Binary Search

The reading on loop invariants identified four different loop invariants for a binary search and discussed how two of those invariants could be used to create a correct implementation of a binary search. The underlying theme is that a binary search can be implemented if several correct ways, but also in many, many incorrect ways. The basic challenge is to consistently set variables left, right, and middle, so that always have the same conceptual interpretation.

1. Following Version 2 in the reading on loop invariants, write a binary-search method binarySearch2 within a BinarySearch class, and write tests for this method for three types of arrays:

   • an array of at least 6 elements in ascending order,
   • an array of at least 6 random elements, and
   • an array of at least 6 elements in descending order.

   Your tests also should include circumstances where the desired item is first in the array, last in the array, and somewhere in the middle.

Since the reading provided considerable analysis for two of the four identified loop invariants, it is natural to consider the details for the other two loop invariants.

2. Consider the following loop invariant for the binary search:

   

   Write method binarySearch3 that implements this pictoral loop invariant, and test it with the same arrays and elements utilized in Step 1.

3. Repeat Step 2 for the following loop invariant, implementing a method binarySearch4: