示当前计算时间
                    ts = DateTime.Now.Subtract(dtStart);
                    count = ts.TotalMilliseconds;
                    Console.WriteLine("Total Time:\t" + ts);
                    Console.WriteLine();
                }

                //当N值等于多少时停止程序11111111111
                if (N >= 1111111111)
                {
                    bl = false;
                }

                N++;
            }
            //核心代码结束

            //显示最张运行时间
            dtEnd = DateTime.Now;

            ts = DateTime.Now.Subtract(dtStart);
            count = ts.TotalMilliseconds;

            Console.WriteLine();
            Console.WriteLine("Start Time:\t" + dtStart);
            Console.WriteLine("End Time:\t" + dtEnd);
            Console.WriteLine("Total Time:\t" + ts);

            Console.WriteLine("运行结束！");
            Console.WriteLine();
        }
    }
}

运行结果：
满足f(n) = n的n值列表：
1
Total Time:     00:00:00

199981
Total Time:     00:00:00.0156250

199982
Total Time:     00:00:00.0156250

199983
Total Time:     00:00:00.0156250

199984
Total Time:     00:00:00.0156250

199985
Total Time:     00:00:00.0156250

199986
Total Time:     00:00:00.0156250

199987
Total Time:     00:00:00.0156250

199988
Total Time:     00:00:00.0156250

199989
Total Time:     00:00:00.0156250

199990
Total Time:     00:00:00.0156250

200000
Total Time:     00:00:00.0156250

200001
Total Time:     00:00:00.0156250

1599981
Total Time:     00:00:00.0937500

1599982
Total Time:     00:00:00.0937500

1599983
Total Time:     00:00:00.0937500

1599984
Total Time:     00:00:00.1093750

1599985
Total Time:     00:00:00.1093750

1599986
Total Time:     00:00:00.1093750

1599987
Total Time:     00:00:00.1093750

1599988
Total Time:     00:00:00.1093750

1599989
Total Time:     00:00:00.1093750

1599990
Total Time:     00:00:00.1093750

2600000
Total Time:     00:00:00.1718750

2600001
Total Time:     00:00:00.1718750

35000000
Total Time:     00:00:02.2656250

35000001
Total Time:     00:00:02.2656250

35199981
Total Time:     00:00:02.2812500

35199982
Total Time:     00:00:02.2812500

35199983
Total Time:     00:00:02.2812500

35199984
Total Time:     00:00:02.2812500

35199985
Total Time:     00:00:02.2968750

35199986
Total Time:     00:00:02.2968750

35199987
Total Time:     00:00:02.2968750

35199988
Total Time:     00:00:02.2968750

35199989
Total Time:     00:00:02.2968750

35199990
Total Time:     00:00:02.2968750

35200000
Total Time:     00:00:02.2968750

35200001
Total Time:     00:00:02.2968750

500000000
Total Time:     00:00:35.3593750

500000001
Total Time:     00:00:35.3750000

500199981
Total Time:     00:00:35.3906250

500199982
Total Time:     00:00:35.3906250

500199983
Total Time:     00:00:35.3906250

500199984
Total Time:     00:00:35.3906250

500199985
Total Time:     00:00:35.3906250

500199986
Total Time:     00:00:35.3906250

500199987
Total Time:     00:00:35.3906250

500199988
Total Time:     00:00:35.3906250

500199989
Total Time:     00:00:35.3906250

500199990
Total Time:     00:00:35.3906250

500200000
Total Time:     00:00:35.4062500

500200001
Total Time:     00:00:35.4062500

501599981
Total Time:     00:00:35.5000000

501599982
Total Time:     00:00:35.5000000

501599983
Total Time:     00:00:35.5000000

501599984
Total Time:     00:00:35.5156250

501599985
Total Time:     00:00:35.5156250

501599986
Total Time:     00:00:35.5156250

501599987
Total Time:     00:00:35.5156250

501599988
Total Time:     00:00:35.5156250

501599989
Total Time:     00:00:35.5156250

501599990
Total Time:     00:00:35.5156250

502600000
Total Time:     00:00:35.5937500

502600001
Total Time:     00:00:35.5937500

535000000
Total Time:     00:00:37.9218750

535000001
Total Time:     00:00:37.9218750

535199981
Total Time:     00:00:37.9375000

535199982
Total Time:     00:00:37.9375000

535199983
Total Time:     00:00:37.9375000

535199984
Total Time:     00:00:37.9531250

535199985
Total Time:     00:00:37.9531250

535199986
Total Time:     00:00:37.9531250

535199987
Total Time:     00:00:37.9531250

535199988
Total Time:     00:00:37.9531250

535199989
Total Time:     00:00:37.9531250

535199990
Total Time:     00:00:37.9531250

535200000
Total Time:     00:00:37.9531250

535200001
Total Time:     00:00:37.9531250

1111111110
Total Time:     00:01:20.2812500


Start Time:     2006-9-11 2:00:05
End Time:       2006-9-11 2:01:25
Total Time:     00:01:20.2812500
运行结束！

posted @ 2006-09-11 10:13  Jailu  阅读(530)  评论(2)  编辑  收藏  举报