(Points nearest to each other) Listing 8.3 gives a program that finds two * * points in a two-dimensional space nearest to each other. Revise the program so * * that it finds two points in a three-dimensional space nearest to each other. * * Use a two-dimensional array to represent the points. Test the program using * * the following points: * * double[][] points = {{-1, 0, 3}, {-1, -1, -1}, {4, 1, 1}, * * {2, 0.5, 9}, {3.5, 2, -1}, {3, 1.5, 3}, {-1.5, 4, 2}, * * {5.5, 4, -0.5}}; * * The formula for computing the distance between two points (x1, y1, z1) and * * (x2, y2, z2) is √(x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2.

Points in a two-dimensional space nearest to each other. This program finds two points in a three-dimensional space nearest to each other.

Explanation:

public class Exercise_08_07 {

public static void main(String[] args) {

 double[][] points = {{-1, 0, 3}, {-1, -1, -1}, {4, 1, 1},                      

 {2, 0.5, 9}, {3.5, 2, -1}, {3, 1.5, 3}, {-1.5, 4, 2},                          

 {5.5, 4, -0.5}};

 int p1 = 0, p2 = 1, p3 = 3; // Initial two points

 double shortestDistance = distance(points[p1][0], points[p1][1], points[p1][2],

 points[p2][0], points[p2][p1], points[p3][p2]); // Initialize shortest Distance

 for (int i = 0; i < points.length; i++) {

 for (int j = i + 1; j < points.length; j++) {

   double distance = distance(points[i][0], points[i][1], points[i][2],

   points[j][0], points[j][1], points[j][2]); // Find distance

   if (shortestDistance > distance) {

   p1 = i; // Update p1

   p2 = j; // Update p2

   shortestDistance = distance; // Update shortestDistance

   }

 }

 }

 System.out.println("The closest two points are " +

 "(" + points[p1][0] + ", " + points[p1][1] + ") and (" +

   points[p2][0] + ", " + points[p2][1] + ")");

}

public static double distance(

 double x1, double y1, double z1, double x2, double y2, double z2) {

 return Math.sqrt(Math.pow(x2 - x1, 2) +  

 Math.pow(y2 - y1, 2) + Math.pow(y2 - y1, 2));

}

}

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