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By Clifford A. Shaffer

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Extra resources for A Practical Introduction to Data Structures and Algorithm Analysis Third Edition (Java Version)

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Note that P ∪ Q = Q ∪ P and that P ∩ Q = Q ∩ P, but in general P − Q = Q − P. In this example, Q − P = {10}. Note that the set {4, 3, 5} is indistinguishable from set P, because sets have no concept of order. Likewise, set {4, 3, 4, 5} is also indistinguishable from P, because sets have no concept of duplicate elements. The powerset of a set S is the set of all possible subsets for S. Consider the set S = {a, b, c}. The powerset of S is {∅, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}}. Sometimes we wish to define a collection of elements with no order (like a set), but with duplicate-valued elements.

Define an ADT for a list of integers. First, decide what functionality your ADT should provide. 4 should give you some ideas. Then, specify your ADT in Java in the form of an abstract class declaration, showing the functions, their parameters, and their return types. Briefly describe how integer variables are typically represented on a computer. 2? Define an ADT for a two-dimensional array of integers. Specify precisely the basic operations that can be performed on such arrays. Next, imagine an application that stores an array with 1000 rows and 1000 columns, where less than 10,000 of the array values are non-zero.

A simple Java function for generating a random permutation is as follows. Here, the n values of the sequence are stored in positions 0 through n − 1 of array A, function swap(A, i, j) exchanges elements i and j in array A, and Random(n) returns an integer value in the range 0 to n − 1 (see the Appendix for more information on swap and Random). random(i)); // swap A[i-1] with } // a random element Boolean variables: A Boolean variable is a variable (of type boolean in Java) that takes on one of the two values true and false.

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