** Sparse Arrays**

In a * sparse* array, most elements
are zero or empty.

A two-dimensional array of dimension *n* takes *O(n ^{2})* storage;
that gets expensive fast as

What we would like to do is to store only the nonzero elements in a lookup structure; if we look up an element and don't find it, we can return zero.

For example, we could have an array of size *n* for the first index;
this could contain pointers to a linked list or tree of values
using the second index as the search key.

(defun sparse-aref (arr i j) (or (second (assoc j (aref arr i))) 0))

(setq myarr (make-array '(10) :initial-contents '(nil nil ((3 77) (2 13)) nil ((5 23)) nil nil ((2 47) (6 52)) nil nil))) >(sparse-aref myarr 7 6) 52 >(sparse-aref myarr 7 4) 0