As indicated in the text, a two-dimensional array is actually a one-dimensional array of r...

As indicated in the text, a two-dimensional array is actually a one-dimensional array of references to other (subordinate) one-dimensional arrays. In the text examples, all the subordinate arrays had the same length. But these subordinate arrays may have different lengths. The following code fragment creates a two-dimensional array whose five rows have lengths ranging from a minimum length of three elements to a maximum length of seven elements:

public static void main(String[] args){    int rows = 5;    int minCols = 3;    int[][] array2D = new int[rows][0];    for (int j=0; j

Output:

in row 0, number of columns = 3in row 1, number of columns = 4in row 2, number of columns = 5in row 3, number of columns = 6in row 4, number of columns = 7

This pattern in which the number of columns increases linearly with the number of rows is typical of many computer-science algorithms. In this particular case, the total number of elements equals 3 + 4 + 5 + 6 + 7 = 25. Suppose that you wanted a general formula for the total number of elements as a function of arbitrary values for

rows

minCols.

a) Factor out the minimum number of columns from the rest of the numbers in the series to obtain a series that starts at zero:

3 + 4 + 5 + 6 + 7 = (5 * 3) + (0 + 1 + 2 + 3 + 4)

b) Add the reversed sequence to the sequence that starts at zero to obtain a sequence of identical values:

0
1
2
3
4
+4
+3
+2
+1
+0
4
4
4
4
4 = 5 * 4

Use these two tricks and the fact that

5 = rows

3 = minCols

rows

minCols.