Gym101635K Blowing Candles

题目链接：http://codeforces.com/gym/101635

题目大意：

　　推荐一篇文章：https://blog.csdn.net/wang_heng199/article/details/74477738

　　该题就是要求凸包的宽度（即平行切线间的最小距离）。

AC代码：

#include <bits/stdc++.h>

using namespace std;
const double inf = 2e9;
const double esp = 1e-8;
int sgn(double x){
    if(fabs(x)<esp) return 0;
    if(x<0) return -1;
    else    return 1;
}
struct Point{
    double x,y;
    Point (double _x=0,double _y=0){
        x=_x,y=_y;
    }
    Point operator - (const Point &b) const{
        return Point(x-b.x,y-b.y);
    }
    double operator ^ (const Point &b) const {
        return x*b.y-y*b.x;
    }
    double operator * (const Point &b) const {
        return x*b.x+y*b.y;
    }
    void input(){
        scanf("%lf%lf",&x,&y);
    }
};
double dist(Point a,Point b){
    return sqrt((a-b)*(a-b));
}
const int maxn = 2e5+5;
Point List[maxn];
int Stack[maxn],top;
bool _cmp(Point p1,Point p2){
    double tmp=(p1-List[0])^(p2-List[0]);
    if(sgn(tmp)>0)   return true;
    else if(sgn(tmp)==0 && sgn(dist(p1,List[0])-dist(p2,List[0])) <= 0)
        return true;
    else
        return false;
}
void Graham(int n){
    Point p0=List[0];
    int k=0;
    for(int i=1;i<n;i++){
        if(p0.y>List[i].y || (p0.y == List[i].y && p0.x > List[i].x)){
            p0=List[i];
            k=i;
        }
    }
    swap(List[k],List[0]);
    sort(List+1,List+n,_cmp);
    if(n==1){
        top = 1;
        Stack[0]=0;
        return;
    }
    if(n==2){
        top=2;
        Stack[0]=0,Stack[1]=1;
        return;
    }
    Stack[0]=0,Stack[1]=1;
    top=2;
    for(int i=2;i<n;i++){
        while(top>1 &&
              (sgn((List[Stack[top-1]]-List[Stack[top-2]])^(List[i]-List[Stack[top-2]]))<=0))
                top--;
        Stack[top++]=i;
    }
}
double rotating_calipers(Point p[],int n){
    double ans=inf;
    Point v;
    int cur=1;
    for(int i=0;i<n;i++){
        v=p[i]-p[(i+1)%n];
        while(sgn(v^(p[(cur+1)%n]-p[cur]))<0)
            cur=(cur+1)%n;
        ans=min(ans,
                ((p[cur]-p[(i+1)%n])^(p[i]-p[(i+1)%n]))/(dist(p[i],p[(i+1)%n])));
    }
    return ans;
}
Point p[maxn];
int main(){
    int N,R;
    scanf("%d%d",&N,&R);
    for(int i=0;i<N;i++)
        List[i].input();

    Graham(N);
    for(int i=0;i<top;i++)
        p[i]=List[Stack[i]];
    double ans=rotating_calipers(p,top);
    printf("%.16lf
",ans);
    return 0;
}