I have recently begun studying different data science principles, and have had a particular interest as of late in fuzzy matching. For preface, I'd like to include smarter fuzzy searching in a proprietary language named "4D" in my workplace, so access to libraries is pretty much non existent. It's also worth noting that client side is single threaded currently, so taking advantage of multi-threaded matrix manipulations is out of the question.
I began studying the levenshtein algorithm and got that implemented, but it's well known for the slowness. Further, it builds a matrix by looping through both words, creating an O(mn) efficiency in time.
That got me thinking, what's the advantage in using the Levenshtein algorithm, vs just a single for loop that checks the character at every index, compares, and throws back a -1 if incorrect (among checking for length of string, etc), producing an O(n) time efficiency? Or does Levenshtein do extra checks that I'm unaware of?