#include<iostream>
#include<ctime>
#include<cmath>
#include<algorithm>
using namespace std;

#define number 1000000

typedef struct point
{
	float x,y;
}point;//定義二維點point，橫縱座標範圍均為【-100,100】

void setpoints(point *points,int num)
{      //隨機生成兌點陣列points中的二維點，
	srand(unsigned(time(NULL)));
	for(int i=0;i<num;i++)
	{
		points[i].x=(rand()%20000)/100.0-100;//調整rand，使得橫座標範圍在【-100,100】
		points[i].y=(rand()%20000)/100.0-100;
	}
}

float Distance(point a,point b)
{  //計算平面上任意兩點之間的距離
	return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
}

bool CmpX(point a,point b)
{   //自定義排序
	return a.x<b.x;
}

float ClosestPair(point points[],int num,point &a,point &b)
{
    float distance;       
    float d1,d2;           
    int i=0,j=0,k=0;      
    point a1,b1,a2,b2;     

    if(num<2)
		return number;   
    
	if(num==2)
    {
        a=points[0];
        b=points[1];
        distance=Distance(points[0],points[1]);
    }
    else
    {
        point *s1=new point[num];     //開闢兩個子集
        point *s2=new point[num];  

        sort(points,points+num,CmpX); 
        float mid=points[(num-1)/2].x;  

        for(i=0;i<num/2;i++)
            s1[i]=points[i];
        for(j=0,i=num/2;i<num;i++)
            s2[j++]=points[i];
        d1=ClosestPair(s1,num/2,a1,b1);            
        d2=ClosestPair(s2,num-num/2,a2,b2);  

		if(d1<d2) { distance=d1; a=a1; b=b1;}
        else { distance=d2; a=a2; b=b2;}

        //求解跨分割線並在δ×2δ區間內的最近點對
        point *s=new point[num];   
        for(i=0,k=0;i<num;i++)
            if(abs(points[i].x-mid)<=distance)  s[k++]=points[i];

        for(i=0;i<k;i++)
            for(j=i+1;j<=i+7&&j<k;j++)    
            {
                if(Distance(s[i],s[j])<distance)
                {//如果跨分割線的兩點距離小於已知最小距離，則記錄該距離
                    distance=Distance(s[i],s[j]);
                    a=s[i];
                    b=s[j];
                }
            }
    }
    return distance;
}


int main()
{
	int N;
	point a,b;
	float d;
	cout<<"請輸入二維點個數：";
	cin>>N;

	if(N<2)
		cout<<"請輸入大於或等於2的點個數！"<<endl;
	else
	{
		point *points=new point[N];
		setpoints(points,N);
		d=ClosestPair(points,N,a,b);
		cout<<"隨機生成的"<<N<<"個二維點如下（按橫座標排序後的點對）："<<endl;
		for(int i=0;i<N;i++)
		{
			cout<<"("<<points[i].x<<","<<points[i].y<<")"<<endl;
		}
		cout<<endl<<"最近點對為："<<"("<<a.x<<","<<a.y<<")和"<<"("<<b.x<<","<<b.y<<")"<<endl<<"最近點對距離為："<<d<<endl; 
	}
	return 0;
}