K - Blowing Candles

Posted 2020-11-02 jadelemon

凸包 + 旋转卡壳 模本

 

c++ code:

#include <bits/stdc++.h>

using namespace std;
const int N=3e5+7;

struct point{
    double x, y;
    point(){}
    point(double x, double y) : x(x), y(y) {}
    friend point operator + (const point &a, const point &b){
        return point(a.x + b.x, a.y + b.y);
    }
    friend point operator - (const point &a, const point &b){
        return point(a.x - b.x, a.y - b.y);
    }
    friend point operator * (const point &a, const double &b){
        return point(a.x * b, a.y * b);
    }
    friend point operator / (const point &a, const double &b){
        return point(a.x / b, a.y / b);
    }
    friend bool operator == (const point &a, const point &b){
        return a.x == b.x && a.y == b.y;
    }
};
double r;
double dis(point a,point b)
{
    return sqrt((a.x-b.x)*(a.x-b.x)*1.0+(a.y-b.y)*(a.y-b.y));
}
double cross(point a,point b,point c) //计算叉乘
{
    return (c.x - a.x) * (b.y - a.y) - (b.x - a.x) * (c.y - a.y);
}
double  det(point a, point b)
{
    return a.x * b.y - a.y * b.x;
}
double dot(point a, point b)
{
    return a.x * b.x + a.y * b.y;
}
struct polygon_convex
{
    vector<point> p;
    polygon_convex(int size = 0){
        p.resize(size);
    }
};
bool comp_less(const point &a, const point &b)
{
    return a.x - b.x < 0 || a.x - b.x == 0 && a.y - b.y < 0;
}
polygon_convex convex_hull(vector<point> a)
{
    polygon_convex res(2 * a.size() + 5);
    sort(a.begin(), a.end(), comp_less);
    a.erase(unique(a.begin(), a.end()), a.end());
    int m = 0;
    for(int i = 0; i < a.size(); i ++){
        while(m > 1 && det(res.p[m - 1] - res.p[m - 2], a[i] - res.p[m - 2]) <= 0) -- m;
        res.p[m ++] = a[i];
    }
    int k = m;
    for(int i = int(a.size()) - 2; i >= 0; i --){
        while(m > k && det(res.p[m - 1] - res.p[m - 2], a[i] - res.p[m - 2]) <= 0) -- m;
        res.p[m ++] = a[i];
    }
    res.p.resize(m);
    if(a.size() > 1) res.p.resize(m - 1);
    return res;
}
polygon_convex a;
point p[N];
double rotating_caliper(point *p,int n)
{
     int j=1;
     r=2*r;
     p[n]=p[0];
     for (int i=0;i<n;i++)
     {
         while (cross(p[i],p[i+1],p[j+1])-cross(p[i],p[i+1],p[j])<=0)
            j=(j+1)%n;
        r=min(r,fabs(cross(p[i],p[i+1],p[j]))/dis(p[i],p[i+1]));
    }
    return r;
}
int main()
{
    int n;
    scanf("%d%lf",&n,&r);
    point node;
    for(int i=0;i<n;i++)
    {
        scanf("%lf%lf",&node.x,&node.y);
        a.p.push_back(node);
    }
    a=convex_hull(a.p);
    n=a.p.size();
    for(int i=0;i<n;i++)
        p[i]=a.p[i];
    if(n<=2)
        printf("0.000000000000\n");
    else
        printf("%.12lf\n",rotating_caliper(p,n));
    return 0;
}