題意:
? ? ? 給你四個點,問你第四個點是否在前三個點圍成的三角形的外接圓上.
思路:

? ? ? 水題,就是練練用魔板罷了,當該三角形是銳角三角形的時候,圓心是任意兩條邊中垂線的交點,半徑是圓心到任意一點的距離,否則圓心就是最長的那條邊的中點位置,半徑就是最長的那條邊的一半..

#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) //角度轉弧度 {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) //向量減 {return Vector( A.x - B.x, A.y - B.y ); } Vector operator*( Vector A, double p ) //向量數乘 {return Vector( A.x * p, A.y * p ); } Vector operator/( Vector A, double p ) //向量數除 {return Vector( A.x / p, A.y / p ); } bool operator<(const Point& A, const Point& B ) //兩點比較 {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 ) //兩點相等 {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)//兩點式 {v=e-s;}}; double Dot(Vector A,Vector B)//向量點乘 {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)//向量夾角 {return acos(Dot(A,B)/Length(A)/Length(B)); } double Cross(Vector A,Vector B)//向量叉積 {return A.x*B.y-A.y*B.x; } double Area2(Point A,Point B,Point C )//向量有向面積 {return Cross(B-A,C-A); } double Dist(Point A,Point B) {return Length(A-B); } Vector Rotate(Vector A, double rad)//向量逆時針旋轉 {return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad)); } Vector Normal(Vector A)//向量單位法向量 {double L=Length(A);return Vector(-A.y/L,A.x/L); } Point GetLineIntersection(Line l1,Line l2)//兩直線交點 {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)//點到直線的距離 {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)//點到線段的距離 {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)// 點在直線上的投影 {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)//點在線段上包括端點 {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)//直線平行 {return dcmp(Cross(l1.e-l1.s,l2.e-l2.s))==0; } bool SegmentProperIntersection(Line l1,Line l2)//線段相交 {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) //多邊形有向面積 {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; }

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