一、前言
老师给出的要求：
阅读下面程序，请回答如下问题：
问题1：这个程序要找的是符合什么条件的数？
问题2：这样的数存在么？符合这一条件的最小的数是什么？
问题3：在电脑上运行这一程序，你估计多长时间才能输出第一个结果？时间精确到分钟（电脑：单核CPU 4.0G Hz，内存和硬盘等资源充足）。
问题4：在多核电脑上如何提高这一程序的运行效率?
（注：该程序、用C#语言编写，但是只要有C语言基础完全没有阅读压力，如果对部分语句不懂请自行查询）
using System;
using System.Collections.Generic;
using System.Text;
namespace FindTheNumber
{
class Program
{
static void Main(string[] args)
{
int [] rg ={2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19，20,21,22,23,24,25,26,27,28,29,30,31};
for (Int64 i = 1; i < Int64.MaxValue; i++)
{
int hit = 0;
int hit1 = -1;
int hit2 = -1;
for (int j = 0; (j < rg.Length) && (hit <=2) ; j++)
{
if ((i % rg[j]) != 0)
{
hit++;
if (hit == 1)
{
hit1 = j;
}
else if (hit == 2)
{
hit2 = j;
}
else
break;
}
}
if ((hit == 2)&& (hit1+1==hit2))
{
Console.WriteLine("found {0}", i);
}
}
}
}
}
二、分析
自己第一次看到这个C#代码时候，就觉得C#继承了C及C++语言的特性。首先我看着别扭，我把它写成了c语言。
Int64相当于2^64次方，10^20次方，相当于10亿=10^10次方。
(1)当i=1
j=0 i%rg[0]=1%2=1 1!=0 hit++ hit=1 hit1=j=0;
j=1 i%rg[1]=1%3=1 1!=0 hit++ hit=2 hit1=j=1;
j=2 i%rg[2]=1%4=1 1!=0 hit++ hit=3 break跳出当前循环。判断是否符合条件，不符合
(2)当i=2
j=0 i%rg[0]=2%2=0 0==0
j=1 i%rg[1]=2%3=2 2!=0 hit++ hit=1 hit1=j=1;
j=2 i%rg[2]=2%4=2 2!=0 hit++ hit=2 hit2=j=2;
j=3 i%rg[3]=2%5=2 2!=0 hit++ hit=3 break跳出当前循环。判断是否符合条件，不符合
（3）当i=3
j=0 i%rg[0]=3%2=1 1！=0 hit++ hit=1 hit1=j=0;
j=1 i%rg[1]=3%3=0 0==0 hit++ hit=2 hit2=j=1;
j=2 i%rg[2]=3%4=1 1!=0 hit++ hit=3 break跳出当前循环。判断是否符合条件，不符合
（4）当i=4
j=0 i%rg[0]=4%2=0 0==0
j=1 i%rg[1]=4%3=1 1！=0 hit++ hit=1 hit1=j=1;
j=2 i%rg[2]=4%4=0 0==0
j=3 i%rg[3]=4%5=4 4！=0 hit++ hit=2 hit2=j=3；
j=4 i%rg[3]=4%6=4 4！=0 hit++ hit=3 break跳出当前循环。判断是否符合条件，不符合
。。。。。。。
。。。。。。。。。
从这儿看出来：条件是：最终要是hit==2&&hit1+1==hit2；相邻的两个数同时取余后！=0，就一定满足条件hit1+1==hit2
只有当相邻的两个数是在最后出现，break，前面所有的数都能被整除，那么问题来了，相邻两个数一定是一个奇数和一个偶数。偶数可以拆分为之前的2*相关的数。也就是说，偶数可以用之前的两个数来表示。即不存在这样的数。
三、解答
Int64相当于2^64次方，10^20次方，相当于10亿=10^10次方。
问题1：这个程序要找的是符合什么条件的数？
答：这个程序要找的数，相邻两个数是质数的数。
问题2：这样的数存在么？符合这一条件的最小的数是什么？
答：这样的数不存在。
问题3：在电脑上运行这一程序，你估计多长时间才能输出第一个结果？时间精确到分钟（电脑：单核CPU 4.0G Hz，内存和硬盘等资源充足）。（我的电脑是四核，3，4GHz）
答：测试的数据是1亿，用时5.034秒。
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" alt="" />
测试的数据是10亿，用时51.160秒。（基本上是满足增大10倍，时间上也是增大10倍）
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" alt="" />
所以，我们可以考虑认为：当数据达到10^20时，5.034*10^11秒=839 000 0000分钟。
问题4：在多核电脑上如何提高这一程序的运行效率?
答：多核电脑中，提高每个核的运算效率。实施多线程的控制，把这些数均分到多段，一段一个核，在每一个核中计算每一段的这些数，把每一个核的运算结果输出，多线程控制输入，运算，控制。
附带一张转换成C语言的代码（用Codeblock测得时间）
#include<cstdio>
#include<cstdlib>
#include<iostream>
using namespace std;
int main()
{
long long i,j;
int a[]={2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31};
for(i=1;i<1000000000;i++)//1亿
{
int hit=0;
int hit1=-1;
int hit2=-1;
for(j=0;j<30&&hit<=2;j++)
{
if(i%a[j]!=0)
{
hit++;
if(hit==1)
hit1=j;
else if(hit==2)
hit2=j;
else
break; }
}
if(hit==2&&(hit1+1==hit2))
cout<<i<<endl;
}
return 0;
}
四、总结
1、分析问题的方式从简单到难。
2、从逻辑上进行推理，变换逻辑思维解决问题。
3、自己需要学习的知识还有很多，自己会每天进步一点。