Laboratory 9 Array Searching Week of 11 April, 2005

Objective

When you use a list or an array, you often need to be able to find values in the list. We will examine two methods of searching for a particular value: sequential and binary.

Key Concepts

• Array manipulation and searching

Getting Started

Using the procedures in the previous laboratories, copy the files Sequential.java, Searcher.java, Binary.java, and BinarySearcher.java for your manipulation.

Sequential Search

• Open the program file Sequential.java. This class implements a sequential search. The class has two instance variables. Variable list represents the list to be examined. Variable comparisons keeps track of the number of comparisons performed in the last search, The class provides the following constructor and methods.
   
• Sequential(int[] a)
   
  • Uses a as the list to be searched.
     
• search(int key)
   
  • Returns whether key is a value in the list. If it is, then the index of the first occurrence is returned; otherwise -1 is returned
     
• getComparisons()
   
  • Returns the number of  element comparisons performed in the most recent search.
     
• Open program Searcher.java. This program uses Sequential to search through two lists, Both lists contains the same values. However, the second list is sorted. The program prompts its user for a key and uses Sequential to search for the key. The program outputs the results of the search.
   
• Compile Sequential.java and Searcher.java.
   
• Run the program six times using as the key values 6, 11, 21, 22, 54, and 91. Record the number of searches the program reports as comments in Searcher.java.
   
• With randomly arranged data and a random key value which is actually present in the list, generally a program will examine approximately half the list to find the key value. If the key value is not present, the entire list will be examined. If we know instead that the data is already ordered (sorted), then generally we can do much better, whether or not the key is present.
   
• How did sorting affect the average number of comparisons? Probably not very much, because the program has not been modified to take advantage of the sorting. A significant advantage can be realized if we use the fact that the data has been sorted. Let’s now modify the search class to achieve this advantage.
   
• Because the data is sorted, we can stop searching for the key value once we find a list value that is greater than the one for which we are searching. Modify the Sequential class to add a new public method searchSorted() to terminate the search accordingly. Essentially, this will be a copy of the search() method, with the addition of code that will cause loop to terminate (and the method to return -1) once the value in the list is greater than the key value for which we are searching. Thus, searchSorted() will have a single int parameter named key. If key is found in the list, then searchSorted() should perform the same action as search().
   
• Modify program Searcher.java so that the initialization of index2 is performed using searchSorted() (line 23).
   
• Submit the completed programs Sequential.java and Searcher.java.

Binary Search

The binary search described in this section is a more efficient search than the modified sequential search. For example, when you search for a name in a phone book, you probably don’t start at the beginning and search straight through. You further exploit the fact that the names are in sorted order to speed up your search.

The binary search can be implemented as an iterative technique in which each iteration eliminates half of the remaining values from further consideration. The search starts with the middle list element and decides which half of the data to examine further. In the next iteration, the middle element from the half of the data values that can possibly contain the key value is determined, and from it, the range of possible positions for the key value is restricted further. The process is repeated until the search finds the key value or until the search determines that there are no more potential positions to consider.

• Open and compile the class Binary.java. The class provides a constructor and two methods
   
  • Binary(int[] a)
     
    • Uses a as the list to be searched. It is assumed that a is sorted.
       
  • search(int key)
     
    • Performs a binary search that returns whether key is a value in the list. If it is, then the index of the first occurrence is returned; otherwise -1 is returned
       
  • getComparisons()
     
    • Returns the number of  element comparisons performed in the most recent search.
       
• Examine the method search() in Binary.java to determine how the binary search algorithm is implemented. In particular, notice that value mid is used as an index of the middle element of the values currently being considered.
   
• Modify the BinarySearcher.java program to use a Binary object instead of a Sequential object in the definition of s2.
   
• Run the program six times using as the key values 6, 11, 21, 22, 54, and 91. Record the number of searches the program reports as comments in BinarySearcher.java.
   
• Submit the completed program Binary.java and BinarySearcher.java.

As list size increases, the efficiency improvement of binary search over sequential search is very dramatic. For example binary search requires at most 20 comparisons for a list of size 1000. Sequential search might make 1000 comparisons!

Finishing Up

• Copy any files you wish to keep to your own drive.
   
• Delete all of the files you copied or created on the laboratory machine.

Homework J6

Use any remaining time in the lab to work on HW J6.