Java Program To Print Pascal Triangle

Chapter: Interview Programs Last Updated: 19-10-2016 16:19:41 UTC

Program:

            /* ............... START ............... */
                
import java.util.Scanner;

public class JavaPascalTriangle {

	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		System.out.print("Enter the number of rows to print: ");
		int rows = scanner.nextInt();
		System.out.println("Pascal Triangle:");
		print(rows);
		scanner.close();
	}

	public static void print(int n) {
		for (int i = 0; i < n; i++) {
			for (int k = 0; k < n - i; k++) {
				System.out.print(" ");
			}
			for (int j = 0; j <= i; j++) {
				System.out.print(pascal(i, j) + " ");
			}
			System.out.println();
		}
	}

	public static int pascal(int i, int j) {
		if (j == 0 || j == i) {
			return 1;
		} else {
			return pascal(i - 1, j - 1) + pascal(i - 1, j);
		}
	}
}
                /* ............... END ............... */
        

Output

Enter the number of rows to print: 5
Pascal Triangle:
     1 
    1 1 
   1 2 1 
  1 3 3 1 
 1 4 6 4 1 

Notes:

  • Following are the characteristics of Pascal’s triangle
  • The number of elements in a row is equal to the rowth number i.e. first row contains one element, second row contains two elements, third row contains three elements and so on.
  • Each row of a Pascal’s Triangle can be calculated from the previous row. Each row begins and ends with the number 1. The remaining numbers in a row is calculated from the sum of the left number and right number on the previous row. For example, the second element in the 3rd row is the sum of the 1st element and the 2nd element of the 2nd row. Similarly the third element in the 4th row is the sum of the 2nd element and the 3rd element of 3rd row. Similar concept applies for other elements.
  • The sum of numbers in each row is twice the sum of numbers in the previous row.
  • The diagonals adjacent to the border diagonals contains natural numbers in order.

Tags

Print Pascal Triangle, Java, Interview Programs

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