Data Structures and Algorithm Analysis - Computer Science at ...

Sec. 4.4 Dictionaries 1314.3.3 Comparison of Array-Based and Linked QueuesAll member functions for both the array-based and linked queue implementationsrequire constant time. The space comparison issues are the same as for the equivalentstack implementations. Unlike the array-based stack implementation, there isno convenient way to store two queues in the same array, unless items are alwaystransferred directly from one queue to the other.4.4 DictionariesThe most common objective of computer programs is to store and retrieve data.Much of this book is about efficient ways to organize collections of data recordsso that they can be stored and retrieved quickly. In this section we describe asimple interface for such a collection, called a dictionary. The dictionary ADTprovides operations for storing records, finding records, and removing records fromthe collection. This ADT gives us a standard basis for comparing various datastructures.Before we can discuss the interface for a dictionary, we must first define theconcepts of a key and comparable objects. If we want to search for a given recordin a database, how should we describe what we are looking for? A database recordcould simply be a number, or it could be quite complicated, such as a payroll recordwith many fields of varying types. We do not want to describe what we are lookingfor by detailing and matching the entire contents of the record. If we knew everythingabout the record already, we probably would not need to look for it. Instead,we typically define what record we want in terms of a key value. For example, ifsearching for payroll records, we might wish to search for the record that matchesa particular ID number. In this example the ID number is the search key.To implement the search function, we require that keys be comparable. At aminimum, we must be able to take two keys and reliably determine whether theyare equal or not. That is enough to enable a sequential search through a databaseof records and find one that matches a given key. However, we typically wouldlike for the keys to define a total order (see Section 2.1), which means that wecan tell which of two keys is greater than the other. Using key types with totalorderings gives the database implementor the opportunity to organize a collectionof records in a way that makes searching more efficient. An example is storing therecords in sorted order in an array, which permits a binary search. Fortunately, inpractice most fields of most records consist of simple data types with natural totalorders. For example, integers, floats, doubles, and character strings all are totallyordered. Ordering fields that are naturally multi-dimensional, such as a point in twoor three dimensions, present special opportunities if we wish to take advantage oftheir multidimensional nature. This problem is addressed in Section 13.3.