1. Use the skeleton code for class Pattern to complete the methods the generate the patterns as shown in the section of the sample output. Create a method for each pattern. In addition, you need to add a print method to print these patterns.

   Each of these methods takes a 2D array variable as input parameter, generates a pattern and stores back into the 2D array variable. The print method is just responsible for printing a pattern.

   A skeleton code for class Pattern as below:

   import java.util.Scanner; public class Pattern { public static void main(String[] args) { Scanner input = new Scanner(System.in); System.out.println("Enter the height and width of a rectangle: "); int height = input.nextInt(); //The height of the rectangle int width = input.nextInt(); //The width of the rectangle System.out.println("Enter the row and column indice for a point through which two 45 degree diagonals pass: "); int r = input.nextInt(); //The row index int c = input.nextInt(); //The column index int rows = height + 1; //The number of rows of the rectangle int cols = width + 1; //The number of columns of the rectangle int [][] a = new int[rows][cols]; //Create a 2D array with size of rows by cols System.out.println(" A rectangle with 0's in the upper triangle and 1's in the lower triangle:"); createRectangle(a); print(a); System.out.println(" Two 45 degree diagonals pass through a point (" + r + ", " + c + "):"); createTwoDiagonals(a, r, c); print(a); System.out.println(" A rectangle with a half-sized rectangular hole:"); createRectangularHole(a); print(a); System.out.println(" A rectangle with a circular hole:"); createCircularHole(a); print(a); System.out.println(" A rectangle with a sin curve:"); createSinCurve(a); print(a); } //This method takes an allocated 2D array and create a 2D pattern and store into the array. public static void createRectangularHole(int [][] p) { int rows = p.length; int cols = p[0].length; int h = rows - 1; int w = cols - 1; for (int i = 0; i 

Enter the height and width of a rectangle: 20 34 Enter the row and column indice for a point through which two 45 degree diagonal s pass: 8 18 A rectangle with O's in the upper triangle and i's in the lower triangle: Read this handout for mathematical formula for this question. eeeeee1 1 1 1 1 1 1 1 1 1 1 1 1111111 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1111111111111111 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1111111111111111111 eeeeeeeee1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 eeeeeee1 1 1 1 1 1 1 1 1 1 1 1 1 1 eeeeee 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 eeee1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Read this handout for mathematical formula for this question. Two 45 degree diagonals pass through a point (8, 18): 1 1 1 11 11 eeee1e0o1 eeeee Two 45 degree diagonals pass through a point (8, 18): 1 10 1 1 1 1 11 11 1 eee1 1 1 1 1 1 1 1 eeeeee 1 1 000 A rectangle with a half-sized rectangular hole: eeeeeeeee1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 eeeeeeeee1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 eeeeeeeee1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 eeeeeeeee1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 eeeeeeeee1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 eeeeeeeee1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 eeeeeeeee1 1 1 11 1 1 eeeeeeeee1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 A rectangle with a circular hole. The radius of the hole = 1/4 max(width, height of the rectangle). 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 A rectangle with a sin curve: eee 0e111100 1 eeee1eeeeee 1 1 1 1 1 1 eee1 eeeeeeeeeeee1 eeeee1eeeeee1 1 1 1 1 11 Enter the height and width of a rectangle: 20 34 Enter the row and column indice for a point through which two 45 degree diagonal s pass: 8 18 A rectangle with O's in the upper triangle and i's in the lower triangle: Read this handout for mathematical formula for this question. eeeeee1 1 1 1 1 1 1 1 1 1 1 1 1111111 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1111111111111111 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1111111111111111111 eeeeeeeee1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 eeeeeee1 1 1 1 1 1 1 1 1 1 1 1 1 1 eeeeee 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 eeee1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Read this handout for mathematical formula for this question. Two 45 degree diagonals pass through a point (8, 18): 1 1 1 11 11 eeee1e0o1 eeeee Two 45 degree diagonals pass through a point (8, 18): 1 10 1 1 1 1 11 11 1 eee1 1 1 1 1 1 1 1 eeeeee 1 1 000 A rectangle with a half-sized rectangular hole: eeeeeeeee1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 eeeeeeeee1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 eeeeeeeee1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 eeeeeeeee1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 eeeeeeeee1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 eeeeeeeee1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 eeeeeeeee1 1 1 11 1 1 eeeeeeeee1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 A rectangle with a circular hole. The radius of the hole = 1/4 max(width, height of the rectangle). 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 A rectangle with a sin curve: eee 0e111100 1 eeee1eeeeee 1 1 1 1 1 1 eee1 eeeeeeeeeeee1 eeeee1eeeeee1 1 1 1 1 11