Resizable Arrays in Optimal Time and Space

We present simple, practical and eecient data structures for the fundamental problem of maintaining a resizable one-dimensional array, Al::l + n ? 1], of xed-size elements, as elements are added to or removed from one or both ends. Our structures also support access to the element in position i. All operations are performed in constant time. The extra space (i.e., the space used past storing the n current elements) is O(p n) at any point in time. This is shown to be within a constant factor of optimal, even if there are no constraints on the time. If desired, each memory block can be made to have size 2 k ? c for a speciied constant c, and hence the scheme works eeectively with the buddy system. The data structures can be used to solve a variety of problems with optimal bounds on time and extra storage. These include stacks, queues, randomized queues, priority queues, and deques.