A simple, efficient, and flexible implementation of flexible arrays

Abstract

Flexible arrays can grow and shrink at both sides. Operations on flexible arrays are the usual ones: element inspection and assignment of a value to an array element. Additional operations are hiext, extending the array at its high end with an entry; loext, extension at the low end; hirem, removing the last element of the array; and lorem, removing the first element of the array.

It is shown how so-called leaf trees can be used to implement flexible arrays efficiently. The implementation is simple (no rotations are involved) and yields nicely shaped trees. The implementation is flexible, in the sense that a large class of additional operations, such as computation of the minimum and maximum of the array, can be easily added to the repertoire of operations without affecting time complexities. The standard flexible array operations take O(log n) time, where n is the size of the flexible array. Additional operations, such as minimum and maximum take O(1) time.