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By Clifford A. Shaffer

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19 Think of an algorithm to find the maximum value in an (unsorted) array. Now, think of an algorithm to find the second largest value in the array. Which is harder to implement? Which takes more time to run (as measured by the number of comparisons performed)? Now, think of an algorithm to find the third largest value. Finally, think of an algorithm to find the middle value. Which is the most difficult of these problems to solve? 20 An unsorted list of integers allows for constant-time insert simply by adding a new integer at the end of the list.

Here are some examples of this notation in use. First define two sets, P and Q. P = {2, 3, 5}, Q = {5, 10}. 25 26 Chap. 1 Set notation. |P| = 3 (because P has three members) and |Q| = 2 (because Q has two members). The union of P and Q, written P ∪ Q, is the set of elements in either P or Q, which is {2, 3, 5, 10}. The intersection of P and Q, written P ∩ Q, is the set of elements that appear in both P and Q, which is {5}. The set difference of P and Q, written P − Q, is the set of elements that occur in P but not in Q, which is {2, 3}.

The implementation of the data type as a data structure is its physical form. 1 illustrates this relationship between logical and physical forms for data types. When you implement an ADT, you are dealing with the physical form of the associated data type. When you use an ADT elsewhere in your program, you are concerned with the associated data type’s logical form. Some sections of this book focus on physical implementations for a given data structure. Other sections use the logical ADT for the data type in the context of a higher-level task.

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A Practical Introduction to Data Structures and Algorithm Analysis Third Edition (Java Version) by Clifford A. Shaffer


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