poj 2142 The Balance

 

扩展欧几里得的运用：

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<algorithm>
#include<cmath>
#include<queue>
#include<set>
#include<map>
#include<cstring>
#include<vector>
#define LL long long
using namespace std;
LL Ex_Gcd( LL a , LL b , LL &x , LL &y )
{
   if( b ==0 )
   {
       x = 1 ; y = 0;
       return a;        
   }
   LL mod = Ex_Gcd( b , a%b , x , y );
   LL temp = x;
   x = y;
   y = temp - ( a / b ) * y;
   return mod;
}
int main(  )
{
    LL A,B,C,x,y,X,Y;
    while( scanf( "%I64d %I64d %I64d",&A,&B,&C ),A||B||C )
    {
           LL mod = Ex_Gcd( A , B , x ,y );
           A /= mod;
           B /= mod;
           C /= mod;
          //当x是最小正整数解 
           X = ( (x*C)%B + B )%B;
           Y = ( C - X*A )/B;
           if( Y < 0 ) Y = -Y;
           //当y是最小正整数解  
           y = ( (y*C)%A + A )%A;
           x = ( C - y*B )/A;
           if( x < 0 ) x = -x;
           //判断和最小  
           if( x + y < X + Y )
           {
               X = x ; Y = y;
           }
           printf( "%I64d %I64d\n",X,Y);    
    }
    //system( "pause" );
    return 0;
}