最近点对

 

//最近点对
//1.分:
//  把所有点递归分到小于等于3个点
//  然后3个点或2个点两两之间Brute force找出最近的两点距离dlf, 和 drg,并返回这两点
//2.并:
//  找出每分界线之间最短的dmid,跟据排序后X序列
//                ^
// .  .  |  . . . |
//   .  .| . . .  d
// .   . |  . . . |
// <-d ->| <-d->  v
//
//

#include <iostream>
#include <algorithm>
#include <cmath>

using std::cin;
using std::cout;
using std::sort;
using std::sqrt;

#define MAX 100
//#define _DEBUG__

struct Point
{
	double x;
	double y;
};

struct Point_Y
{
	int index;
	Point point;
};

int n = 0;
Point *X = NULL;
Point_Y * Y = NULL;

bool cmpX(Point a, Point b)
{
	return a.x < b.x;
}

bool cmpY(Point_Y a, Point_Y b)
{
	return a.point.y < b.point.y;
}

void SortX()
{
	if (X != NULL)
	  sort(X, X + n, cmpX);
#ifdef _DEBUG__
	for (int i = 0; i < n; ++i)
		cout << "x=" << X[i].x << "y=" << X[i].y << "\n";
#endif
}

void Copy()
{
	if (X != NULL && Y != NULL){
		for (int i = 0; i < n; ++i){
			Y[i].index = i;
			Y[i].point.x = X[i].x;
			Y[i].point.y = X[i].y;
		}
	}
}

void SortY()
{
	if (Y != NULL)
		sort(Y, Y + n, cmpY);
}

double Distance(Point &a, Point &b)
{
	return ((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y));
}

double fabs(double a)
{
	return a > 0.0 ? a : -a;
}

void Find_Close_Pair(Point_Y * Y, int low, int hight, Point &node_a, Point &node_b, double &dist)
{
	if (hight - low == 1){//2点
		node_a = X[low], node_b = X[hight];
       dist = Distance(node_a, node_b);
	} 
	else if(hight - low == 2){//3点
		 if (Distance(X[low], X[low + 1]) < Distance(X[low], X[hight])
			&& Distance(X[low], X[low + 1]) < Distance(X[low + 1], X[hight]))
			node_a = X[low], node_b = X[low + 1];
		 else if (Distance(X[low + 1], X[hight]) < Distance(X[low], X[hight]))
			node_a = X[low + 1], node_b = X[hight];
		 else node_a = X[low], node_b = X[hight];
		 dist = Distance(node_a, node_b);  
	}
	else{//下面运用分治法
		//分
		int mid = (hight - low) / 2;
		Point_Y *XL = new Point_Y[mid + 1];
		Point_Y *XR = new Point_Y[mid + 1];
		int xl = 0, xr = 0;
		mid += low;

		for (int i = 0; i < hight - low + 1; ++i){
			if (Y[i].index <= mid)
				XL[xl++] = Y[i];
			else
				XR[xr++] = Y[i];
		}
		Point nal, nbl, nar, nbr;
		double distl, distr;

		Find_Close_Pair(XL, low, mid, nal, nbl, distl);
		Find_Close_Pair(XR, mid + 1, hight, nar, nbr, distr);

		if (distl < distr)
			node_a = nal, node_b = nbl, dist = distl;
		else
			node_a = nar, node_b = nbr, dist = distr;
		//并
		Point *Comb = new Point[hight - low + 1];
		int count_comb = 0;
		for (int i = 0; i < hight - low + 1; ++i)
			if (fabs(X[mid].x - Y[i].point.x) < dist){//找出当前子集合中在离最中间的线(X[m].x)
												  //横座标小于dist的当前子集合中所有点
				Comb[count_comb].x = Y[i].point.x, Comb[count_comb].y = Y[i].point.y;
				count_comb++;
			}
		for (int i = 0; i < count_comb; ++i)//两两之间的距离
			for (int j = i + 1; (j < count_comb) && (fabs(Comb[i].y - Comb[j].y) < dist); ++j)
				if (Distance(Comb[i], Comb[j]) < dist)
					node_a = Comb[i], node_b = Comb[j], dist = Distance(Comb[i], Comb[j]);
		delete []XL;
		delete []XR;
		delete []Comb;
	}
}

void Init()
{
	for (int i = 0; i < n; ++i){
		cin >> X[i].x >> X[i].y;
	}
}

void MinClosePair()
{
	Init();
	SortX();
	Copy();
	SortY();
	Point node_a, node_b;
	double dist = 0.0;
	Find_Close_Pair(Y, 0, n - 1, node_a, node_b, dist);
#ifdef __DEBUG__
	cout << sqrt(dist) << '\n';
	cout << "A (" << node_a.x << "," << node_a.y << ")\n";
	cout << "B (" << node_b.x << "," << node_b.y << ")\n";
#endif
	printf("%.2lf\n", sqrt(dist) / 2.0);
}

int main(void)
{
	while (cin >> n){
	  if (n == 0) break;
	  X = new Point[n];
	  Y = new Point_Y[n];
	  MinClosePair();
	  delete []X;
	  delete []Y;
	}
	return 0;
}