[计算几何]离大海的最远点在哪里

#include<iostream>
#include<cstdio>
#include<cmath>
#include<queue>
#define eps 1e-9
#define ld long double
#define MAXN 200000
#define pa pair<ld,int> 
#define mp(x,y) make_pair(x,y)
using namespace std;
//********************
struct P{
    ld x,y;
    P(ld _x=0,ld _y=0):x(_x),y(_y){}
}s[MAXN+5];
struct L{P u,v;}l[MAXN+5];
P operator+(P x,P y){return P(x.x+y.x,x.y+y.y);}
P operator-(P x,P y){return P(x.x-y.x,x.y-y.y);}
ld operator*(P x,P y){return x.x*y.y-y.x*x.y;}
P operator/(P x,ld y){return P(x.x/y,x.y/y);}
P operator*(P x,ld y){return P(x.x*y,x.y*y);}
ld dot(P x,P y){return x.x*y.x+x.y*y.y;}
ld dis(P x){return sqrt(x.x*x.x+x.y*x.y);}
P operator*(L a,L b){return a.u+a.v*(b.v*(a.u-b.u)/(a.v*b.v));}
//********************
int n,ne[MAXN+5],la[MAXN+5];
priority_queue<pa > q;
bool mark[MAXN+5];
 
L solve(L a,L b){return (L){a*b,a.v*dis(b.v)-b.v*dis(a.v)};}
 
ld calc(int x)
{
    P p=solve(l[la[x]],l[x])*solve(l[x],l[ne[x]]);
    //cout<<"calc"<<x<<" "<<-fabs(p*l[x].v/dis(l[x].v))<<endl;
    return -fabs((l[x].v*(p-l[x].u))/dis(l[x].v));
}
 
int main()
{
    scanf("%d",&n);
    for(int i=1;i<=n;i++)scanf("%Lf%Lf",&s[i].x,&s[i].y);
    for(int i=1;i<=n;i++)ne[i-1]=i,la[i]=i-1;
    la[1]=n,ne[n]=1;
    for(int i=1;i<=n;i++)l[i]=(L){s[i],s[i]-s[la[i]]};
    for(int i=1;i<=n;i++)q.push(mp(calc(i),i));
    for(int i=2;i<n;i++)
    {
        while(!q.empty()&&mark[q.top().second])q.pop();
        int x=q.top().second;mark[x]=1;
        la[ne[x]]=la[x];ne[la[x]]=ne[x];
        q.push(mp(calc(la[x]),la[x]));
        q.push(mp(calc(ne[x]),ne[x]));
    }
    printf("%0.8Lf",-q.top().first);
    return 0;
}