/*///////////////////////////////////
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范数（模的平方）
向量的模(求线段距离/两点距离)
点乘
叉乘
判断向量垂直
判断a1-a2与b1-b2垂直
判断线段垂直
判断向量平行
判断a1-a2与b1-b2平行
判断线段平行
求点在线段上的垂足
求点关于直线的对称点
判断P0,P1,P2三点位置关系,Vector p0-p2 在p0-p1的相对位置
判断p1-p2与p3-p4是否相交
判断线段是否相交
a,b两点间的距离
点到直线的距离
点到线段的距离
两线段间的距离(相交为0)
求两线段的交点
求直线交点
中垂线
向量a,b的夹角，范围[0,180]
向量（点）极角，范围[-180,180]
角度排序(从x正半轴起逆时针一圈)范围为[0,180)
判断点在多边形内部
凸包(CCW/CW)
求向量A,向量B构成三角形的面积
(旋转卡壳)求平面中任意两点的最大距离
三点所成的外接圆
三点所成的内切圆
过点p求过该点的两条切线与圆的两个切点
极角(直线与x轴的角度)
点与圆的位置关系
已知点与切线求圆心
已知两直线和半径,求夹在两直线间的圆
求与给定两圆相切的圆
多边形(存储方式:点->线)
半平面交
求最近点对的距离(分治)
*////////////////////////////////////
#include
#include
#include
#include
#include
using namespace std;
#define EPS (1e-10)
#define equals(a, b) (fabs(a-b) Polygon;//多边形(存点)
typedef vector Pol;//多边形（存边）
class Circle
{
public:
Point c;
double r;
Circle(Point c=Point(), double r=0.0):c(c), r(r) {}
Point point(double a)
{
return Point(c.x + cos(a)*r, c.y + sin(a)*r);
}
};//圆
Point operator + (Point a, Point b)
{
return Point(a.x+b.x, a.y+b.y);
}
Point operator - (Point a, Point b)
{
return Point(a.x-b.x, a.y-b.y);
}
Point operator * (Point a, double p)
{
return Point(a.x*p, a.y*p);
}
Point operator / (Point a, double p)
{
return Point(a.x/p, a.y/p);
}
//排序左下到右上
bool operator < (const Point &a,const Point &b)
{
return a.xEPS ) return CCW;
if( cross(a, b)<-EPS ) return CW;
if( dot(a, b)<-EPS ) return BACK;
if( norm(a)b.y) swap(a,b);
if(a.yEPS) x=!x;
}
return (x? 2 : 0);
}
//凸包(CCW/CW)
Polygon andrewScan(Polygon s)
{
Polygon u, l;
if(s.size()<3) return s;
sort(s.begin(), s.end());
u.push_back(s[0]);
u.push_back(s[1]);
l.push_back(s[s.size()-1]);
l.push_back(s[s.size()-2]);
for(int i=2; i=2 && ccw(u[n-2], u[n-1], s[i])!=CW; n--)
u.pop_back();
u.push_back(s[i]);
}
for(int i=s.size()-3; i>=0; i--)
{
for(int n=l.size(); n>=2 && ccw(l[n-2], l[n-1], s[i])!=CW; n--)
l.pop_back();
l.push_back(s[i]);
}
reverse(l.begin(), l.end());
for(int i=u.size()-2; i>=1; i--) l.push_back(u[i]);
return l;
}
//求向量A,向量B构成三角形的面积
double TriArea(Vector a, Vector b)
{
return 0.5*abs(cross(a,b));
}
//求平面中任意两点的最大距离(旋转卡壳)
double RotatingCalipers(const Polygon& s)
{
Polygon l;
double dis, maxn=0.0;
int len, i, k;
l=andrewScan(s);
len=l.size();
if(len>=3)
{
for(i=0, k=2; i=cross(l[k%len]-l[i], l[k%len]-l[(i+1)%len]))
k++;
dis=max(norm(l[k%len]-l[i]), norm(l[k%len]-l[(i+1)%len]));
if(dis>maxn) maxn=dis;
}
}
else maxn=norm(l[1]-l[0]);
return maxn;
}
//三点所成的外接圆
Circle CircumscribedCircle(Point a, Point b, Point c)
{
double x=0.5*(norm(b)*c.y+norm(c)*a.y+norm(a)*b.y-norm(b)*a.y-norm(c)*b.y-norm(a)*c.y)
/(b.x*c.y+c.x*a.y+a.x*b.y-b.x*a.y-c.x*b.y-a.x*c.y);
double y=0.5*(norm(b)*a.x+norm(c)*b.x+norm(a)*c.x-norm(b)*c.x-norm(c)*a.x-norm(a)*b.x)
/(b.x*c.y+c.x*a.y+a.x*b.y-b.x*a.y-c.x*b.y-a.x*c.y);
Point O(x, y);
double r=abs(O-a);
Circle m(O, r);
return m;
}
//三点所成的内切圆
Circle InscribedCircle(Point a, Point b, Point c)
{
double A=abs(b-c), B=abs(a-c), C=abs(a-b);
double x=(A*a.x+B*b.x+C*c.x)/(A+B+C);
double y=(A*a.y+B*b.y+C*c.y)/(A+B+C);
Point O(x, y);
Line l(a, b);
double r=getDistanceLP(l, O);
Circle m(O, r);
return m;
}
//过点p求过该点的两条切线与圆的两个切点
Segment TangentLineThroughPoint(Circle m, Point p)
{
Point c=m.c;
double l=abs(c-p);
double r=m.r;
double k=(2*r*r-l*l+norm(p)-norm(c)-2*p.y*c.y+2*c.y*c.y)/(2*(p.y-c.y));
double A=1+(p.x-c.x)*(p.x-c.x)/((p.y-c.y)*(p.y-c.y));
double B=-(2*k*(p.x-c.x)/(p.y-c.y)+2*c.x);
double C=c.x*c.x+k*k-r*r;
double x1, x2, y1, y2;
x1=(-B-sqrt(B*B-4*A*C))/(2*A);
x2=(-B+sqrt(B*B-4*A*C))/(2*A);
y1=(2*r*r-l*l+norm(p)-norm(c)-2*(p.x-c.x)*x1)/(2*(p.y-c.y));
y2=(2*r*r-l*l+norm(p)-norm(c)-2*(p.x-c.x)*x2)/(2*(p.y-c.y));
Point p1(x1, y1), p2(x2, y2);
Segment L(p1, p2);
return L;
}
//极角(直线与x轴的角度)
double PolarAngle(Vector a)
{
Point p0(0.0, 0.0);
Point p1(1.0, 0.0);
Point p2(a.x, a.y);
Vector b=p1;
double ans=0;
if(ccw(p0, p1, p2)==CW) ans=180-acos(dot(a, b)/(abs(a)*abs(b)))*180/acos(-1);
else if(ccw(p0, p1, p2)==CCW) ans=acos(dot(a, b)/(abs(a)*abs(b)))*180/acos(-1);
else ans=0;
if(ans>=180) ans-=180;
if(ans<0) ans+=180;
return ans;
}
//点与圆的位置关系
int CircleContain(Circle m, Point p)
{
double r=m.r;
double l=abs(p-m.c);
if(r>l) return 2;
if(r==l) return 1;
if(r2*r)
{
printf("[]\n");
}
else if(abs(p-m)==2*r)
{
Circle c((p+m)/2, r);
printf("[(%.6f,%.6f)]\n", c.c.x, c.c.y);
}
else if(abs(p-m)c2.c.x) swap(c1, c2);
else if(c1.c.x==c2.c.x && c1.c.y>c2.c.y) swap(c1, c2);
printf("[(%.6f,%.6f),(%.6f,%.6f)]\n", c1.c.x, c1.c.y, c2.c.x, c2.c.y);
}
else if(abs(p-m)<2*r)
{
double s=abs(p-m);
double d=sqrt(r*r-(r-s)*(r-s));
Point m1, m2;
m1=(m+(l.p1-l.p2)/abs(l.p1-l.p2)*d);
m2=(m-(l.p1-l.p2)/abs(l.p1-l.p2)*d);
Circle c1(m1+(p-m)/abs(p-m)*r, r);
Circle c2(m2+(p-m)/abs(p-m)*r, r);
if(c1.c.x>c2.c.x) swap(c1, c2);
else if(c1.c.x==c2.c.x && c1.c.y>c2.c.y) swap(c1, c2);
printf("[(%.6f,%.6f),(%.6f,%.6f)]\n", c1.c.x, c1.c.y, c2.c.x, c2.c.y);
}
return ;
}
bool cmp_CircleTangentToTwoLinesWithRadius(Circle x, Circle y)
{
if(x.c.x==y.c.x) return x.c.y T;
T.push_back(c1);
T.push_back(c2);
T.push_back(c3);
T.push_back(c4);
sort(T.begin(), T.end(), cmp_CircleTangentToTwoLinesWithRadius);
printf("[(%.6f,%.6f),(%.6f,%.6f),(%.6f,%.6f),(%.6f,%.6f)]\n", T[0].c.x, T[0].c.y, T[1].c.x, T[1].c.y, T[2].c.x, T[2].c.y, T[3].c.x, T[3].c.y);
}
//求与给定两圆相切的圆
void CircleTangentToTwoDisjointCirclesWithRadius(Circle C1, Circle C2)
{
double d = abs(C1.c-C2.c);
if(dd) printf("[]\n");
else
{
double sita = angle(C2.c - C1.c);
double da = acos((C1.r*C1.r + d*d - C2.r*C2.r) / (2 * C1.r*d));
Point p1 = C1.point(sita - da), p2 = C1.point(sita + da);
if(p1.x>p2.x) swap(p1, p2);
else if(p1.x==p2.x && p1.y>p2.y) swap(p1, p2);
if (p1 == p2) printf("[(%.6f,%.6f)]\n", p1.x, p1.y);
else printf("[(%.6f,%.6f),(%.6f,%.6f)]\n", p1.x, p1.y, p2.x, p2.y);
}
}
//多边形(存储方式:点->线)
Pol Polygon_to_Pol(Polygon L)
{
Pol S;
Segment l;
for(int i=0; i+1EPS)
return a.angle>b.angle;
return ccw(b.p1, b.p2, a.p1)!=CW;
}
int intersection_of_half_planes(Pol s)
{
Segment deq[1505];
Segment l[1505];
Point p[1505];
memset(deq, 0, sizeof(deq));
memset(l, 0, sizeof(l));
memset(p, 0, sizeof(p));
sort(s.begin(), s.end(), SortAnglecmp);
int cnt=0;
for(int i=0; iEPS)
l[++cnt]=s[i];
int le=1,ri=1;
for(int i=1; i<=cnt; i++)
{
while(ri>le+1 && ccw(l[i].p1, l[i].p2, intersectL(deq[ri-1],deq[ri-2]))==CW) ri--;
while(ri>le+1 && ccw(l[i].p1, l[i].p2, intersectL(deq[le],deq[le+1]))==CW) le++;
deq[ri++]=l[i];
}
while(ri>le+2 && ccw(deq[le].p1, deq[le].p2, intersectL(deq[ri-1],deq[ri-2]))==CW) ri--;
while(ri>le+2 && ccw(deq[ri-1].p1, deq[ri-1].p2, intersectL(deq[le],deq[le+1]))==CW) le++;
//***************getArea******************
/*
if(ri<=le+2)
{
printf("0.00\n");
return 0;
}
deq[ri]=deq[le];
cnt=0;
for(int i=le; ile+2) return 1;
return 0;
}
//求最近点对的距离(分治)
//************************************************************************
bool cmpxy(Point a, Point b)
{
if(a.x != b.x) return a.x < b.x;
else return a.y < b.y;
}
bool cmpy(Point a, Point b)
{
return a.y < b.y;
}
int n;
Point closest_p[100010];//将点都存入closest_p中！
Point closest_tmpt[100010];
double Closest_Pair(int left,int right)
{
double d = INF;
if(left == right) return d;
if(left + 1 == right)
return getDistance(closest_p[left],closest_p[right]);
int mid = (left+right)/2;
double d1 = Closest_Pair(left,mid);
double d2 = Closest_Pair(mid+1,right);
d = min(d1,d2);
int k = 0;
for(int i = left; i <= right; i++)
if(fabs(closest_p[mid].x - closest_p[i].x) <= d)
closest_tmpt[k++] = closest_p[i];
sort(closest_tmpt,closest_tmpt+k,cmpy);
for(int i = 0; i
