hdu4720 三角形的外接圆

题意:

      给你四个点,问你第四个点是否在前三个点围成的三角形的外接圆上.

思路:

      水题,就是练练用魔板罢了,当该三角形是锐角三角形的时候,圆心是任意两条边中垂线的交点,半径是圆心到任意一点的距离,否则圆心就是最长的那条边的中点位置,半径就是最长的那条边的一半..

#include <cstdio>
#include <cmath>
#include <algorithm>
#define maxn 60
#define eps 1e-7
using namespace std;
int dcmp(double x)    //控制精度
{
    if(fabs(x)<eps) return 0;
    else return x<0?-1:1;
}
double toRad(double deg)   //角度转弧度
{
    return deg/180.0*acos(-1.0);
}
struct Point
{
    double x,y;
    Point(){}
    Point(double x,double y):x(x),y(y) {}
    void input()
    {
        scanf("%lf %lf",&x,&y);
    }
};
typedef Point Vector;
Vector operator+( Vector A, Vector B )       //向量加
{
    return Vector( A.x + B.x, A.y + B.y );
}
Vector operator-(Vector A,Vector B)       //向量减
{
    return Vector( A.x - B.x, A.y - B.y );
}
Vector operator*( Vector A, double p )      //向量数乘
{
    return Vector( A.x * p, A.y * p );
}
Vector operator/( Vector A, double p )      //向量数除
{
    return Vector( A.x / p, A.y / p );
}
bool operator<(const Point& A, const Point& B )   //两点比较
{
    return dcmp( A.x - B.x ) < 0 || ( dcmp( A.x - B.x ) == 0 && dcmp( A.y - B.y ) < 0 );
}
bool operator==( const Point& a, const Point& b )   //两点相等
{
    return dcmp( a.x - b.x ) == 0 && dcmp( a.y - b.y ) == 0;
}
struct Line
{
    Point s,e;
    Vector v;
    Line() {}
    Line(Point s,Point v,int type)://法向量式
        s(s),v(v){}
    Line(Point s,Point e):s(s),e(e)//两点式
    {v=e-s;}

};
double Dot(Vector A,Vector B)//向量点乘
{
    return A.x*B.x+A.y*B.y;
}
double Length(Vector A)//向量模
{
    return sqrt(Dot(A,A));
}
double Angle(Vector A,Vector B)//向量夹角
{
    return acos(Dot(A,B)/Length(A)/Length(B));
}
double Cross(Vector A,Vector B)//向量叉积
{
    return A.x*B.y-A.y*B.x;
}
double Area2(Point A,Point B,Point C )//向量有向面积
{
    return Cross(B-A,C-A);
}
double Dist(Point A,Point B)
{
    return Length(A-B);
}
Vector Rotate(Vector A, double rad)//向量逆时针旋转
{
    return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));
}
Vector Normal(Vector A)//向量单位法向量
{
    double L=Length(A);
    return Vector(-A.y/L,A.x/L);
}
Point GetLineIntersection(Line l1,Line l2)//两直线交点
{
    Point P=l1.s;
    Vector v=l1.v;
    Point Q=l2.s;
    Vector w=l2.v;
    Vector u=P-Q;
    double t=Cross(w,u)/Cross(v,w);
    return P+v*t;
}
double DistanceToLine(Point P,Line L)//点到直线的距离
{
    Point A,B;
    A=L.s,B=L.e;
    Vector v1=B-A,v2=P-A;
    return fabs(Cross(v1,v2))/Length(v1);
}
double DistanceToSegment(Point P, Line L)//点到线段的距离
{
    Point A,B;
    A=L.s,B=L.e;
    if(A==B) return Length(P-A);
    Vector v1=B-A,v2=P-A,v3=P-B;
    if (dcmp(Dot(v1,v2))<0) return Length(v2);
    else if (dcmp(Dot(v1,v3))>0) return Length(v3);
    else return fabs(Cross(v1,v2)) / Length(v1);
}
Point GetLineProjection(Point P,Line L)// 点在直线上的投影
{
    Point A,B;
    A=L.s,B=L.e;
    Vector v=B-A;
    return A+v*(Dot(v,P-A)/Dot(v,v));
}
bool OnSegment(Point p,Line l)//点在线段上包括端点
{
    Point a1=l.s;
    Point a2=l.e;
    return dcmp(Cross(a1-p,a2-p))==0&&dcmp(Dist(p,a1)+Dist(p,a2)-Dist(a1,a2))==0;
}
bool Paralled(Line l1,Line l2)//直线平行
{
    return dcmp(Cross(l1.e-l1.s,l2.e-l2.s))==0;
}
bool SegmentProperIntersection(Line l1,Line l2)//线段相交
{
    if(Paralled(l1,l2))
    {
        return false;
    }
    Point t=GetLineIntersection(l1,l2);
    if(OnSegment(t,l1))
    {
        return true;
    }
    return false;
}
int ConvexHull(Point *p,int n,Point *ch)    //求凸包
{
    sort(p,p+n);
    int m=0;
    for ( int i = 0; i < n; ++i )
    {
        while ( m > 1 && Cross( ch[m - 1] - ch[m - 2], p[i] - ch[m - 2] ) <= 0 ) --m;
        ch[m++] = p[i];
    }
    int k = m;
    for ( int i = n - 2; i >= 0; --i )
    {
        while ( m > k && Cross( ch[m - 1] - ch[m - 2], p[i] - ch[m - 2] ) <= 0 ) --m;
        ch[m++] = p[i];
    }
    if ( n > 1 ) --m;
    return m;
}
double PolygonArea(Point *p,int n)   //多边形有向面积
{
    double area=0;
    for (int i=1;i<n-1;++i)
        area+=Cross(p[i]-p[0],p[i+1]-p[0]);
    return area/2.0;
}

double dis(Point A ,Point B)
{
   double tmp = (A.x - B.x) * (A.x - B.x) + (A.y - B.y) * (A.y - B.y);
   return sqrt(tmp);
}

typedef struct
{
   double dis;
   Point A ,B;
}EDGE;

EDGE edge[5];

bool campp(EDGE a ,EDGE b)
{
   return a.dis < b.dis;
}

int main ()
{
   int t ,i ,cas = 1;
   Point p1 ,p2 ,p3 ,p;
   Point O;
   double R;
   scanf("%d" ,&t);
   while(t--)
   {
      scanf("%lf %lf" ,&p1.x ,&p1.y);
      scanf("%lf %lf" ,&p2.x ,&p2.y);
      scanf("%lf %lf" ,&p3.x ,&p3.y);
      scanf("%lf %lf" ,&p.x ,&p.y);
      edge[1].A = p1 ,edge[1].B = p2;
      edge[2].A = p1 ,edge[2].B = p3;
      edge[3].A = p2 ,edge[3].B = p3;
      edge[1].dis = dis(p1 ,p2);
      edge[2].dis = dis(p1 ,p3);
      edge[3].dis = dis(p2 ,p3);
      sort(edge + 1 ,edge + 3 + 1 ,campp);
      if(edge[1].dis * edge[1].dis + edge[2].dis * edge[2].dis <= edge[3].dis * edge[3].dis)
      {
         O.x = (edge[3].A.x + edge[3].B.x) / 2;
         O.y = (edge[3].A.y + edge[3].B.y) / 2;

         R = edge[3].dis / 2;
      }
      else
      {
         Line L1 = Line((p1 + p2)/2 ,Normal(p1 - p2),1);
         Line L2 = Line((p1 + p3)/2 ,Normal(p1 - p3),1);
         O = GetLineIntersection(L1 ,L2);
         R = dis(O ,p1);
      }
      double diss = dis(p ,O);
      if(diss <= R) printf("Case #%d: Danger\n" ,cas ++);
      else printf("Case #%d: Safe\n" ,cas ++);
   }
   return 0;
}