# Exercise 10.3.4

It is often desirable to keep all elements of a doubly linked list compact in storage, using, for example, the first $m$ index locations in the multiple-array representation. (This is the case in a paged, virtual-memory computing environment.) Explain how to implement the procedures ALLOCATE-OBJECT and FREE-OBJECT so that the representation is compact. Assume that there are no pointers to elements of the linked list outside the list itself. (Hint: Use the array implementation of a stack.)

We can allocate elements in the beginning of the array. Whenever we deallocate an element, other than the last (in the stack), we need to shift all elements after it left and then update all the indices that point beyond the deleted element (by decrementing them). This will take linear time. As an optimization, whenever we deallocate the last element in the array, we don't need to scan the array and update pointers.