Mastering Algorithms with C

Chapter 10. Heaps and Priority Queues

Many problems rely on being able to determine quickly the largest or smallest element from a set that is undergoing frequent insertions and deletions. One way to approach this problem is to keep a set sorted. This way, the largest or smallest element, depending on whether we sort the data in ascending or descending order, is always the one at the beginning of the set. However, sorting a set over and over again is costly. In addition, because it is not our goal to keep every element in order, we end up doing more work than we really need to. To quickly determine only the largest or smallest element, we need only keep this element where we can find it. Heaps and priority queues let us do this in an efficient way.

This chapter covers:

Heaps

Trees organized so that we can determine the node with the largest value quickly. The cost to preserve this property is less than that of keeping the data sorted. We can also organize a heap so that we can determine the smallest value just as easily.

Priority queues

Data structures naturally derived from heaps. In a priority queue, data is organized in a heap so that we can determine the node with the next highest priority quickly. The “priority” of an element can mean different things in different problems.

Some applications of heaps and priority queues are:

Sorting

Specifically, an algorithm called heapsort. In heapsort, the data to be sorted begins in a heap. Nodes are extracted from the heap one at a time ...