BZOJ 1069: [SCOI2007]最大土地面积(旋转卡壳）

题目链接~ 

1069: [SCOI2007]最大土地面积

思路很简单，极角排序求完凸包后，在凸包上枚举对角线，然后两边分别来两个点旋转卡壳一下，搞定！

不过计算几何的题目就是这样，程序中间的处理还是比较麻烦的，写的时候要很小心，特别是存点和枚举的时候要注意是个循环。

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<cmath>
#include<algorithm>

#define For(i,a,b) for(register int i=a;i<=b;++i)
#define Dwn(i,a,b) for(register int i=a;i>=b;--i)
#define Re register

using namespace std;

const int N=2005;

struct P{
    double x,y;
}st[N],O,p[N];
int n,top=-1;

P operator -(P a,P b){
    P t; t.x=a.x-b.x; t.y=a.y-b.y; return t;
}
double operator *(P a,P b){
    return a.x*b.y-b.x*a.y;
} 
double Dis(P a,P b){
    return sqrt( (a.x-b.x)*(a.x-b.x) + (a.y-b.y)*(a.y-b.y) );
}
int Xx(P a){
    if(a.x-O.x>0 &&a.y-O.y>=0)return 1;
    if(a.x-O.x<=0&&a.y-O.y>0 )return 2;
    if(a.x-O.x<0 &&a.y-O.y<=0)return 3;
    if(a.x-O.x>=0&&a.y-O.y<0 )return 4;
}
bool cmp(const P a,const P b){
    int aX=Xx(a);
    int bX=Xx(b);
    if(aX!=bX)return aX<bX;
    double cx= (a-O)*(b-O);
    if(cx==0)return a.x<b.x;
    else return cx>0;
}
bool cmpY(const P a,const P b){
    return a.y<b.y;
}

void TuBao(){
    st[++top]=p[1];
    st[++top]=p[2];
    For(i,3,n+1){
        while( (p[i]-st[top-1])*(st[top]-st[top-1])>=0 ) top--;
        st[++top]=p[i];
    }
}

double ans=0;
void SpinStir(){
    P p1,p2;
    int i1,i2;
    For(x,0,top-1){
        i1=(x+3)%top; p1=st[i1];
        i2=(x+1)%top; p2=st[i2];
        For(y,x+2,top-1){
            int Ni; P Np;
            
            Ni=(i1+1)%top; 
            Np=st[Ni];
            while(Ni!=x&&(Np-st[y])*(st[x]-st[y])>(p1-st[y])*(st[x]-st[y])){
                i1=Ni; p1=Np;     Ni=(i1+1)%top; Np=st[Ni];
            } 
            
            Ni=(i2+1)%top;
            Np=st[Ni];
            while(Ni!=y&&(Np-st[x])*(st[y]-st[x])>(p2-st[x])*(st[y]-st[x])){
                i2=Ni; p2=Np;    Ni=(i2+1)%top; Np=st[Ni];
            }
             
            double Sm=(p1-st[y])*(st[x]-st[y])/2 + (p2-st[x])*(st[y]-st[x])/2;
            ans=max(ans,Sm);
        }
    }
}

int main(){
    //freopen("ex.in","r",stdin);
    
    scanf("%d",&n);
    For(i,1,n){
        scanf("%lf%lf",&p[i].x,&p[i].y);
    }
    sort(p+1,p+n+1,cmpY);
    O=p[1];
    sort(p+2,p+n+1,cmp);
    p[n+1]=p[1]; 
    TuBao(); 
    SpinStir();
    printf("%.03lf",ans);
    return 0;
    
}