Problem

1. An upper triangular matrix is a square matrix in which all entries below the main diagonal are 0. Describe the modifications necessary to use the access array method to store an upper triangular matrix.

2. Consider a table of the triangular shape shown in Figure 9.7, where the columns are indexed from -n to n and the rows from 0 to n.

(a) Devise an index function that maps a table of this shape into a sequential array.

(b) Write a function that will generate an access array for finding the first entry of each row of a table of this shape within the contiguous array.

(c) Write a function that will reflect the table from left to right. The entries in column 0 (the central column) remain unchanged, those in columns -1 and 1 are swapped, and so on.