# Computer Algorithms: Interpolation Search

## Overview

I wrote about binary search in my previous post, which is indeed one very fast searching algorithm, but in some cases we can achieve even faster results. Such an algorithm is the “interpolation search” – perhaps the most interesting of all searching algorithms. However we shouldn’t forget that the data must follow some limitations. In first place the array must be sorted. Also we must know the bounds of the interval.

Why is that? Well, this algorithm tries to follow the way we search a name in a phone book, or a word in the dictionary. We, humans, know in advance that in case the name we’re searching starts with a “B”, like “Bond” for instance, we should start searching near the beginning of the phone book. Thus if we’re searching the word “algorithm” in the dictionary, you know that it should be placed somewhere at the beginning. This is because we know the order of the letters, we know the interval (a-z), and somehow we intuitively know that the words are dispersed equally. These facts are enough to realize that the binary search can be a bad choice. Indeed the binary search algorithm divides the list in two equal sub-lists, which is useless if we know in advance that the searched item is somewhere in the beginning or the end of the list. Yes, we can use also jump search if the item is at the beginning, but not if it is at the end, in that case this algorithm is not so effective.

So the interpolation search is based on some simple facts. The binary search divides the interval on two equal sub-lists, as shown on the image bellow.

What will happen if we don’t use the constant ½, but another more accurate constant “C”, that can lead us closer to the searched item.