Quoit Design

Have you ever played quoit in a playground? Quoit is a game in which flat rings are pitched at some toys, with all the toys encircled awarded.
In the field of Cyberground, the position of each toy is fixed, and the ring is carefully designed so it can only encircle one toy at a time. On the other hand, to make the game look more attractive, the ring is designed to have the largest radius. Given a configuration of the field, you are supposed to find the radius of such a ring.

Assume that all the toys are points on a plane. A point is encircled by the ring if the distance between the point and the center of the ring is strictly less than the radius of the ring. If two toys are placed at the same point, the radius of the ring is considered to be 0.

The input consists of several test cases. For each case, the first line contains an integer N (2 <= N <= 100,000), the total number of toys in the field. Then N lines follow, each contains a pair of (x, y) which are the coordinates of a toy. The input is terminated by N = 0.

For each test case, print in one line the radius of the ring required by the Cyberground manager, accurate up to 2 decimal places.

2
0 0
1 1
2
1 1
1 1
3
-1.5 0
0 0
0 1.5
0

0.71
0.00
0.75
//刚开始写的超时，未排序
#include<iostream>
#include<stdio.h>
#include<math.h>
#include<algorithm>
#include<string.h>
#include<string>
using namespace std; 
typedef struct
{
	double x,y;
}node;
node a[100000];
bool cmp(node a,node b)
{
	return a.y<b.y;
}
int main()
{
	int n,i,j;
	double r,min;
	while(cin>>n)
	{
		if(n==0)
			break;
		for(i=0;i<n;i++)
			cin>>a[i].x>>a[i].y;
		if(n==2&&a[0].x==a[1].x&&a[0].y==a[1].y)
		{
			cout<<"0.00"<<endl;
			continue;
		}
	    min=sqrt(((a[0].x-a[1].x)*(a[0].x-a[1].x))+((a[0].y-a[1].y)*(a[0].y-a[1].y)));
		for(i=0;i<n;i++)
		{
			for(j=i+1;j<n;j++)
			{
				r=sqrt(((a[i].x-a[j].x)*(a[i].x-a[j].x))+((a[i].y-a[j].y)*(a[i].y-a[j].y)));
			    if(r<min)
					min=r;
			}
		}
		printf("%.2f\n",min/2.0);
	}
	return 0;
}

//改正之后的，，后来看了一下别人的，有的说若对x排序则超时，若对y排序则可以
我还看见有的人是对x+y进行排序的也过了，，sort比qsort效率高
#include<iostream>
#include<stdio.h>
#include<math.h>
#include<algorithm>
#include<string.h>
#include<string>
using namespace std; 
typedef struct
{
	double x,y;
}node;
node a[100000];
bool cmp(node a,node b)
{
	return a.y<b.y;
}
int main()
{
	int n,i;
	double r,min;
	while(cin>>n)
	{
		if(n==0)
			break;
		for(i=0;i<n;i++)
			cin>>a[i].x>>a[i].y;
		if(n==2&&a[0].x==a[1].x&&a[0].y==a[1].y)
		{
			cout<<"0.00"<<endl;
			continue;
		}
		sort(a,a+n,cmp);
	    min=sqrt(((a[0].x-a[1].x)*(a[0].x-a[1].x))+((a[0].y-a[1].y)*(a[0].y-a[1].y)));
		for(i=2;i<n;i++)
		{
			r=sqrt(((a[i-1].x-a[i].x)*(a[i-1].x-a[i].x))+((a[i-1].y-a[i].y)*(a[i-1].y-a[i].y)));
			if(r<min)
				min=r;
		}
		printf("%.2f\n",min/2.0);
	}
	return 0;
}