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;

View Code

#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;

}