All‐in‐one implementation framework for binary heaps. (20th October 2016) - Katajainen, Jyrki
Summary: Even a rough literature review reveals that there are many alternative ways of implementing a binary heap, the fundamental priority‐queue structure loved by us all. Which one of these alternatives is the best in practice? The opinions of crowd‐pullers and textbook authors are aligned: use an array. Of course, the correct answer is 'it depends'. To get from opinions to facts, a framework—a set of class templates—was written that provides a variety of customization options so it could be used to realize a large part of the proposed variants. Also, some of the derived implementations were performance benchmarked. From this work, three conclusions can be drawn: (i) It is difficult to achieve space efficiency and speed at the same time. If n denotes the current number of values in the data structure, ϵ is a small positive real, ϵ  < 1, and | V | denotes the size of the values of type V in bytes, space efficiency means ( 1 + ϵ ) | V | n bytes of space, and speed means O (lg n ) worst‐case time perpush andpop . (ii) If an array‐based solution is sufficient, Williams' original program from 1964 is still to this day hard to beat. (iii) Sometimes a linked structure and clever programming is a viable option. If the binary‐heap variant you need is not available at the software library you are using, reading this essay might save you some headaches. Copyright © 2016 John Wiley & Sons, Ltd.