http://acm.hdu.edu.cn/showproblem.php?pid=4720
包含三个点且最小的圆可能是三角形的外接圆或者是以任意两点连成线段的中点为圆心的园，找出最小的即可，然后判断麻瓜到圆心的距离和圆半径之间的关系，注意求外心的前提是三点不共线
#include <iostream> #include <cstdio> #include <cstring> #include <cmath> #include <algorithm> using namespace std ; const double eps = 1e-8; const double PI = acos(-1.0); int sgn(double x) { if(fabs(x) < eps)return 0; if(x < 0)return -1; else return 1; } struct Point { double x,y; Point(){} Point(double _x,double _y) { x = _x;y = _y; } Point operator -(const Point &b)const { return Point(x - b.x,y - b.y); } //叉积 double operator ^(const Point &b)const { return x*b.y - y*b.x; } //点积 double operator *(const Point &b)const { return x*b.x + y*b.y; } //绕原点旋转角度B（弧度值），后x,y的变化 void transXY(double B) { double tx = x,ty = y; x = tx*cos(B) - ty*sin(B); y = tx*sin(B) + ty*cos(B); } }; struct Line { Point s,e; Line(){} Line(Point _s,Point _e) { s = _s;e = _e; } //两直线相交求交点 //第一个值为0表示直线重合，为1表示平行，为0表示相交,为2是相交 //只有第一个值为2时，交点才有意义 pair<int,Point> operator &(const Line &b)const { Point res = s; if(sgn((s-e)^(b.s-b.e)) == 0) { if(sgn((s-b.e)^(b.s-b.e)) == 0) return make_pair(0,res);//重合 else return make_pair(1,res);//平行 } double t = ((s-b.s)^(b.s-b.e))/((s-e)^(b.s-b.e)); res.x += (e.x-s.x)*t; res.y += (e.y-s.y)*t; return make_pair(2,res); } }; //*两点间距离 double dist(Point a,Point b) { return sqrt((a-b)*(a-b)); } //*判断三点共线 bool online(Point p1, Point p2, Point p3) { return sgn(p3.x-min(p1.x,p2.x)) >= 0 && sgn(p3.x-max(p1.x,p2.x)) <= 0 && sgn(p3.y-min(p1.y,p2.y)) >= 0 && sgn(p3.y-max(p1.y,p2.y)) <= 0; } //*判断线段相交 bool inter(Line l1,Line l2) { return max(l1.s.x,l1.e.x) >= min(l2.s.x,l2.e.x) && max(l2.s.x,l2.e.x) >= min(l1.s.x,l1.e.x) && max(l1.s.y,l1.e.y) >= min(l2.s.y,l2.e.y) && max(l2.s.y,l2.e.y) >= min(l1.s.y,l1.e.y) && sgn((l2.s-l1.e)^(l1.s-l1.e))*sgn((l2.e-l1.e)^(l1.s-l1.e)) <= 0 && sgn((l1.s-l2.e)^(l2.s-l2.e))*sgn((l1.e-l2.e)^(l2.s-l2.e)) <= 0; } //判断直线和线段相交 bool Seg_inter_line(Line l1,Line l2) //判断直线l1和线段l2是否相交 { return sgn((l2.s-l1.e)^(l1.s-l1.e))*sgn((l2.e-l1.e)^(l1.s-l1.e)) <= 0; } //点到直线距离 //返回为result,是点到直线最近的点 Point PointToLine(Point P,Line L) { Point result; double t = ((P-L.s)*(L.e-L.s))/((L.e-L.s)*(L.e-L.s)); result.x = L.s.x + (L.e.x-L.s.x)*t; result.y = L.s.y + (L.e.y-L.s.y)*t; return result; } //点到线段的距离 //返回点到线段最近的点 Point NearestPointToLineSeg(Point P,Line L) { Point result; double t = ((P-L.s)*(L.e-L.s))/((L.e-L.s)*(L.e-L.s)); if(t >= 0 && t <= 1) { result.x = L.s.x + (L.e.x - L.s.x)*t; result.y = L.s.y + (L.e.y - L.s.y)*t; } else { if(dist(P,L.s) < dist(P,L.e)) result = L.s; else result = L.e; } return result; } //计算多边形面积 //点的编号从0~n-1 double CalcArea(Point p[],int n) { double res = 0; for(int i = 0;i < n;i++) res += (p[i]^p[(i+1)%n])/2; return fabs(res); } //*判断点在线段上 bool OnSeg(Point P,Line L) { return sgn((L.s-P)^(L.e-P)) == 0 && sgn((P.x - L.s.x) * (P.x - L.e.x)) <= 0 && sgn((P.y - L.s.y) * (P.y - L.e.y)) <= 0; } //*判断点在凸多边形内 //点形成一个凸包，而且按逆时针排序（如果是顺时针把里面的<0改为>0） //点的编号:0~n-1 //返回值： //-1:点在凸多边形外 //0:点在凸多边形边界上 //1:点在凸多边形内 int inConvexPoly(Point a,Point p[],int n) { for(int i = 0;i < n;i++) { if(sgn((p[i]-a)^(p[(i+1)%n]-a)) < 0)return -1; else if(OnSeg(a,Line(p[i],p[(i+1)%n])))return 0; } return 1; } //*判断点在任意多边形内 //射线法，poly[]的顶点数要大于等于3,点的编号0~n-1 //返回值 //-1:点在凸多边形外 //0:点在凸多边形边界上 //1:点在凸多边形内 int inPoly(Point p,Point poly[],int n) { int cnt; Line ray,side; cnt = 0; ray.s = p; ray.e.y = p.y; ray.e.x = -100000000000.0;//-INF,注意取值防止越界 for(int i = 0;i < n;i++) { side.s = poly[i]; side.e = poly[(i+1)%n]; if(OnSeg(p,side))return 0; //如果平行轴则不考虑 if(sgn(side.s.y - side.e.y) == 0) continue; if(OnSeg(side.s,ray)) { if(sgn(side.s.y - side.e.y) > 0)cnt++; } else if(OnSeg(side.e,ray)) { if(sgn(side.e.y - side.s.y) > 0)cnt++; } else if(inter(ray,side)) cnt++; } if(cnt % 2 == 1)return 1; else return -1; } //判断凸多边形 //允许共线边 //点可以是顺时针给出也可以是逆时针给出 //点的编号0~n-1 bool isconvex(Point poly[],int n) { bool s[3]; memset(s,false,sizeof(s)); for(int i = 0;i < n;i++) { s[sgn( (poly[(i+1)%n]-poly[i])^(poly[(i+2)%n]-poly[i]) )+1] = true; if(s[0] && s[2])return false; } return true; } //过三点求圆心坐标 Point waixin(Point a,Point b,Point c) { double a1 = b.x - a.x, b1 = b.y - a.y, c1 = (a1*a1 + b1*b1)/2; double a2 = c.x - a.x, b2 = c.y - a.y, c2 = (a2*a2 + b2*b2)/2; double d = a1*b2 - a2*b1; return Point(a.x + (c1*b2 - c2*b1)/d, a.y + (a1*c2 -a2*c1)/d); } int main() { int t ; scanf("%d",&t) ; for(int cas=1 ;cas<=t ;cas++) { Point p[5] ; for(int i=0 ;i<4 ;i++) scanf("%lf%lf",&p[i].x,&p[i].y) ; Point o ; double dis=1e20 ; for(int i=0 ;i<3 ;i++) { Point temp=Point((p[i].x+p[(i+1)%3].x)/2,(p[i].y+p[(i+1)%3].y)/2) ; double r=max(dist(temp,p[0]),max(dist(temp,p[1]),dist(temp,p[2]))) ; if(dis>r) { dis=r ; o=temp ; } } if(!online(p[0],p[1],p[2])) { Point temp=waixin(p[0],p[1],p[2]) ; double r=max(dist(temp,p[0]),max(dist(temp,p[1]),dist(temp,p[2]))) ; if(dis>r) { dis=r ; o=temp ; } } printf("Case #%d: ",cas) ; if(sgn(dist(o,p[3])-dis)<=0)puts("Danger") ; else puts("Safe") ; } return 0 ; }
