旋转卡壳部分模板

凸包直径

旋转卡壳凸包直径详解

//计算凸包直径，输入凸包ch，顶点个数为n，按逆时针排列，输出直径的平方

int rotating_calipers(int n)

{

    int q = 1;

    int ans = 0;

    ch[n] = ch[0];

    for(int i = 0 ; i < n;  i++)

    {

        while(mul(ch[i+1],ch[q+1],ch[i])>mul(ch[i+1],ch[q],ch[i]))//枚举凸包一条边并扫描其它点，通过计算三角形面积的方法找到最远的点

        q = (q+1)%n;

        ans = max(ans,max(dis(ch[i]-ch[q]),dis(ch[i+1]-ch[q+1])));

    }    

    return ans;

}

 凸包间最小距离

struct Point

{

    double x,y;

    Point(double x=0,double y=0):x(x),y(y) {} //构造函数 方便代码编写

}p[N],q[N];

typedef Point pointt;

pointt operator + (Point a,Point b)

{

    return Point(a.x+b.x,a.y+b.y);

}

pointt operator - (Point a,Point b)

{

    return Point(a.x-b.x,a.y-b.y);

}

int dcmp(double x)

{

    if(fabs(x)<eps) return 0;

    else return x<0?-1:1;

}

bool operator == (const Point &a,const Point &b)

{

    return dcmp(a.x-b.x)==0&&dcmp(a.y-b.y)==0;

}

double dot(Point a,Point b)

{

    return a.x*b.x+a.y*b.y;

}

double  dis(Point a)

{

    return sqrt(dot(a,a));

}

double cross(Point a,Point b)

{

    return a.x*b.y-a.y*b.x;

}

void anticlock(Point p[],int n)//逆时针排序

{

    for(int i = 0 ; i < n-2 ; i++)

    {

        double k = cross(p[i+1]-p[0],p[i+2]-p[0]);

        if(dcmp(k)>0) return ;

        else if(dcmp(k)<0)

        {

            reverse(p,p+n);

            return ;

        }

    }

}

double distoline(Point a,Point b,Point c)//点到线段ab的最短距离

{

    if(dcmp(dis(a-b))==0) return dis(a-c);

    if(dcmp(dot(a-b,a-c))<0) return dis(a-c);

    if(dcmp(dot(b-a,b-c))<0) return dis(b-c);

    return fabs(cross(a-b,a-c))/dis(a-b);

}

double dist(Point a,Point b,Point c,Point d)//线段ab和cd间的最短距离

{

    double ans = distoline(a,b,c);

    ans = min(ans,distoline(a,b,d));

    ans = min(ans,distoline(c,d,a));

    ans = min(ans,distoline(c,d,b));

    return ans;

}

double mul(Point a,Point b,Point c)

{

    return cross(b-a,c-a);

}

double  solve(Point p[],int n,Point q[],int m)

{

    int i;

    int miny = 0,maxy = 0;

    for(i = 0;i < n; i++)

    {

        if(p[i].y<p[miny].y)

        miny = i;

    }

    for(i =0 ; i< m ; i++)

    if(q[i].y>q[maxy].y) maxy = i;

    double ans = dis(p[miny]-q[maxy]);

    for(i = 0 ;i < n; i++)

    {

        double tmp;

        while(tmp = mul(p[miny],p[miny+1],q[maxy+1])-mul(p[miny],p[miny+1],q[maxy])>eps)

        maxy = (maxy+1)%m;

        if(dcmp(tmp)>0) ans = min(ans,distoline(p[miny],p[miny+1],q[maxy]));

        else

        ans = min(ans,dist(p[miny],p[miny+1],q[maxy],q[maxy+1]));//边-边

        miny = (miny+1)%n;

    }

    return ans;

}