Data Structures and Algorithms in Java[1].pdf - Fulvio Frisone

Code Fragment 8.5: Algorithm
PriorityQueueSort. Note that the elements of the
input sequence S serve as keys of the priority queue P.
8.2 Implementing a Priority Queue with a List
In this section, we show how to implement a priority queue by storing its entries in a
list S. (See Chapter 6.2.) We provide two realizations, depending on whether or not
we keep the entries in S sorted by key. When analyzing the running time of the
methods of a priority queue implemented with a list, we will assume that a
comparison of two keys takes O(1) time.
8.2.1 Implementation with an Unsorted List
As our first implementation of a priority queue P, let us consider storing the entries
of P in a list S, where S is implemented with a doubly linked list. Thus, the elements
of S are entries (k,x), where k is the key and x is the value.
Fast Insertions and Slow Removals
A simple way of performing operation insert(k,x) on P is to create a new entry
object e = (k,x) and add it at the end of list S, by executing method addLast(e)
on S. This implementation of method insert takes O(1) time.
The above insertion algorithm implies that S will be unsorted, for always inserting
entries at the end of S does not take into account the ordering of the keys. As a
consequence, to perform operation min or removeMin on P, we must inspect all
the elements of list S to find an entry (k, x) of S with minimum k. Thus, methods
min and removeMin take O(n) time each, where n is the number of entries in P
460