vaibhawraj / Levenshtein-Sequence-Python

List all possible Levenshtein (i.e., edit) sequences from one string to another with optimal number of inserts/deletes/replaces.

Backtracking to find Levenshtein Sequence

"The Levenshtein distance is a string metric for measuring the difference between two sequences. Informally, the Levenshtein distance between two words is the minimum number of single-character edits (insertions, deletions or substitutions) required to change one word into the other." - Wikipedia

Levenshtein Distance has a lot of use case in NLP. In simplest algorithm of word prediction, Levenshtein Distance is used to find the most similar word. Even in spell correction/detection methodology, Levenshtein Distance can be used to predict the correct spelling of word from a given dictionaty. Typically, Program computes the Levenshtein distance of target word against each word of the dictionary. Word with minimum of distance is prioritize and predicted.

How to find Levenshtein distance??

Levenshtein distance is very popular application of Dynamic Programming (DP). Since Levenshtein Distance between two strings has the Optimal Substructure property and requires recomputation of sub-problems, Dynamic Programming can be used to memonize the intermediate solution for substructures

Does two string have unique solution??

Not Always, In most of the cases, There are multiple Levenshtein sequence between two string with equal distance. All solutions are correct though

Scope of this implementation

This python script is focused to find all Levenshtein Sequence possible. And it requires backtracking the path for finding all the solutions

Usage

    $ sequence.py "paris" "alice"

Output

Program will list down all the sequence of minimum edit operation requires to convert "paris" to "alice":

• paris delete p(0) -> aris replace r with l(1) -> alis replace s with c(3) -> alic insert e(3) -> alice
• paris delete p(0) -> aris replace r with l(1) -> alis insert c(2) -> alics replace s with e(4) -> alice