Create closestpairofpoints.cpp

O(nlogn) implementation of closest pair of points

code/closestpairofpoints.cpp

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+#include<iostream>
+#include<cstdlib>
+#include<cmath>
+#include<cfloat>
+#include<ctime>
+using namespace std;
+float xfirstx;
+float yfirsty;
+float xsecondx;
+float ysecondy;
+class mymath{
+public:
+  float mysqrt(const float x){
+  const double prec=0.00001;
+  float low,high,anstry;
+    if (x < 1){
+    low = x;
+    high = 1;
+   }
+   else{
+    low = 1;
+    high = x;
+   }
+   while ((high-low) > prec){
+    anstry = (low+high)/2;
+    if(anstry*anstry>x)
+     high=anstry;
+    else
+     low=anstry;
+   }
+   return (low + high)/2;
+  }
+};
+class points{
+  float x;
+  float y;
+public:
+  float showx(){
+      return x;
+  }
+  float showy(){
+      return y;
+  }
+  void setx(float in){
+    x=in;
+  }
+  void sety(float in){
+    y=in;
+  }
+  int xpartition(points arr[],int p,int q){
+  int k=p;
+  for(int i=p+1;i<=q;i++){
+    if(arr[i].showx()<arr[p].showx()){
+      k++;
+      points temp=arr[k];
+      arr[k]=arr[i];
+      arr[i]=temp;
+    }
+  }
+  points temp=arr[p];
+  arr[p]=arr[k];
+  arr[k]=temp;
+  return k;
+    }
+  int ypartition(points arr[],int p,int q){
+  int k=p;
+  for(int i=p+1;i<=q;i++){
+    if(arr[i].showy()<arr[p].showy()){
+      k++;
+      points temp=arr[k];
+      arr[k]=arr[i];
+      arr[i]=temp;
+    }
+  }
+    points temp=arr[p];
+    arr[p]=arr[k];
+    arr[k]=temp;
+    return k;
+      }
+  void xquicksort(points arr[],int p,int q){
+    if(p<q){
+    int k=xpartition(arr,p,q);
+    xquicksort(arr,p,k-1);
+    xquicksort(arr,k+1,q);
+    }
+  }
+  void yquicksort(points arr[],int p,int q){
+    if(p<q){
+    int k=ypartition(arr,p,q);
+    yquicksort(arr,p,k-1);
+    yquicksort(arr,k+1,q);
+    }
+  }
+  float absolutevalue(float x){
+    if(x<0) return -x;
+    else return x;
+  }
+
+  float dist(points a, points b){
+    mymath callobj;
+    return callobj.mysqrt(((a.showx()-b.showx())*(a.showx()-b.showx())+(a.showy()-b.showy())*(a.showy()-b.showy())));
+}
+float findinstrip(points strip[],float del,int length){
+float mind=del;
+    int j;
+    for(int i=0;i<length;i++){
+      for(int j=i+1;j<length && strip[j].showy()-strip[i].showy()<mind;j++){
+        if(strip[0].dist(strip[i],strip[j])<mind){
+          mind=strip[0].dist(strip[i],strip[j]);
+          xfirstx=strip[i].showx();
+          yfirsty=strip[i].showy();
+          xsecondx=strip[j].showx();
+          ysecondy=strip[j].showy();
+      }
+    }
+  }
+  return mind;
+}
+float findclosestpair(points xsorted[],points ysorted[], int n){
+  if(n<=5){
+    static float d=FLT_MAX;
+    for(int i=0;i<n;i++){
+      for(int j=i+1;j<n;j++){
+        if(xsorted[0].dist(xsorted[i],xsorted[j])<d){
+          d=xsorted[0].dist(xsorted[i],xsorted[j]);
+          xfirstx=xsorted[i].showx();
+          yfirsty=xsorted[i].showy();
+          xsecondx=xsorted[j].showx();
+          ysecondy=xsorted[j].showy();
+        }
+      }
+    }
+    return d;
+  }
+  else{
+  int mid=n/2;
+  float xmid=xsorted[mid].showx();
+  points yl[mid+1],yr[n-mid-1];
+  int ylpos=0,yrpos=0;
+  for(int i=0;i<n;i++){
+      if(ysorted[i].showx()<=xmid){
+        yl[ylpos]=ysorted[i];
+        ylpos++;
+      }
+      else{
+        yr[yrpos]=ysorted[i];
+        yrpos++;
+      }
+    }
+  float lmin=findclosestpair(xsorted,yl,mid+1);
+  float rmin=findclosestpair(xsorted+mid+1,yr,n-mid-1);
+  float del=min(lmin,rmin);
+  int ypos=0;
+  points ystrip[n];
+  for(int i=0;i<n;i++){
+      if(xsorted[0].absolutevalue(ysorted[i].showx()-xmid)<del){
+        ystrip[ypos]=ysorted[i];
+        ypos++;
+      }
+}
+if(del<findinstrip(ystrip,del,ypos))  return del;
+else return findinstrip(ystrip,del,ypos);
+}
+}
+};
+int main(){
+int n;
+points callingobject;
+cout<<"Give the number of points : ";
+cin>>n;
+points input[n],xsorted[n],ysorted[n];
+// srand(time(NULL));
+for(int i=0;i<n;i++){
+  input[i].setx(((float)(rand())/(float)(RAND_MAX))*(100));
+  input[i].sety(((float)(rand())/(float)(RAND_MAX))*(100));
+  xsorted[i]=input[i];
+  ysorted[i]=input[i];
+}
+int time1=clock();
+callingobject.xquicksort(xsorted,0,n-1);
+callingobject.yquicksort(ysorted,0,n-1);
+float distance=callingobject.findclosestpair(xsorted,ysorted,n);
+int time2=clock();
+cout<<"The closest pair of points are ("<<xfirstx<<","<<yfirsty<<") and ("<<xsecondx<<","<<ysecondy<<")."<<endl;
+cout<<"The distance between them is "<<distance<<"."<<endl;
+cout<<"The time taken for the computation is "<<(time2-time1)<<" microseconds"<<endl;
+return 0;
+}