The Levenshtein distance algorithm calculates the minimum number of edits (insertions, deletions, or substitutions) needed to transform one string into another. It utilizes a matrix to store the distances between all prefixes of the two strings, and iteratively fills this matrix using dynamic programming. The final value in the matrix represents the Levenshtein distance between the two original strings.

• Implement the algorithm: Write a function levenshtein_distance(string1, string2) that accurately calculates the Levenshtein distance between two input strings.