求最大公约数Great Common Divisor的三种算法

本文链接：https://blog.youkuaiyun.com/Micro_lee/article/details/1378788

本文介绍并实现了三种不同的最大公约数(GCD)算法：欧几里得算法、连续整数检测算法及使用埃拉托色尼筛法进行质因数分解的方法。通过实际代码示例展示了每种算法的应用。

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/*****************************************************/
/*                                                   */
/*       求最大公约数Great Common Divisor的三种算法       */
/*       1、使用欧几里得算法                         */
/*       2、使用连续整数检测算法                     */
/*       3、使用中学时代的算法(使用埃拉托色尼筛)     */
/*       Author:lixiongwei                           */
/*       Time:06/11/11 Sun.                          */
/*       WIN XP+(TC/Win_TC/VC++6.0)                  */
/*                                                   */
/*****************************************************/
#include <stdio.h>
#include <conio.h>
#include <stdlib.h>
#define MAX 5000
/******************函数原型声明***********************/
unsigned int my_gcd1(unsigned int m,unsigned int n);
unsigned int my_gcd2(unsigned int m,unsigned int n);
unsigned int my_gcd3(unsigned int m,unsigned int n);
int my_sieve(unsigned int n,unsigned int *L);

int main()
{
    unsigned int m,n;

    printf("Please enter two number: ");
    scanf("%u %u",&m,&n);
    printf("/nGreat Common Divisor: my_gcd1(%u,%u) = %u/n/n",m,n,my_gcd1(m,n));
    printf("Great Common Divisor: my_gcd2(%u,%u) = %u/n/n",m,n,my_gcd2(m,n));
    printf("Great Common Divisor: my_gcd3(%u,%u) = %u/n/n",m,n,my_gcd3(m,n));

getch();
return 0;
}

/*******使用欧几里得算法函数:my_gcd1()定义部分*******/
unsigned int my_gcd1(unsigned int m,unsigned int n)
{
unsigned int temp=m;
unsigned int r;

    if(m < n) /* swap m,n*/
    {
        m = n;
        n = temp;
    }

    if(0 == m)
    {
        printf("You must enter one number much than zero!");
        getch();
        exit(1);/*abnormity*/
    }

    while(n != 0)
    {
        r = m % n;
        m = n;
        n = r;
    }

return m;
}

/*****使用连续整数检测算法函数:my_gcd2()定义部分*****/
unsigned int my_gcd2(unsigned int m,unsigned int n)
{
unsigned int t;

    if( (0 == m)&&(0 == n) )
    {
        printf("You must enter one number much than zero!");
        getch();
        exit(1);/*abnormity*/
    }
    if(0 == m)
        return n;
    if(0 == n)
        return m;

    t = (m < n) ? m : n;
    while(1)
    {
        if( ((m % t) == 0)&&((n % t) == 0) )
            break;
        else
            --t;
    }

return t;
}

/****使用中学时代的算法(使用埃拉托色尼筛) 函数:my_gcd3()定义部分****/
unsigned int my_gcd3(unsigned int m,unsigned int n)
{
    unsigned int ml[MAX];
    unsigned int nl[MAX];
    unsigned int mr[MAX];
    unsigned int nr[MAX];
    unsigned int t=1;
    int i,jm,jn,mi,ni;
    int zm=0,zn=0;

    for(i=0; i<MAX; ++i)
    {
        ml[i]=0;
        nl[i]=0;
        mr[i]=0;
        nr[i]=0;
    }

mi=my_sieve(m,ml);
ni=my_sieve(n,nl);

    i=0;jm=0;
    while(i < mi)
    {
        while(1)
        {
            if( (m%ml[i])==0 )
            {
                mr[jm]=ml[i];
                m=m/ml[i];
                ++jm;
             }
             else
                break;
         }/*inside while end*/
         ++i;
    }/*out while end*/

    i=0;jn=0;
    while(i < ni)
    {
        while(1)
        {
            if( (n%nl[i])==0 )
            {
                nr[jn]=nl[i];
                n=n/nl[i];
                ++jn;
             }
             else
                break;
         }/*inside while end*/
         ++i;
    }/*out while end*/

    for(zm=0,zn=0; (zm<jm)&&(zn<jn); )
    {
        if(mr[zm] < nr[zn])
          ++zm;
        if(mr[zm] > nr[zn])
          ++zn;
        if(mr[zm] == nr[zn])
        { t=t*mr[zm]; zm++;zn++;}
    }

return t;
}

/*******************埃拉托色尼筛函数定义部分************************/
int my_sieve(unsigned int n,unsigned int *L)
{
int i;
unsigned int p,j,A[MAX];

    for(p = 2; p <= n; ++p)
        A[p]=p;
    for(p = 2; p*p <= n; ++p)
    {
        if(A[p] != 0)
        {
            j = p*p;
            while(j <= n)
            {
                A[j]=0;
                j += p;
            }
         }/*end if*/
    }/*end for*/

    i = 0;
    for(p=2; p<=n; ++p)
    {
        if(A[p] != 0)
        {
            L[i]=A[p];
            ++i;
        }
     }

return i;
}