【bzoj1069】最大土地面积

#include<stdio.h>
#include<stdlib.h>
#include<iostream>
#include<string>
#include<string.h>
#include<algorithm>
#include<math.h>
#include<queue>
#include<map>
#include<vector>
#include<set>
#define il inline
#define re register
using namespace std;
typedef double db;
const int N=3001;
const db eps=1e-8;
struct P{db x,y;} a[N],s[N];
int n,top;db ans=0;
il P operator-(P a,P b){
    return (P){a.x-b.x,a.y-b.y};
} 
il db operator*(P a,P b){
    return a.x*b.y-a.y*b.x;
}
il db S(P a,P b,P c){
    return fabs((a-b)*(a-c))/2;
}
il db dis(P a){
    return a.x*a.x+a.y*a.y;
}
il db cmp(P x,P y){
    return (x-a[1])*(y-a[1])>0;
}
il void print(P a){
    printf("(%lf,%lf)\n",a.x,a.y);
}
int main(){
    scanf("%d",&n);
    for(int i=1;i<=n;i++){
        scanf("%lf%lf",&a[i].x,&a[i].y);
    }
    for(int i=1;i<=n;i++)
        if(a[i].y<a[1].y||(a[i].y==a[1].y&&a[i].x<a[1].x)) swap(a[1],a[i]);
    sort(a+2,a+n+1,cmp);
    s[1]=a[1];s[2]=a[2];top=2;
    for(int i=3;i<=n;i++){
        while(top>1&&(a[i]-s[top-1])*(s[top]-s[top-1])>=0) top--;
        s[++top]=a[i];
    } 
    if(top==4){
        ans=S(s[1],s[2],s[3])+S(s[1],s[3],s[4]);
        printf("%.3lf",ans);
        return 0;
    }
//    for(int i=1;i<=top;i++) print(s[i]);
    for(int i=0;i<top;i++) s[i]=s[i+1];
    n=top;
    for(int i=0;i<n;i++){
        for(int j=(i+1)%n,k=(i+2)%n,l=(i+3)%n;k!=(i-2+n)%n;k=(k+1)%n){
            while(S(s[i],s[j],s[k])<S(s[i],s[(j+1)%n],s[k])) j=(j+1)%n;
            while(S(s[i],s[l],s[k])<S(s[i],s[(l+1)%n],s[k])) l=(l+1)%n;
        //    cout<<i<<" "<<j<<" "<<k<<" "<<l<<endl;
            ans=max(S(s[i],s[j],s[k])+S(s[i],s[k],s[l]),ans);
        }
    }
    printf("%.3lf",ans);
    return 0;
}