BZOJ 1069 Luogu P4166 最大土地面积 (凸包)

题目链接: (bzoj)https://www.lydsy.com/JudgeOnline/problem.php?id=1069

(luogu)https://www.luogu.org/problemnew/show/P4166

题解: 水题，凸包极角排序之后枚举凸四边形对角线(i,j)然后找面积最大的点(k)，(k)随着(i,j)是单调的

但是有个易错点，就是双指针那个(k)前移的条件必须是前移后大于等于原来，如果写成大于就只有50(详见代码)

查了半天发现原因居然是: 数据里有重点! 一旦有重点就会出现(k)一直在重点处进不动的情况。呜呜呜好坑啊

代码

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cassert>
#include<algorithm>
#include<cmath>
using namespace std;
 
const double EPS = 1e-8;
int dcmp(double x) {return x<-EPS ? -1 : (x>EPS ? 1 : 0);}
struct Point
{
    double x,y;
    Point() {}
    Point(double _x,double _y) {x = _x,y = _y;}
};
bool cmpy(Point x,Point y) {return dcmp(x.y-y.y)<0 || (dcmp(x.y-y.y)==0 && dcmp(x.x-y.x)<0);}
bool cmpx(Point x,Point y) {return dcmp(x.x-y.x)<0 || (dcmp(x.x-y.x)==0 && dcmp(x.y-y.y)<0);}
typedef Point Vector;
Point operator +(Point x,Point y) {return Point(x.x+y.x,x.y+y.y);}
Point operator -(Point x,Point y) {return Point(x.x-y.x,x.y-y.y);}
Point operator *(Point x,double y) {return Point(x.x*y,x.y*y);}
Point operator /(Point x,double y) {return Point(x.x/y,x.y/y);}
double Dot(Vector x,Vector y) {return x.x*y.x+x.y*y.y;}
double Cross(Vector x,Vector y) {return x.x*y.y-x.y*y.x;}
double EuclidDist(Point x,Point y) {return sqrt((x.x-y.x)*(x.x-y.x)+(x.y-y.y)*(x.y-y.y));}
Vector rotate(Vector x,double ang) {return Vector(x.x*cos(ang)-x.y*sin(ang),x.x*sin(ang)+x.y*cos(ang));}
const int N = 2000;
Point a[N+3];
Point ch[(N<<1)+3];
int stk[N+3];
double area[N+3][N+3];
int n,tp;
 
bool cmp(Point x,Point y) {return dcmp(Cross(x-a[1],y-a[1]))>0;}
 
void Convex_Hull()
{
    for(int i=2; i<=n; i++)
    {
        if(cmpy(a[i],a[1])==true) {swap(a[i],a[1]);}
    }
    sort(a+2,a+n+1,cmp);
    stk[1] = 1; stk[2] = 2; tp = 2;
    for(int i=3; i<=n; i++)
    {
        while(dcmp(Cross(a[i]-a[stk[tp-1]],a[stk[tp]]-a[stk[tp-1]]))>0) {tp--;}
        tp++; stk[tp] = i;
    }
    for(int i=1; i<=tp; i++) ch[i] = a[stk[i]];
    for(int i=1; i<=tp; i++) ch[i+tp] = ch[i];
//  printf("chsize=%d
",tp);
//  for(int i=1; i<=tp; i++) printf("(%lf %lf)
",ch[i].x,ch[i].y);
}
 
int main()
{
    scanf("%d",&n); for(int i=1; i<=n; i++) scanf("%lf%lf",&a[i].x,&a[i].y);
    Convex_Hull();
    if(tp==3)
    {
        double ans = fabs(Cross(ch[2]-ch[1],ch[3]-ch[1]))/2.0,ans2 = 1e11;
        for(int i=1; i<=n; i++)
        {
            if(i==stk[1]||i==stk[2]||i==stk[3]) continue;
            double cur = min(min(fabs(Cross(a[i]-ch[1],ch[2]-ch[1])),fabs(Cross(a[i]-ch[2],ch[3]-ch[2]))),fabs(Cross(a[i]-ch[3],ch[1]-ch[3])))/2.0;
            ans2 = min(ans2,cur);
        }
        printf("%lf
",ans-ans2);
        return 0;
    }
    double ans = 0.0;
    for(int i=1; i<=tp; i++)
    {
        int k = i+1;
        for(int j=i+2; j<=i+tp-2; j++)
        {
            while(k+1<j && dcmp(Cross(ch[k+1]-ch[i],ch[j]-ch[i])-Cross(ch[k]-ch[i],ch[j]-ch[i]))>=0) {k++;}
            area[i][(j-1)%tp+1] = Cross(ch[k]-ch[i],ch[j]-ch[i])/2.0;
//          printf("i%d j%d k%d %lf
",i,j,k,area[j]);
        }
    }
    for(int i=1; i<=tp; i++)
    {
        for(int j=i+2; j<=tp; j++)
        {
            double tmp = area[i][j]+area[j][i];
//          printf("area[%d][%d]=%lf
",i,j,area[i][j]);
//          printf("area[%d][%d]=%lf
",j,i,area[j][i]);
            ans = max(ans,tmp);
        }
    }
    printf("%.3lf
",ans);
    return 0;
}