Question

public static int findEscapeCount(double x,
                                  double y,
                                  int maxIterations)

Determines how many iterations of the following operation are required until the condition (a * a + b * b) > 4 is reached:

   tempA = a * a - b * b + x
   tempB = 2 * a * b + y
   a = tempA
   b = tempB
 

where a and b are initially zero, and x and y are given parameters. For example, with x = 1 and y = 0.5, after one iteration a should be 1 and b should be 0.5. After two iterations a should be 1.75 and b should be 1.5, at which point the method returns with value 2 since (1.75)² + (1.5)² = 5.3, which is greater than 4. If the condition (a * a + b * b) > 4 is not reached within maxIterations, the method just returns maxIterations.

Parameters:

x - given x value

y - given y value

maxIterations - maximum number of iterations to attempt

Returns:

number of iterations required to get (a * a + b * b) > 4, or maxIterations

Answer 1

Please find the code below:

FindMaxInteration.java

package classes10;

import java.util.Scanner;

public class FindMaxInteration {
   private static double a=0;
   private static double b=0;
   public static int findEscapeCount(double x,double y,int maxIterations){
       int iteration = 0;
       while(!((a * a + b * b) > 4)){
           iteration++;
           double tempA = a * a - b * b + x;
           double tempB = 2 * a * b + y;
           a = tempA;
           b = tempB;
           if(iteration>maxIterations){
               return maxIterations;
           }
       }
       return iteration;
   }
   public static void main(String[] args) {
       Scanner sc = new Scanner(System.in);
       double x,y;
       int maxIteration;
       System.out.print("Enter value of x : ");
       x = sc.nextDouble();
       System.out.print("Enter value of y : ");
       y = sc.nextDouble();
       System.out.print("Enter value of max iteration : ");
       maxIteration = sc.nextInt();
       System.out.println("Escape count is "+findEscapeCount(x, y, maxIteration));
   }
}

output: