最大空凸包模板

Posted 2020-10-14 啦啦啦天啦噜

inline double sgn(double x, double y)
{
    return fabs(x-y)<eps;
}

inline int sgn(int x, int y)
{
    return x==y;
}

struct point
{
    double x,y;
};

double cross(point a, point b, point o)
{
    return (a.x-o.x)*(o.y-b.y)-(a.y-o.y)*(o.x-b.x);
}

double dist(point a, point b)
{
    return (a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y);
}
point o;

bool cmp_angle(point a,point b)
{
    if(sgn(cross(a,b,o),0.0))
    {
        return dist(a,o)<dist(b,o);
    }
    return cross(a,o,b)>0;
}

double empty_convex(point p[], int pn)
{
    double ans=0;
    memset(dp,0,sizeof(dp));

    for(int i=0; i<pn; i++)
    {
        int j = i-1;
        while(j>=0 && sgn(cross(p[i], p[j], o),0.0)) j--;//coline

        bool flag= j==i-1;

        while(j>=0)
        {
            int k = j-1;
            while(k >= 0 && cross(p[i],p[k],p[j])>0) k--;
            double area = fabs(cross(p[i],p[j],o))/2;
            if(k >= 0)area+=dp[j][k];
            if(flag) dp[i][j]=area;
            ans=max(ans,area);
            j=k;
        }
        if(flag)
        {
            for(int j=1; j<i; j++)
            {
                dp[i][j] = max(dp[i][j],dp[i][j-1]);
            }
        }
    }
    return ans;
}

double largest_empty_convex(point p[], int pn)
{
    point data[maxn];
    double ans=0;
    for(int i=0; i<pn; i++)
    {
        o=p[i];
        int dn=0;
        for(int j=0; j<pn; j++)
        {
            if(p[j].y>o.y||(p[j].y==o.y&&p[j].x>=o.x))
            {
                data[dn++]=p[j];
            }
        }
        sort(data, data+dn, cmp_angle);
        ans=max(ans, empty_convex(data, dn));
    }
    return ans;
}