Chebyshev distance between two points

The java program finds distance between two points using chebyshev distance equation. The points can be a scalar or a vector.

1D distance metric
It measures distance between two points by absolute difference between them. Each point has one element.

2-Dimensional distance metric
It measures distance between two points (2D vector) by selecting maximum absolute difference on 2D vector element absolute difference.

N-Dimensional distance metric
It measures distance between two N-Dimensional vector by selecting maximum absolute difference on the two N-D vector element.

Example Calculation on 2D vectors

This is an example calculation shown below explain how to find the distance between two vectors using Chebyshev distance formula. A vector,array of elements declared and initialized in Java using one dimensional array.

        int A[] = { 2 ,6 };    // 2D vector A 
 
 int B[] = { 4,1 };    // 2D vector B
 
 max  -   operators finds  greatest value in a array 
 
   find  distance between two vectors A and B using 
              Chebyshev distance equation
   
   ||A-B||     =  max { abs(A[0]-B[0])  ,  abs(A[1]-B[1]) } 
   
               =  max { abs(2-4) , abs(6-1) };
      
        =  max { abs(-2) , abs(5) }; 
      
        =  max {2 , 5}; 
      
   ||A-B||     =  5 ;
      
   
      
   Chebyshev Distance between vectors A=[2,6] and B=[4,1] is 5     

public class Chebyshev {

 public static double distance(double x, double y) {  
  return  Math.abs(x-y);  
 }
  
 public static double distance(int x, int y) {  
  return Math.abs(x-y);          
 }
 
 
 public static double distance(double x[], double y[]) {
  
  double ds=0.0; 
  for(int n=0;n<x.length;n++)      
    ds=Math.max(ds,Math.abs(x[n]-y[n]));
  
  return  ds;  
 }
  
 public static double distance(int x[], int y[]) {
  
  double ds=0.0;
  for(int n=0;n<x.length;n++) {
   ds=Math.max(ds,Math.abs(x[n]-y[n]));
  }
  return  ds;            
 }
 
 
  public static double[] distance(int x[][], int y[]) {
  
    double ds[]=new double[x.length];
  for(int n=0;n<x.length;n++)
   ds[n]= distance(x[n],y);   
  return  ds;            
 }
 
  public static double[] distance(double x[][], double y[]) {
  
  double ds[]=new double[x.length];
  for(int n=0;n<x.length;n++)
   ds[n] = distance(x[n],y);   
  return  ds;            
 }

}

import java.util.Arrays;

public class ChebyshevMain {

public static void main(String[] args) 
  {  
    System.out.println("\n1D - Distance on integer" );
    System.out.println("Chebyshev Distance between scalar 
                       int x and y" );
          
    int ix=20; 
    int iy=30;          
    double dist=Chebyshev.distance(ix, iy);
    System.out.println("x="+ix +",y="+iy);
    System.out.println("Distance :" + dist);
  
    System.out.println("\n1D - Distance on double " );
    System.out.println("Chebyshev Distance between scalar 
                                 double x and y" );
    double dx=2.6; 
    double dy=3.2;          
    double ds2=Chebyshev.distance(dx, dy);
    System.out.println("x="+dx +",y="+dy);
    System.out.println("Distance :" + ds2);
     
     
    System.out.println("\n2D - Distance on integer" );
    System.out.println("Chebyshev Distance between 
                      vector int x and y");
    int aix[]={2,3};
    int aiy[]={3,5};          
    double ds3=Chebyshev.distance(ix, iy);     
    System.out.println("x="+Arrays.toString(aix) 
                   +",y="+Arrays.toString(aiy));
    System.out.println("Distance :" + ds3);
     

    System.out.println("\n2D - Distance on integer" );
    System.out.println("Chebyshev Distance between 
                             vector double x and y");     
    double adx[]={2.4,3.1};
    double ady[]={3.1,5.6};      
    System.out.println("x="+Arrays.toString(adx) 
                  +",y="+Arrays.toString(ady)); 
     double ds4=Chebyshev.distance(adx, ady);
     System.out.println("Distance :" + ds4);
     
     System.out.println("nChebyshev Distance between 
               set of int vector x and vector int y" );
    int aix2[][]={ {2,3,5} ,{1,7,4}};
    int aiy2[]={3,5,7};          
    double ds5[]=Chebyshev.distance(aix2, aiy2);     
    System.out.println("x="+Arrays.toString(aix2[0]) + "," 
 + Arrays.toString(aix2[1]) +",y="+Arrays.toString(aiy2));
    System.out.println( "Distance :" + Arrays.toString(ds5) );
     
             
    System.out.println("nChebyshev Distance between 
    set of vector double x and a vector double y " );
    double adx2[][]={ {2.4,3.1,5.2},{1.2,7.2,4.5}};
    double ady2[]={3.1,5.6,7.8};          
    double ds6[]=Chebyshev.distance(adx2, ady2);
     
    System.out.println("x="+ Arrays.toString(adx2[0])+","
       +Arrays.toString(adx2[1])   +",y="+Arrays.toString(ady2));
    System.out.println( "Distance :" + Arrays.toString(ds6) );   
     
 }

}

Output

1D - Distance on integer
Chebyshev Distance between scalar int x and y
x=20,y=30
Distance :10.0

1D - Distance on double
Chebyshev Distance between scalar double x and y
x=2.6,y=3.2
Distance :0.6000000000000001

2D - Distance on integer
Chebyshev Distance between vector int x and y
x=[2, 3],y=[3, 5]
Distance :2.0

2D - Distance on double
Chebyshev Distance between vector double x and y
x=[2.4, 3.1],y=[3.1, 5.6]
Distance :2.4999999999999996

Chebyshev Distance between set of int vector x and vector int y
x=[2, 3, 5],[1, 7, 4],y=[3, 5, 7]
Distance :[2.0, 3.0]

Chebyshev Distance between set of vector double x 
                      and a vector double y 
x=[2.4, 3.1, 5.2],[1.2, 7.2, 4.5],y=[3.1, 5.6, 7.8]
Distance :[2.5999999999999996, 3.3]

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