算法笔记-----计算两点距离----O(n2)简单实现

#include<stdlib.h>
#include<stdio.h>
#include<iostream>
#include<math.h>
#include<algorithm>
#include <time.h>

#define MAX 99999
using namespace std;

struct point{           //点结构
    double x,y;
};

double Distance(point a,point b){
    return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
}
bool cmp(point a,point b){          //按y升排序辅助函数
    return a.y<b.y;
}
bool cmp2(point a,point b){          //按x升排序辅助函数
    return a.x<b.x;
}
double closestPoint(point s[],int low,int high,point rec[]){
    double d1,d2,d3,d;
    int mid,i,j,index;
    double x1,y1,x2,y2;         //记录点对的位置
    point P[high-low+1],temp1[2],temp2[2],temp3[2];         //辅助空间
    if(high-low==1){             //两个点的情况
        rec[0].x=s[low].x;rec[0].y=s[low].y;
        rec[1].x=s[high].x;rec[1].y=s[high].y;
        return Distance(s[low],s[high]);
    }
    if(high-low==2){            //三个点的情况
        d1=Distance(s[low],s[low+1]);
        d2=Distance(s[low+1],s[high]);
        d3=Distance(s[low],s[high]);
        if((d1<d2)&&(d1<d3)){
            rec[0].x=s[low].x;rec[0].y=s[low].y;
            rec[1].x=s[low+1].x;rec[1].y=s[low+1].y;
            return d1;
        }
        else if(d2<d3){
            rec[0].x=s[low+1].x;rec[0].y=s[low+1].y;
            rec[1].x=s[high].x;rec[1].y=s[high].y;
            return d2;
        }
        else {
            rec[0].x=s[low].x;rec[0].y=s[low].y;
            rec[1].x=s[high].x;rec[1].y=s[high].y;
            return d3;
        }
    }
    mid=(low+high)/2;       //其他情况递归
    d1=closestPoint(s,low,mid,rec);
    temp1[0]=rec[0];
    temp1[1]=rec[1];
    d2=closestPoint(s,mid+1,high,rec);
    temp2[0]=rec[0];
    temp2[1]=rec[1];
    if(d1<d2){
        d=d1;
        rec[0]=temp1[0];
        rec[1]=temp1[1];
    }
    else {
        d=d2;
        rec[0]=temp2[0];
        rec[1]=temp2[1];
    }
    index=0;
    for(i=mid;(i>=low)&&((s[mid].x-s[i].x)<d);i--)      //点集合p1
        P[index++]=s[i];
    for(i=mid+1;(i<=high)&&((s[i].x-s[mid].x)<d);i++)      //点集合p2
        P[index++]=s[i];
    sort(P,P+index,cmp);                    //升序排列
    for(i=0;i<index;i++){
        for(j=j+1;j<index;i++){
            if((P[j].y-P[i].y)>=d)
                break;
            else {
                d3=Distance(P[i],P[j]);
                if(d3<d){
                    rec[0].x=P[i].x;rec[0].y=P[i].y;
                    rec[1].x=P[j].x;rec[1].y=P[j].y;
                    d=d3;
                }
            }
        }
    }
    return d;
}

//double closestPoints(double x[],double y[],int n){
//    double x1,x2,y1,y2;                      //记录下标
//    double dist,minDist=MAX;
//    for(int i=0;i<n;i++)
//        for(int j=i+1;j<n;j++){
//            dist=(x[i]-x[j])*(x[i]-x[j])+(y[i]-y[j])*(y[i]-y[j]);       //计算距离
//            if(dist<minDist){
//                minDist=dist;
//                x1=x[i];y1=y[i];
//                x2=x[j];y2=y[j];
//            }
//        }
//    cout<<"最近点对为：("<<x1<<","<<y1<<")-("<<x2<<","<<y2<<")";      //输出坐标
//    return minDist;
//}



int mainz(){

    point p[100];            //设定点的集合
    int d=50;
    srand((unsigned)time(NULL));
    for(int i = 0; i < 25;i++ )
    {
        p[i].x = rand()%d+1;
        p[i].y = rand()%d+1;
        d++;
        cout<<p[i].x<<"--"<<p[i].y<<"  ";
    }
    printf("
");
    int n=25;
    double minDist;

//    cout<<"输入点的个数：
";      //输入点的个数
//    cin>>n;
//    cout<<"输入点集:（x,y）
";
//    for(int i=0;i<n;i++)
//        cin>>p[i].x>>p[i].y;

    sort(p,p+n,cmp2);
    point index[2];
    minDist=closestPoint(p,0,n-1,index);
    cout<<"最小距离点对为：("<<index[0].x<<","<<index[0].y<<"),("<<index[1].x<<","<<index[1].y<<")
";
    cout<<"最小距离为：
"<<minDist;      //输出点对的最小问题
    return 0;
}