poj 3449 Geometric Shapes

输入输出超恶心的，这个题要注意的是线段不是规范相交，也算相交，没有图形包含的情况；

思路：计算几何。思路并不复杂，枚举当前几何体的所有边和其他几何体的所有边比较。另外，已知正方形的一对不相邻的顶点(x0,y0),(x2,y2)，可以由方程组：

x1 + x3 = x0 + x2;

x1 - x3 =y0- y2  ;

y1 + y3 = y0 + y2;

y3 - y1 = x0 - x2  ;

求得另一对不相邻的顶点(x1,y1),(x3,y3)。

矩形另外一个点为 x3 = x0 + x2 - x1 ,y3 = y0 + y2 - y1;

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<algorithm>
#include<cmath>
#include<cstring>
using namespace std;
class Point{
public:
      double x,y;    
};
class Polygon {
public:
      int n,N;
      char num;
      Point point[24];
      int node[30];
      bool operator < (Polygon b) const {
            return num < b.num;
        }
}polygon[30];
int Input( int n , int cnt ,char num){
    for( int i = 0 ; i < n ; i ++ ){
       scanf( " (%lf,%lf)",&polygon[cnt].point[i].x,&polygon[cnt].point[i].y );    
    }
    polygon[cnt].n = n;    
    polygon[cnt].num = num; 
    cnt ++;
    return cnt;
}
void Get_tri( int n ){
    polygon[n-1].n = 4;
    polygon[n-1].point[3].x=polygon[n-1].point[0].x+polygon[n-1].point[2].x-polygon[n-1].point[1].x;
    polygon[n-1].point[3].y=polygon[n-1].point[0].y+polygon[n-1].point[2].y-polygon[n-1].point[1].y;
}
void Get_point( int n ){
    Point p,m;
    polygon[n-1].point[2] = polygon[n-1].point[1];
    p.x = ( polygon[n-1].point[0].x + polygon[n-1].point[2].x )/2.0;
    p.y = ( polygon[n-1].point[0].y + polygon[n-1].point[2].y )/2.0;
    m.x =  polygon[n-1].point[0].x - p.x; m.y =  polygon[n-1].point[0].y - p.y;
    polygon[n-1].point[1].x = -m.y + p.x; polygon[n-1].point[1].y = m.x + p.y;
    m.x =  polygon[n-1].point[2].x - p.x; m.y =  polygon[n-1].point[2].y - p.y;
    polygon[n-1].point[3].x = -m.y + p.x; polygon[n-1].point[3].y = m.x + p.y;
    polygon[n-1].n = 4;
}
double on_segment( Point p1 , Point p2  , Point q  ){
   return ( p1.x - q.x)*( p2.y - q.y ) - ( p2.x - q.x )*( p1.y - q.y );
}
double Min( double a , double b ){
     return a < b ?a : b;
    }
double Max( double a, double b ){
    return a > b ? a : b;
    }
int dcmp( double x)
{
   if( fabs( x )< 1.0e-8) return 0;
   if( x < 0 ) return -1;
   return 1; 
}
bool judge( Point p1 , Point p2 ,Point q ){
    double max_x = Max( p1.x ,p2.x );
    double min_x = Min( p1.x ,p2.x );
    if( q.x >= min_x && q.x <= max_x  )
        return true;
    return false;
}
bool segment( Point p1 , Point p2 , Point q1 ,Point q2 ){
    int d1 = dcmp(on_segment( p1 , p2 , q1 ));
    int d2 = dcmp(on_segment( p1 , p2 , q2 ));
    int d3 = dcmp(on_segment( q1 , q2 , p1 ));
    int d4 = dcmp(on_segment( q1 , q2 , p2 ));
    if( d1*d2 < 0 && d3*d4< 0 ) return true;
    if( d1==0 && judge( p1 , p2 , q1 )) return true;
    if( d2==0 && judge( p1 , p2 , q2 )) return true;
    if( d3==0 && judge( q1,  q2 , p1 )) return true;
    if( d4==0 && judge( q1 , q2 , p2 ))return true;
    return false;    
}
bool Cross( int n , int m ){
    int t = polygon[n].n ,tt=polygon[m].n;
   for( int k = 0 ; k < t ; k ++ ){
      for( int l = 0 ; l <tt ; l ++ ){
        if(segment(polygon[n].point[k],polygon[n].point[(k+1)%t],polygon[m].point[l],polygon[m].point[(l+1)%tt] ))
          return true;
        }
    }    
    return false;  
}
void Solve( int n ){
    for( int i = 0 ; i < n ; i ++ )
         polygon[i].N = 0;
    for( int i = 0 ; i < n ; i++ ){        
        for( int j = i+1 ; j < n ; j ++ ){
            if( Cross( i , j ) ){
    //            printf( "%d %d\n",i,j );
              polygon[i].node[polygon[i].N++] = j;
              polygon[j].node[polygon[j].N++] = i;
             }
            }
        }    
}
int main(  ){
    char num[3],str[100];
    int cnt = 0,n;
    while( scanf( "%s",num ) , num[0]!='.' ){
        if( num[0] != '-' ){
            scanf( "%s",str );
            switch( str[0] ){
               case 's':cnt = Input( 2 ,cnt,num[0] );
                        Get_point( cnt ); break;
               case 'l':cnt = Input( 2 ,cnt,num[0] ); break;
               case 't':cnt = Input( 3 ,cnt,num[0] );break;
               case 'p':scanf( "%d",&n );cnt = Input( n ,cnt,num[0] );break;
               case 'r':cnt = Input( 3 ,cnt,num[0] );
                        Get_tri( cnt );break;
            }
        }
        else {
            sort( polygon , polygon + cnt );
            Solve( cnt );
            for( int i =0 ; i < cnt ; i ++ ){
               if( polygon[i].N ==0 ) printf( "%c has no intersections\n",polygon[i].num );
               else { printf( "%c intersects with ",polygon[i].num );
                    if( polygon[i].N == 1 )printf( "%c\n",polygon[polygon[i].node[0]].num );
                    else if( polygon[i].N == 2 ) 
                    printf( "%c and %c\n",polygon[polygon[i].node[0]].num,polygon[polygon[i].node[1]].num );
                    else
                    {int j;
                    for(  j = 0 ; j < polygon[i].N -1; j ++ )
                      printf( "%c, ",polygon[polygon[i].node[j]].num );
                          printf( "and %c\n",polygon[polygon[i].node[j]].num );                    

                   }
            }            
            }
            puts( "" );
            cnt = 0;    
        }
    }
    //system( "pause" );
    return 0;
}