Binary Search

Instructions

Your task is to implement a binary search algorithm.

A binary search algorithm finds an item in a list by repeatedly splitting it in half, only keeping the half which contains the item we're looking for. It allows us to quickly narrow down the possible locations of our item until we find it, or until we've eliminated all possible locations.

The algorithm looks like this:

• Find the middle element of a sorted list and compare it with the item we're looking for.
• If the middle element is our item, then we're done!
• If the middle element is greater than our item, we can eliminate that element and all the elements after it.
• If the middle element is less than our item, we can eliminate that element and all the elements before it.
• If every element of the list has been eliminated then the item is not in the list.
• Otherwise, repeat the process on the part of the list that has not been eliminated.

Here's an example:

Let's say we're looking for the number 23 in the following sorted list: [4, 8, 12, 16, 23, 28, 32].

• We start by comparing 23 with the middle element, 16.
• Since 23 is greater than 16, we can eliminate the left half of the list, leaving us with [23, 28, 32].
• We then compare 23 with the new middle element, 28.
• Since 23 is less than 28, we can eliminate the right half of the list: [23].
• We've found our item.

Track Specific Notes

If the element is not present in the array, return the symbol 'not-found. The array will be passed as a vector.

Running and testing your solutions

From the command line

Simply type make chez if you're using ChezScheme or make guile if you're using GNU Guile. Sometimes the name for the scheme binary on your system will differ from the defaults. When this is the case, you'll need to tell make by running make chez chez=your-chez-binary or make guile guile=your-guile-binary.

From a REPL

• Enter (load "test.scm") at the repl prompt.
• Develop your solution in binary-search.scm reloading as you go.
• Run (test) to check your solution.

Failed Test Cases

If some of the test cases fail, you should see the failing input and the expected output. The failing input is presented as a list because the tests call your solution by (apply binary-search input-list). To learn more about apply see The Scheme Programming Language -- Chapter 5

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Source

Wikipedia