Gym - 101673:B Craters (几何，求凸包)

题意：给定几个圆，求最短的围合，把这几个包围起来，而且到圆的距离都不小于10.

思路：把每个圆的半径+10，边等分5000份，然后求凸包即可。

#include<bits/stdc++.h>
using namespace std;
#define mp make_pair
typedef long long ll;
const double inf=1e200;
const double eps=1e-;
const double pi=*atan(1.0);
int dcmp(double x){ return fabs(x)<eps?:(x<?-:);}
struct point{
    double x,y;
    point(double a=,double b=):x(a),y(b){}
};
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);}
point rotate(point A,double rad){
    return point(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));
}
bool operator ==(const point& a,const point& b) {
     return dcmp(a.x-b.x)==&&dcmp(a.y-b.y)==;
}
double dot(point A,point B){ return A.x*B.x+A.y*B.y;}
double det(point A,point B){ return A.x*B.y-A.y*B.x;}
double det(point O,point A,point B){ return det(A-O,B-O);}
double length(point A){ return sqrt(dot(A,A));}
double angle(point A,point B){ return acos(dot(A,B)/length(A)/length(B));}
double area(vector<point>p){
    double ans=; int sz=p.size();
    for(int i=;i<sz-;i++) ans+=det(p[i]-p[],p[i+]-p[]);
    return ans/2.0;
}
double seg(point O,point A,point B){
    if(dcmp(B.x-A.x)==) return (O.y-A.y)/(B.y-A.y);
    return (O.x-A.x)/(B.x-A.x);
}

pair<double,int>s[*];
double polyunion(vector<point>*p,int N){ //有多个才加*
    double res=;
    for(int i=;i<N;i++){
        int sz=p[i].size();
        for(int j=;j<sz;j++){
            int m=;
            s[++m]=mp(,);
            s[++m]=mp(,);
            point a=p[i][j],b=p[i][(j+)%sz];
            for(int k=;k<N;k++){
                if(i!=k){
                    int sz2=p[k].size();
                    for(int ii=;ii<sz2;ii++){
                        point c=p[k][ii],d=p[k][(ii+)%sz2];
                        int c1=dcmp(det(b-a,c-a));
                        int c2=dcmp(det(b-a,d-a));
                        if(c1==&&c2==){
                            if(dcmp(dot(b-a,d-c))){
                                s[++m]=mp(seg(c,a,b),);
                                s[++m]=mp(seg(c,a,b),-);
                            }
                        }
                        else{
                            double s1=det(d-c,a-c);
                            double s2=det(d-c,b-c);
                            if(c1>=&&c2<) s[++m]=mp(s1/(s1-s2),);
                            else if(c1<&&c2>=) s[++m]=mp(s1/(s1-s2),-);
                        }
                    }
                }
            }
            sort(s+,s+m+);
            double pre=min(max(s[].first,0.0),1.0),now,sum=;
            int cov=s[].second;
            for(int j=;j<=m;j++){
                now=min(max(s[j].first,0.0),1.0);
                if(!cov) sum+=now-pre;
                cov+=s[j].second;
                pre=now;
            }
            res+=det(a,b)*sum;
        }
    }
    return res/;
}
bool cmp(point a,point b){ return a.x==b.x?a.y<b.y:a.x<b.x; }
void convexhull(point *a,int n,point *ch,int &top)
{
    sort(a+,a+n+,cmp);
    top=;
    for(int i=;i<=n;i++){
        while(top>=&&det(ch[top-],ch[top],a[i])<=) top--;
        ch[++top]=a[i];
    }
    int ttop=top;
    for(int i=n-;i>=;i--){
        while(top>ttop&&det(ch[top-],ch[top],a[i])<=) top--;
        ch[++top]=a[i];
    }
}
point ch[],p[]; vector<point>pp[];
int main()
{
    int N,i,j,tot=,top; double ans,one=pi/,x,y,r;
    scanf("%d",&N);
    for(i=;i<=N;i++){
        scanf("%lf%lf%lf",&x,&y,&r); r+=;
        for(j=;j<=;j++){
            tot++; p[tot].x=x+r*cos(one*j); p[tot].y=y+r*sin(one*j);
        }
    }
    convexhull(p,tot,ch,top);
    for(i=;i<top;i++) ans+=length(ch[i]-ch[i+]);
    printf("%.10lf\n",ans);
    return ;
}