The Deap-A Double-Ended Heap to Implement Double-Ended Priority Queues

A priority queue is a data type where the element with the smallest key value can be found and deleted, and new elements can be inserted. It is also called a priority queue when the element with the largest key value is wanted, instead of the smallest. In some cases, it is interesting to find and delete both the smallest and the largest element, as well as to be able to insert new elements. A structure with these operations may be called a double-ended priority queue, or priority deque for short. A common way of implementing priority queues is through a heap-an implicit data structure first introduced by Williams (71. Some attempts to implement double-ended priority queues with heaps or heap-like structures have been made. Some examples of this are the MinMaxHeap [l] and the structure with two heaps placed ‘back-to-back’ in a suitable way, proposed by Williams. In this paper, a double-ended heap, called Deap, is presented. This structure is a mixture of the MinMaxHeap and the priority deque proposed by Williams. Also, the use of binary search of a path in a heap is used. This binary search technique is presented in [3,5]. The asymptotic results of all three implementations are the same. That is: (1) finding the largest and the smallest element takes constant time, (2) deleting the maximum or minimum element, or inserting a new element takes O(log n) time, (3) the structure can be constructed in linear time, and (4) no additional pointers are required.