Computer science: abstraction to implementation by Keller R.

By Keller R.

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There is no occurrence of set(A, i, V) and provided that i > 0 and i < size(A). These summarize an abstract array, independent of any "concrete" array (concrete meaning a specific implementation, rather than an abstraction). This kind of thinking should be undertaken whenever building an abstraction. That is, begin by asking the question What are the properties that connect the operators? The answers to such questions are what guide the choice or development of implementations, which will be the subject of much of this book.

As an example, consider the characterization of an array. The typical behavioral aspects of arrays are these: • We can make an array of a specified length. • We can set the value of the element at any specified index of the array. Exploring Abstractions: Information Structures • 53 We can get the value of the element at any specified index. These are the things that principally characterize an array, although we can always add others, such as ones that search an array, search from a given index, search in reverse, etc.

The overall trie would appear as follows: 0 1 2 3 0 5 6 1 0 0 4 1 1 Claremont 2 7 8 9 2 3 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 3 4 5 6 7 8 9 0 4 8 1 9 2 3 0 4 5 6 7 8 0 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 9 5 6 7 8 9 0 Stanford, Palo Alto Figure 26: Sketch of part of a trie representing assignment of sets of cities to zip codes. 1 Berkeley 2 3 9 0 4 5 38 Exploring Abstractions: Information Structures General Graphs as Lists If we omit, in the definition of tree, the condition “there is exactly one root”, thus allowing multiple roots (note that there will always be at least one root if the graph is acyclic), we would define the idea of a forest or set of trees.

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