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-7using 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;}