poj 2954 Triangle

这个题用到了pick定理：

多边形的面积 = 内部的数的和 + 边上的点的和/2  -1;

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<algorithm>
#include<cmath>
#include<queue>
#include<set>
#include<map>
#include<cstring>
#include<vector>
using namespace std;
class Point
{
public:
      int x,y;    
}point[3];
int Gcd( int a , int b )
{
   return  b==0 ? a : Gcd( b , a%b );    
}
int Area( Point a ,Point b, Point c )
{
   return abs( ( a.x - c.x )*( b.y - c.y ) - ( a.y - c.y )*( b.x -c.x ) )/2;    
}
int Edge( Point a ,Point b, Point c )
{
   int E  = 0;
   E += Gcd( abs(a.x - b.x) , abs( a.y - b.y ) );
   E += Gcd( abs(a.x - c.x) , abs( a.y - c.y ) );
   E += Gcd( abs(b.x - c.x) , abs( b.y - c.y ) );
   return E;    
}
int main(  )
{
    while( 1 )
    {
       int cnt = 0;
       for( int i = 0 ; i < 3 ; i ++ )
       {
            scanf( "%d %d",&point[i].x ,&point[i].y );
            if( point[i].x==0 &&point[i].y ==0  )
                cnt++;    
       }
       if( cnt==3 ) break;
       int area = Area( point[0] , point[1] ,point[2] );
       int edge = Edge( point[0] , point[1] ,point[2] );  
       printf( "%d\n",area + 1 - edge/2);    
    }
    //system( "pause" );
    return 0;
}