Skip this screen if you don't care about the math and want to know how the implementation works.

The mathematical definition is as follows: the Levenshtein distance between two strings a and b can be calculated by:

This makes sense, we're inputting a and b and are arriving an outcome after processing the two values somehow.

So how do we process them?

By using an indicator function, which is a defined as a function defined on a set X that indicates membership of an element in a subset A of X. This is represented by a 1 in all elements of A where there's a membership and a 0 for all elements of X not in A.

So the following:

Is the indicator function equal to 0 when ai = bj (when the letters are the same in the same position) and equal to 1 otherwise (if they differ).

To calculate the actual distance, we use:

The above is the distance between the first i characters of a and the first j characters of b.

Confused? Don't worry, we'll move beyond the math in the next section.