CS 1713 -- Pascal class

The Java class `Pascal`:

Here is a Java Pascal class that creates a two-dimensional array in a triangular shape, and stores numbers in it so that it becomes what is known as

Pascal's Triangle:

A triangular array of numbers, starting with 1, 1 1, 1 2 1, 1 3 3 1, 1 4 6 4 1, where the first and last entries are 1's and the other entries are the sum of the entry directly above and the entry above and one place to the left; see the examples below.
These numbers are just the coeficients of the expansion of (x+1)ⁿ, shown in boldface below:
The Java code below is color coded, so that:
- Green is for the code that creates storage for the triangle and then inserts the proper numbers.
  - Assume for simplicity that the constant SIZE is 6.
  - The line int[][] pascal = new int[SIZE][]; creates a 1-dimensional array of 6 references to 1-dimensional arrays. The six arrays referenced are not yet created.
  - Next comes the main for loop that marches down through the rows, where the variable y takes on the row numbers 0, 1, 2, 3, 4, and 5.
  - Inside this loop, the line pascal[y] = new int[y+1]; creates each row in turn. In each case the length of the row is one bigger than the row number.
  - For each row, the first 1 is inserted, all the middle numbers are inserted with the inner for loop, and the final 1 is inserted.
- Red is for the code that prints the triangle, row by row.
  - This uses the same kind of for loop that lets the variable y take on the six row numbers in turn. For each row number, pascal[y] is a reference to a 1-dimensional array, a row, with length pascal[y].length.
- Blue is for code added to the previous printing code that will insert extra blanks so that the triangle looks the way it is usually presented. (I wrote this partly by trial and error. Because of the use of a tab, "\t", this only works for SIZE up to 16 or so.)


// Pascal.java: create and print Pascal's triangle
public class Pascal {
   final static int SIZE = 12;

   public static void main (String[] args) {

      // create the triangle and fill in numbers
      int[][] pascal = new int[SIZE][]; // just the SIZE rows initially
      for (int y = 0; y < pascal.length; y++) { // each row y
         pascal[y] = new int[y+1]; // allocate each row, of increasing lengths
         pascal[y][0] = 1; // set each initial 1 value
         for (int x = 1; x < pascal[y].length - 1; x++) { // columns, except first and last
            // except for 1's, each value is sum of values above and left
            pascal[y][x] = pascal[y-1][x-1] + pascal[y-1][x];
         }
         pascal[y][pascal[y].length - 1] = 1; // set the final 1 value
      }

      // print as an array
      for (int y = 0; y < pascal.length; y++) { // each row y
         for (int x = 0; x < pascal[y].length; x++) // each column x
            System.out.print(pascal[y][x] + "\t");
         System.out.println();
      }
      System.out.println();

      // print with extra spaces, so it looks like a triangle
      for (int y = 0; y < pascal.length; y++) { // each row y
         // extra initial space here
         for (int x = (pascal.length - pascal[y].length)/2; x > 0; x--) {
            System.out.print(" " + "\t");
         }
         for (int x = 0; x < pascal[y].length; x++){ // each column x
            // extra 4 spaces on alternate rows
            if ( (y%2) == 0 ) System.out.print("    ");
            System.out.print(pascal[y][x] + "\t");
         }
         System.out.println();
      }
   }
}

Here is the output with SIZE == 8:


1
1       1
1       2       1
1       3       3       1
1       4       6       4       1
1       5       10      10      5       1
1       6       15      20      15      6       1
1       7       21      35      35      21      7       1

                            1
                        1       1
                    1       2       1
                1       3       3       1
            1       4       6       4       1
        1       5       10      10      5       1
    1       6       15      20      15      6       1
1       7       21      35      35      21      7       1

Here is the output when with SIZE == 12:


1
1       1
1       2       1
1       3       3       1
1       4       6       4       1
1       5       10      10      5       1
1       6       15      20      15      6       1
1       7       21      35      35      21      7       1
1       8       28      56      70      56      28      8       1
1       9       36      84      126     126     84      36      9       1
1       10      45      120     210     252     210     120     45      10     1
1       11      55      165     330     462     462     330     165     55     11       1

                                            1
                                        1       1
                                    1       2       1
                                1       3       3       1
                            1       4       6       4       1
                        1       5       10      10      5       1
                    1       6       15      20      15      6       1
                1       7       21      35      35      21      7       1
            1       8       28      56      70      56      28      8       1
        1       9       36      84      126     126     84      36      9      1
    1       10      45      120     210     252     210     120     45      10     1
1       11      55      165     330     462     462     330     165     55     11       1

Here is the output when with SIZE == 16:


1
1       1
1       2       1
1       3       3       1
1       4       6       4       1
1       5       10      10      5       1
1       6       15      20      15      6       1
1       7       21      35      35      21      7       1
1       8       28      56      70      56      28      8       1
1       9       36      84      126     126     84      36      9       1
1       10      45      120     210     252     210     120     45      10     1
1       11      55      165     330     462     462     330     165     55     11       1
1       12      66      220     495     792     924     792     495     220    66       12      1
1       13      78      286     715     1287    1716    1716    1287    715    286      78      13      1
1       14      91      364     1001    2002    3003    3432    3003    2002   1001     364     91      14      1
1       15      105     455     1365    3003    5005    6435    6435    5005   3003     1365    455     105     15      1

                                                            1
                                                        1       1
                                                    1       2       1
                                                1       3       3       1
                                            1       4       6       4       1
                                        1       5       10      10      5       1
                                    1       6       15      20      15      6       1
                                1       7       21      35      35      21      7       1
                            1       8       28      56      70      56      28      8       1
                        1       9       36      84      126     126     84      36      9       1
                    1       10      45      120     210     252     210     120     45      10      1
                1       11      55      165     330     462     462     330     165     55      11      1
            1       12      66      220     495     792     924     792     495     220     66      12      1
        1       13      78      286     715     1287    1716    1716    1287    715     286     78      13      1
    1       14      91      364     1001    2002    3003    3432    3003    2002    1001    364     91      14      1
1       15      105     455     1365    3003    5005    6435    6435    5005    3003    1365    455     105     15      1

Revision date: 2003-11-05. (Please use ISO 8601, the International Standard.)

The Java class Pascal:

The Java class `Pascal`: