I have published code that shows examples of the Binary Search Algorithm.

In order for this algorithm to be applicable, we need to assume that we’re dealing with a sorted list to start. As a result, instead of proceeding iteratively through each item in the list, the binary search algorithm continually divides the list into two halves and searches each half for the element.

It can be shown that the maximum number of iterations this algorithm requires is equivalent to the number of times that we need to divide the list into halves. This is equivalent to a maximum number of iterations along the order of log₂(n), where n is the number of items in the list.