Largest Triangle （凸包+旋转卡壳求最大三角形）

Largest Triangle 

题意：在二维坐标中给出(n)个点，在这些点中挑(3)个点能组成的面积最大的三角形的面积

AC_Code:

#include <iostream>
#include <cstdio>
#include <cmath>
#include <string>
#include <algorithm>
#include <cstring>
using namespace std;
typedef long long ll;
const int maxn = 5e4+10;
const double eps = 1e-8;


typedef struct Point{
    double x,y;
    Point(double x=0,double y=0):x(x),y(y){}
}Vector;

Vector operator + (const Vector &A, const Vector &B){ return Vector(A.x+B.x,A.y+B.y); }
Vector operator - (const Vector &A, const Vector &B){ return Vector(A.x-B.x,A.y-B.y); }
Vector operator * (const Vector &A, double p){ return Vector(A.x*p,A.y*p); }
Vector operator / (const Vector &A, double p){ return Vector(A.x/p,A.y/p); }

bool operator <(const Point &A,const Point &B){
    return A.x<B.x || (A.x==B.x && A.y<B.y);
}

int dcmp(double x){
    if( fabs(x)<eps ) return 0;
    return x<0 ? -1 : 1;
}

double Cross(const Vector &A, const Vector &B){
    return A.x*B.y-A.y*B.x;
}

double Dot(const Vector &A, const Vector &B){
    return A.x*B.x+A.y*B.y;
}

double Length(const Vector &A){
    return Dot(A,A);
}

double Area2(const Point &A, const Point &B, const Point &C){
    return Cross(B-A,C-A);
}

int ConvexHull(Point *p,int n,Point *ch){
    sort(p,p+n);
    int m=0;
    for(int i=0;i<n;i++){
        while( m>1 && dcmp(Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2]))<=0 ) m--;
        ch[m++]=p[i];
    }
    int k=m;
    for(int i=n-2;i>=0;i--){
        while( m>k && dcmp(Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2]))<=0) m--;
        ch[m++]=p[i];
    }
    if( n>1 ) m--;
    return m;
}

Point p[maxn],ans[maxn];

double RotatingCaliper(int m, Point *ch){
    if( m<=2 ) return 0;
    if( m==3 ) return fabs( Cross(ch[1]-ch[0], ch[2]-ch[0]) )*0.5;
    double ans = 0.0;
    int i,j,k;
    for(i=0;i<m;i++){
        j=(i+1)%m; k=(j+1)%m;
        while( fabs( Area2(ch[i],ch[j],ch[k]) ) < fabs( Area2(ch[i],ch[j],ch[(k+1)%m]) ) ) k=(k+1)%m;

        while( i!=j && k!=i ){
            ans = max(ans, fabs( Area2(ch[i],ch[j],ch[k]) ));
            while( fabs( Area2(ch[i],ch[j],ch[k]) ) < fabs( Area2(ch[i],ch[j],ch[(k+1)%m]) ) ) k=(k+1)%m;
            j=(j+1)%m;
        }
    }
    return ans*0.5;
}

int main()
{
    int n;
    while( ~scanf("%d",&n) ){
        for(int i=0;i<n;i++){
            double x,y; scanf("%lf%lf",&x,&y);
            p[i] = Point(x,y);
        }
        int cnt = ConvexHull(p,n,ans);
        double res = RotatingCaliper(cnt,ans);
        printf("%.7f
",res);
    }
    return 0;
}