Problem 3: [10 marks] Display Pyramid (filename: DisplayPyramid.java)

Design an algorithm and then write a program that prompts the user to enter an integer from 1 to 15 (assume that the user always enters a valid integer) and displays a pyramid, as shown in the following sample run:

Enter a number between 1 and 15: 12

1

2 1 2

3 2 1 2 3

4 3 2 1 2 3 4

5 4 3 2 1 2 3 4 5

6 5 4 3 2 1 2 3 4 5 6

7 6 5 4 3 2 1 2 3 4 5 6 7

8 7 6 5 4 3 2 1 2 3 4 5 6 7 8

9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9

10 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 10

11 10 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 10 11

12 11 10 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 10 11 12