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The 2-D array described in Chapter 2 is a simple rectangular structure consisting of the same number of elements in each row. Other layouts are possible and sometimes required by problems in computer science. For example, the lower triangular array shown on the right is organized such that the rows are staggered with each successive row consisting of one more element than the previous row.
(a) Derive an equation that computes the total number of elements in the lower triangular table for a table of size m × n.
(b) Derive an index equation that maps an element of the lower triangular table onto a one-dimensional array stored in row-major order.
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