Create closestpairofpoints.cpp

O(nlogn) implementation of closest pair of points
This commit is contained in:
neelabhtiwari 2018-10-08 17:58:01 +05:30 committed by GitHub
parent 4da95e9a22
commit 7d2ced82c3
No known key found for this signature in database
GPG Key ID: 4AEE18F83AFDEB23

View File

@ -0,0 +1,188 @@
#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;
}