Binary Search in .NET

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4.1 Binary Search
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This section is about implementing the card-searching algorithm discussed in Section 2.2. We use Java as the implementation language in the first instance in order to illustrate the problems that arise when using a 'real' programming language. In 9 and beyond, we use an idealized programming language that allows us to focus on program design rather than the intricacies of one particular programming language. A word of caution is needed in advance. Java uses the symbol '=' for the assignment operator and the symbol '==' for the equality operator. So, in Java, 'x==0' has the same meaning as 'x = 0' in mathematics, but 'x=0' means something quite different. The difference between the two is evident from that fact that x = 0 conventional equality has the same meaning as 0 = x, whereas x=0 in Javadoes not have the same meaning as 0=x. (In fact, the latter is not even a valid statement.) Mathematical equality is symmetric, whereas assignment is not.
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4: Implementation Issues
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In words, the Java assignment x=0 means that the value referenced by the variable x becomes 0. More briefly, it is read as 'x gets 0' or 'x becomes 0'. This misuse of the equality symbol is a frequent cause of error in Java programs. In order to avoid confusion, we use the teletype font when the Java assignment is intended. We also emphasize the fact that assignment is not symmetric by putting a space immediately after, but not before, the assignment operator in Java programs. On the other hand, we place the equality operator symmetrically between its two operands. Thus, we write 'x= 0' to mean the assignment of the value 0 to the variable x, and 'x == 0' (or 'x = 0', using a non-teletype font) for equality between x andO. The search algorithm in Section 2.2 manipulates an actual deck of cards. In a computer program, we have to represent the physical operations on the decks of cards in terms of operations that are primitive to the programming language. That is, we have to decide how to represent each of the decks of cards, how to represent splitting a deck into two and how to represent the transfer of cards between decks. Also, we have to decide on a specific implementation of the choice of a card in the middle deck of cards. The simplest and most convenient way to represent a deck of cards in a language like Java is an array. An array is a sequence of numbered values. Below is such a sequence. In this case, numbering begins at zero and the values are all names of animals. 0
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The values stored in an array are called the elements of the array. In our example, the elements are 'cat', 'cow', 'dog', etc. The number assigned to each element is called its index. Note that the values in an array may occur more than once (as, for example, 'fox') but the elements are distinct, because each has a unique index. The above array has six elements, but only five values are stored in the array. (The above array is also alphabetically ordered, but, in general, array values need not be ordered.) In Java and similar languages, array elements can be quite complex objects. In a real-life situation, an array element might represent, for example, all the information about a book in a library: its title, author and publisher, date of purchase, location, etc. For simplicity, in our implementation of the searching algorithm of Section 2.2, we assume that the information on each card in the given deck of cards is an integer, and the given card X is an integer value. The representation we choose for the whole deck of cards is thus an array of integers. In a Java program, the text int[] card declares an array (' []') of integers ('i nt') with the name card, implicitly indexed from zero onwards. The length of the array is its number of elements; its value
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