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3919 - 埃及分数

通过次数

0

提交次数

0

时间限制 : 1 秒 内存限制 : 128 MB

  

<span style="font-size:24pt;"><span>•</span></span><span style="font-size:24pt;font-family:宋体;color:black;">古埃及曾经创造出灿烂的人类文明，他们的分数表示却很令人不解。古埃及喜欢把一个分数分解为类似：</span><span style="font-size:24pt;font-family:Arial;color:black;"> 1/a + 1/b </span><span style="font-size:24pt;font-family:宋体;color:black;">的格式。</span>


<span style="font-size:24pt;"><span>•</span></span><span style="font-size:24pt;font-family:Arial;color:black;"><span>&nbsp;&nbsp;&nbsp; </span></span><span style="font-size:24pt;font-family:宋体;color:black;">这里，</span><span style="font-size:24pt;font-family:Arial;color:black;">a </span><span style="font-size:24pt;font-family:宋体;color:black;">和</span><span style="font-size:24pt;font-family:Arial;color:black;"> b </span><span style="font-size:24pt;font-family:宋体;color:black;">必须是不同的两个整数，分子必须为</span><span style="font-size:24pt;font-family:Arial;color:black;"> 1</span>


<span style="font-size:24pt;"><span>•</span></span><span style="font-size:24pt;font-family:Arial;color:black;"><span>&nbsp;&nbsp;&nbsp; </span></span><span style="font-size:24pt;font-family:宋体;color:black;">比如，</span><span style="font-size:24pt;font-family:Arial;color:black;">2/15 </span><span style="font-size:24pt;font-family:宋体;color:black;">一共有</span><span style="font-size:24pt;font-family:Arial;color:black;"> 4 </span><span style="font-size:24pt;font-family:宋体;color:black;">种不同的分解法（姑且称为埃及分解法）：</span>


<span style="font-size:24pt;"><span>•</span></span><span style="font-size:24pt;font-family:Arial;color:black;">1/8 + 1/120</span>


<span style="font-size:24pt;"><span>•</span></span><span style="font-size:24pt;font-family:Arial;color:black;">1/9 + 1/45</span>


<span style="font-size:24pt;"><span>•</span></span><span style="font-size:24pt;font-family:Arial;color:black;">1/10 + 1/30</span>


<span style="font-size:24pt;"><span>•</span></span><span style="font-size:24pt;font-family:Arial;color:black;">1/12 + 1/20</span>


<span style="font-size:24pt;"><span>•</span></span><span style="font-size:24pt;font-family:Arial;color:black;"><span>&nbsp;&nbsp;&nbsp; </span></span><span style="font-size:24pt;font-family:宋体;color:black;">那么，</span><span style="font-size:24pt;font-family:Arial;color:black;"> 2/45 </span><span style="font-size:24pt;font-family:宋体;color:black;">一共有多少个不同的埃及分解呢（满足加法交换律的算同种分解）？</span>


<span style="font-size:24pt;font-family:宋体;color:black;">编程输出满足要求的分解数目。</span>

题目输入

题目输出

一个整数，表示满足要求的分解数目

输入/输出样例

输入格式

no input needed

输出格式

7

C语言解答

#include<stdio.h>
int main()
{
	int a,b;
	int flag=0;
	for(int i=1;i<=10000;i++)
	{
		for(int j=i+1;j<=10000;j++)
		{
			if((45*i+45*j-2*i*j)==0)
			flag++;

		}
	}
	printf("%d\n",flag);
}

C++解答

#include <iostream>
using namespace std;
int main() 
{
	int a,b,cnt=0;
	for(a=1;a<10000;a++)
	{
		for(b=a+1;b<10000;b++)
		{
			if(2*a*b==45*(a+b))
				cnt++;
		}
	}
	cout<<cnt;
	return 0;
}
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