You have stumbled upon a group of mathematicians who are also singer-songwriters. They have written a song for each of their favorite numbers, and, as you can imagine, they have a lot of favorite numbers (like 0 or 73 or 6174).
You are curious to hear the song for your favorite number, but with so many songs to wade through, finding the right song could take a while. Fortunately, they have organized their songs in a playlist sorted by the title — which is simply the number that the song is about.
You realize that you can use a binary search algorithm to quickly find a song given the title.
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.
Binary search only works when a list has been sorted.
The algorithm looks like this:
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].
[23, 28, 32].
Haskell has support for many types of arrays. This exercise uses immutable,
boxed, non-strict arrays from
Data.Array. You can read more about the use of
these arrays on:
As an optional extension to this exercise, try and make the
work for arrays with arbitrary bounds, e.g. arrays for which the first index is
not necessarily 0.