Mastering Algorithms with C

Implementation and Analysis of Priority Queues

There are several ways to implement a priority queue. Perhaps the most intuitive approach is simply to maintain a sorted set of data. In this approach, the element at the beginning of the sorted set is the one with the highest priority. However, inserting and extracting elements require resorting the set, which is an O (n) process in the worst case, where n is the number of elements. Therefore, a better solution is to keep the set partially ordered using a heap. Recall that the node at the top of a heap is always the one with the highest priority, however this is defined, and that repairing the heap after inserting and extracting data requires only O (lg n) time.

A simple way to implement a priority queue as a heap is to typedef PQueue to Heap (see Example 10.3). Since the operations of a priority queue are identical to those of a heap, only an interface is designed for priority queues and the heap datatype serves as the implementation (see Examples Example 10.2 and Example 10.3). To do this, each priority queue operation is simply defined to its heap counterpart. The one exception to this is pqueue_ peek, which has no heap equivalent. This operation works just like pqueue_extract, except that the highest priority element is only returned, not removed.

Example 10.3. Header for the Priority Queue Abstract Datatype

/***************************************************************************** * * * ------------------------------- pqueue.h ...