Answer:
import java.util.Scanner; //Scanner class to take input from user
public class BandMatrix{ // start of the BandMatrix class
public static void main(String[] args) {// start of main() function body
Scanner scanner = new Scanner( System.in );
//creates Scanner class object scanner
int n = scanner.nextInt(); //reads the value of n from user
int width = scanner.nextInt(); //reads input value of width
//the outer and inner loops to form a n by n pattern
for (int i=0; i<n; i++) {
for (int j=0; j<n; j++) {
if (j==i || Math.abs(i-j) <= width) {
/*if the value of j become equal to the value of i OR if the difference between i and j is less than or equal to the value of width input by user then asterisks are printed in the pattern otherwise 0 is printed. This simply moves through each element of and calculates its distance from main diagonal */
System.out.print(" * "); } //displays asterisks when above if condition is true
else { //when the above IF condition evaluates to false
System.out.print(" 0 "); } } //displays 0 in pattern when if condition is false
System.out.println(); } } }
Explanation:
The program is well explained in the comments mentioned with each statement of the program. The program first takes two integer arguments from user i.e. n and width and uses for loops if (j==i || Math.abs(i-j) <= width) condition to print n-by-n pattern with a zero 0 for each element whose distance from the main diagonal is strictly more than width, and an asterisk * for each entry that is not. I will explain the working of loops.
Suppose n=8 and width=0
The first outer for loop has an i variable that is initialized to 0. This loop executes until the value of i exceeds the value of n. So at first iteration i=0. The loop checks if i<n. Its true because n=8 and i=0 So 8>0. Now the program enters the body of outer loop.
There is an inner loop which has a j variable that is initialized to 0. This loop executes until the value of j exceeds the value of n. So at first iteration j=0. The loop checks if j<n. Its true because n=8 and j=0 So 8>0. Now the program enters the body of inner loop.
There is an if statement inside the body of inner loop. It checks each entry whose distance from the main diagonal is strictly less than or equal width and prints asterisks * when the statement evaluates to true otherwise prints a 0. Lets see how it works.
i=0 j=0 So j==i is True. If we check the second part of this if statement then
i - j = 0 - 0 = 0. Math.abs() method is used to return the absolute value of this subtraction in case the result comes out to be a negative number. So the result is 0. As the value of width is 0 so this part is true because i-j=0 and width is also 0. So one asterisk is printed when this condition evaluates to true.
This way the loops keeps executing and printing the asterisks or 0 according to the if statement at each iteration. The program along with its output is attached.
