GCD和LCM

lilybear101

于 2011-10-21 18:10:09 发布

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分类专栏：基本算法

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本文介绍了一种高效计算两个整数的最大公约数（GCD）和最小公倍数（LCM）的方法，包括算法原理、实现代码及实例应用。

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最大公约数和最小公倍数

#include <stdio.h>
#include <stdlib.h>

unsigned __int64 GCD(unsigned __int64 a,unsigned __int64 b)
{
	unsigned __int64 temp;
	if(a<b)
	{
		temp = a;
		a = b;
		b = temp;
	}
	temp = a%b;
	while(temp!=0)
	{
		a = b;
		b = temp;
		temp = a%b;
	}
	return b;
}

unsigned __int64 LCM(unsigned __int64 a,unsigned __int64 b,unsigned __int64 gcd)
{
	return a*(b/gcd);
}


int main()
{
	unsigned __int64 a,b,next;
	unsigned __int64 gcd, lcm, gcdtmp,lcmtmp;	
	int isZero = 0;

	
	scanf("%I64u", &a);
	if(scanf("%I64u", &b)==EOF)
	{
		printf("%I64u %I64u", a,a);
		return 0;
	}

	if(a == 0 || b == 0) 
	{
		printf("0 0");
		return 0;
	}	

	gcd = GCD(a,b);
	lcm = LCM(a,b,gcd);
	
	while(scanf("%I64u", &next)!=EOF)
	{
		if(next == 0 )
		{
			printf("0 0");
			return 0;
		}
		gcdtmp = GCD(b,next);
		lcmtmp = LCM(b,next,gcdtmp);
		gcd = GCD(gcd, gcdtmp);
		gcdtmp = GCD(lcm,lcmtmp);
		lcm = LCM(lcm,lcmtmp,gcdtmp);
		b = next;
	};
	printf("%I64u ", gcd);
	printf("%I64u", lcm);

	return 0;
}