Levenshtein Distance Algorithm in plain english

levenshtein-plain-english.md

Levenshtein Distance Algorithm in plain English

Inputs: Two strings s and t.

Goal: Calculate the minimum number of single-character edits (insertions, deletions, or substitutions) required to transform string s into string t.

1. Initialize the Matrix:

   • Create a matrix dp with dimensions (len(s) + 1) x (len(t) + 1).
   • Initialize the first row with values 0 to len(t) and the first column with values 0 to len(s).

2. Fill in the Matrix:

   • For each cell dp[i][j] in the matrix, where i represents the current position in string s and j represents the current position in string t:
     • If the characters s[i-1] and t[j-1] are equal, set dp[i][j] to the value of the cell diagonally above-left (dp[i-1][j-1]).
     • Otherwise, set dp[i][j] to the minimum of the three adjacent cells' values (dp[i-1][j] + 1, dp[i][j-1] + 1, and dp[i-1][j-1] + 1).

3. Result:

   • The Levenshtein Distance between strings s and t is given by the value in the bottom-right cell of the matrix (dp[len(s)][len(t)]).

Applications:

• Levenshtein Distance is often used in spell checking, DNA sequence alignment, and natural language processing tasks.
• It can also be used in applications where similarity between strings needs to be measured, such as text search engines and plagiarism detection.

Advantages:

• The Levenshtein Distance algorithm provides a quantitative measure of the difference between two strings.
• It is flexible and can handle strings of different lengths.

Limitations:

• The algorithm has a time complexity of O(m * n) where m is the length of string s and n is the length of string t. It can be computationally expensive for very long strings.

The Levenshtein Distance algorithm is a fundamental tool for measuring the similarity and difference between strings by quantifying the number of edit operations needed to transform one string into another.