poj2187（未完、有错）

凸包求直径（socalled。。）

采用Graham+Rotating_Calipers，Graham复杂度nlogn，RC算法复杂度n，所以时间复杂度不会很高。

学习RC算法，可到http://cgm.cs.mcgill.ca/~orm/rotcal.frame.html。

另：http://www.cppblog.com/staryjy/archive/2009/11/19/101412.html

另外，Graham的过程即将整理。。

 

#include <iostream>
#include <math.h>
#include <algorithm>

using namespace std;

#define eps 1e-8
#define zero(x) (((x)>0?(x):-(x))<eps)
struct point{ double x, y; }p[50005],convex[50005];

//计算cross product (P1-P0)x(P2-P0)
double xmult(point p1, point p2, point p0){
	return (p1.x - p0.x)*(p2.y - p0.y) - (p2.x - p0.x)*(p1.y - p0.y);
}
int dist2(point a, point b)
{
	return (a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y);
}
//graham算法顺时针构造包含所有共线点的凸包,O(nlogn)
point p1, p2;
int graham_cp(const void* a, const void* b){
	double ret = xmult(*((point*) a), *((point*) b), p1);
	return zero(ret) ? (xmult(*((point*) a), *((point*) b), p2) > 0 ? 1 : -1) : (ret > 0 ? 1 : -1);
}
void _graham(int n, point* p, int& s, point* ch){
	int i, k = 0;
	for (p1 = p2 = p[0], i = 1; i<n; p2.x += p[i].x, p2.y += p[i].y, i++)
		if (p1.y - p[i].y>eps || (zero(p1.y - p[i].y) && p1.x > p[i].x))
			p1 = p[k = i];
	p2.x /= n, p2.y /= n;
	p[k] = p[0], p[0] = p1;
	qsort(p + 1, n - 1, sizeof(point), graham_cp);
	for (ch[0] = p[0], ch[1] = p[1], ch[2] = p[2], s = i = 3; i < n; ch[s++] = p[i++])
		for (; s>2 && xmult(ch[s - 2], p[i], ch[s - 1]) < -eps; s--);
}

int wipesame_cp(const void *a, const void *b)
{
	if ((*(point *) a).y < (*(point *) b).y - eps) return -1;
	else if ((*(point *) a).y > (*(point *) b).y + eps) return 1;
	else if ((*(point *) a).x < (*(point *) b).x - eps) return -1;
	else if ((*(point *) a).x > (*(point *) b).x + eps) return 1;
	else return 0;
}

int _wipesame(point * p, int n)
{
	int i, k;
	qsort(p, n, sizeof(point), wipesame_cp);
	for (k = i = 1; i < n; i++)
		if (wipesame_cp(p + i, p + i - 1) != 0) p[k++] = p[i];
	return k;
}

//构造凸包接口函数,传入原始点集大小n,点集p(p原有顺序被打乱!)
//返回凸包大小,凸包的点在convex中
//参数maxsize为1包含共线点,为0不包含共线点,缺省为1
//参数clockwise为1顺时针构造,为0逆时针构造,缺省为1
//在输入仅有若干共线点时算法不稳定,可能有此类情况请另行处理!
int graham(int n, point* p, point* convex, int maxsize = 1, int dir = 1){
	point* temp = new point[n];
	int s, i;
	n = _wipesame(p, n);
	_graham(n, p, s, temp);
	for (convex[0] = temp[0], n = 1, i = (dir ? 1 : (s - 1)); dir ? (i < s) : i; i += (dir ? 1 : -1))
		if (maxsize || !zero(xmult(temp[i - 1], temp[i], temp[(i + 1)%s])))
			convex[n++] = temp[i];
	delete []temp;
	return n;
}

int rotating_calipers(point *ch, int n)
{
	int q = 1, ans = 0;
	ch[n] = ch[0];
	for (int p = 0; p < n; p++)
	{
		while (xmult(ch[p + 1], ch[q + 1], ch[p]) > xmult(ch[p + 1], ch[q], ch[p]))
			q = (q + 1)%n;
		ans = max(ans, max(dist2(ch[p], ch[q]), dist2(ch[p + 1], ch[q + 1])));
	}
	return ans;
}
int main()
{
	int n;
	cin >> n;
	for (int i = 0; i < n; i++)
	{
		cin >> p[i].x >> p[i].y;
	}
	graham(n, p, convex,1,0);
	cout << rotating_calipers(convex, n) << endl;
	return 0;
}