凸包内最大三角形

凸包内最大三角形

#define ld double
const ld eps = 1e-9;
const ld PI =acos(-1);
const int N = 2e5 + 50;

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

struct Point {
	double x,y;
	Point(double _x=0,double _y=0) {
		x=_x,y=_y;
	}
	Point operator +(const Point &b)const {
		return Point(x+b.x,y+b.y);
	}
	Point operator -(const Point &b)const {
		return Point(x-b.x,y-b.y);
	}
	double operator ^(const Point &b)const {
		return x*b.y-y*b.x;
	}
	double operator *(const Point &b)const {
		return x*b.x+y*b.y;
	}
	bool operator == (Point b)const {
		return sgn(x-b.x)==0&& sgn(y-b.y)==0;
	}

	bool operator <(Point b)const {
		return sgn(x-b.x)==0?sgn(y-b.y)<0:x<b.x;
	}
	double distance(Point p) {
		return hypot(x-p.x,y-p.y);
	}
	void input() {
		scanf("%lf%lf",&x,&y);
	}
};

int id1,id2,id3;
int n;
Point p[N],list[N];


struct polygon {
	int n;
	Point p[N];
	void input(int _n) {
		n = _n;
		for(int i=0; i<n; i++) {
			p[i].input();
		}
	}
};

polygon vv;

struct cmp {
	Point p;
	cmp(const Point &p0) {
		p = p0;
	}
	bool operator()(const Point &aa,const Point &bb) {
		Point a = aa,b = bb;
		int d = sgn((a-p)^(b-p));
		if(d == 0)return sgn(a.distance(p)-b.distance(p))<0;
		return d > 0;
	}
};
void norm() {
	Point mi= p[0];
	for(int i=1; i<n; i++)mi=min(mi,p[i]);
	sort(p,p+n,cmp(mi));
}

void Graham(polygon &convex) {
	norm();
	int &top=convex.n;
	top = 0;
	if(n == 1) {
		top=1;
		convex.p[0] = p[0];
		return ;
	}
	if(n == 2) {
		top=2;
		convex.p[0] = p[0];
		convex.p[1] = p[1];
		if(convex.p[0] == convex.p[1])top--;
		return ;
	}

	convex.p[0] = p[0];
	convex.p[1] = p[1];
	top = 2;

	for(int i=2; i<n; i++) {
		while(top>1&& sgn((convex.p[top-1]-convex.p[top-2])^(p[i]-convex.p[top-2])) <=0)top--;
		convex.p[top++] = p[i];
	}
	if(convex.n == 2 && (convex.p[0]==convex.p[1]))convex.n--;
}

Point p1,p2,p3;

/******凸包内最大三角形*****/
double rotating(Point p[],int n) {
	double ans = 0;
	Point v;
	for(int i=0; i<n; i++) {
		int j=(i+1)%n;
		int k=(j+1)%n;
		while(j!=i&&k!=i) {
			double res = fabs((p[i]-p[j])^(p[k]-p[i]));
			if(res > ans) {
				ans = res;
//				p1=p[i],p2=p[j],p3=p[k];
			}
			while(((p[i]-p[j])^(p[(k+1)%n]-p[k])) < 0) k=(k+1)%n;
			j=(j+1)%n;
		}
	}
	return ans/2.0;
}

void work() {
	scanf("%d",&n);
	vv.n = n;
	for(int i=0; i<n; i++) {
		p[i].input();
		vv.p[i] = p[i];
	}
	Graham(vv);
	double ans = rotating(vv.p,vv.n);

}