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Therefore, one might conclude that the choice of ADT is arbitrary. However, this is not the case. In general, it is more natural to pose certain questions and perform certain methods under one representation than another. As the above examples illustrate, the set of primary methods is a key factor in selecting an ADT and must be considered in conjunction with the most “natural” representation of the data. 2 Broad ADT groups In the remainder of this chapter, we discuss three major groups of ADTs: partitions over a set of elements, collections of elements (where the elements could by any object including null), and graphs.
Also many data structures for ADTs that are not naturally viewed as a tree, such as PriorityQueue (Chapter 24), OrderedCollection (Chapter 29), and DigitizedOrderedCollection (Chapter 39), use a tree to provide the needed structure. To create the most appropriate implementation for a tree, there are several important questions to consider. For example, • Is it important to have constant time access to the parent of a node? • Is it important to have constant time access to the children of a node?
3, could be used to ﬁnd the desired row and column of the array in logarithmic time. If the currencies are not arranged alphabetically, then a linear time search through all rows and columns may be required. 1. row/column number where we assume the top row is row 0 and the leftmost column is column 0. In particular, since the three letter acronym serves as a distinct identiﬁer (or key) for the currency, the Mapping ADT could be used. 2. Now given two currencies, a good implementation of a Mapping ADT can be used to determine in constant time the row and column numbers of the array entry that holds the desired exchange rate.