[SCOI2007]最大土地面积

Posted 2021-02-08 skip1978

凸包,

#include<cstdio>
#include<algorithm>
#include<iostream>
#include<cmath>
typedef long double ld;
const int maxn = 100100;
int n;
struct T{
    ld x,y;
    inline T(ld a=0,ld b=0){x=a,y=b;}
    inline T& operator += (const T&b){x+=b.x,y+=b.y;return *this;}
    inline T& operator += (const ld&b){x+=b,y+=b;return *this;}
    inline T& operator -= (const T&b){x-=b.x,y-=b.y;return *this;}
    inline T& operator -= (const ld&b){x-=b,y-=b;return *this;}
    inline T& operator *= (const ld&b){x*=b,y*=b;return *this;}
    inline T& operator /= (const ld&b){x/=b,y/=b;return *this;}
    inline T operator + (const T&b)const{return T(x+b.x,y+b.y);}
    inline T operator - (const T&b)const{return T(x-b.x,y-b.y);}
    inline T operator / (const ld&b)const{return T(x/b,y/b);}
    inline T operator * (const ld&b)const{return T(x*b,y*b);}
}a[maxn];
inline ld cross(T a,T b){return a.x*b.y-a.y*b.x;}
inline ld cross(T a,T b,T c){return cross(b-a,c-a);}
const auto cmp = [](T a,T b){
    ld res=cross(a,b);
    return res!=0?res<0:a.x<b.x;
};
T st[maxn];
int top;
inline void up(ld&a,ld b){if(a<b)a=b;}
int main(){
    std::ios::sync_with_stdio(false),std::cin.tie(0);
    std::cin >> n;
    int mn=1;
    for(int i=1;i<=n;++i){
        std::cin >> a[i].x >> a[i].y;
        if(a[i].y<a[mn].y||a[i].y==a[mn].y&&a[i].x<a[mn].x)mn=i;
    }
    std::swap(a[mn],a[1]);
    T p = a[mn];
    for(int i=1;i<=n;++i)a[i]-=p;
    std::sort(a+2,a+n+1,cmp);
    for(int i=1;i<=n;++i){
        st[++top]=a[i];
        while(top>2&&cross(st[top-2],st[top-1],st[top])>=0)st[--top]=a[i];
    }
    ld ans=fabs(cross(st[1],st[2],st[3]))/2;
    for(int a=1;a<=top;++a){
        for(int c=a+2,b=a+1,d=c%top+1;d!=a&&c<=top;++c){
            while(cross(st[a],st[c],st[b%top+1])>cross(st[a],st[c],st[b]) && b%top+1 != c)b=b%top+1;
            while(cross(st[a],st[c],st[d%top+1])<cross(st[a],st[c],st[d]) && d%top+1 != a)d=d%top+1;
            up(ans,fabsl(cross(st[a],st[c],st[b])+fabsl(cross(st[a],st[c],st[d]))));
        }
    }
    printf("%.3Lf",ans/2);
}