Add Damerau-Levenshtein distance algorithm

Author: saahil-mahato

strings/damerau_levenshtein_distance.py

@@ -0,0 +1,73 @@
+"""
+This script is a implementation of the Damerau-Levenshtein distance algorithm.
+
+It's an algorithm that measures the edit distance between two string sequences
+
+More information about this algorithm can be found in this wikipedia article:
+https://en.wikipedia.org/wiki/Damerau%E2%80%93Levenshtein_distance
+"""
+
+
+def damerau_levenshtein_distance(first_string: str, second_string: str) -> int:
+    """
+    Implements the Damerau-Levenshtein distance algorithm that measures
+    the edit distance between two string. This function calculates the true
+    Damerau-Levenshtein distance with adjacent transpositions.
+
+    Parameters:
+        first_string (string): The first string
+        second_string (string): The second string
+
+    Returns:
+        distance (int): The edit distance between the first and second strings
+
+    >>> damerau_levenshtein_distance("cat", "cut")
+    1
+    >>> damerau_levenshtein_distance("kitten", "sitting")
+    3
+    >>> damerau_levenshtein_distance("hello", "world")
+    4
+    >>> damerau_levenshtein_distance("book", "back")
+    2
+    >>> damerau_levenshtein_distance("container", "containment")
+    3
+    """
+
+    # Create a dynamic programming matrix to store the distances
+    dp_matrix = [
+        [None] * (len(second_string) + 1) for _ in range(len(first_string) + 1)
+    ]
+
+    # Initialize the matrix
+    for i in range(len(first_string) + 1):
+        dp_matrix[i][0] = i
+    for j in range(len(second_string) + 1):
+        dp_matrix[0][j] = j
+
+    # Fill the matrix
+    for i in range(1, len(first_string) + 1):
+        for j in range(1, len(second_string) + 1):
+            cost = 0 if first_string[i - 1] == second_string[j - 1] else 1
+
+            dp_matrix[i][j] = min(
+                dp_matrix[i - 1][j] + 1,  # Deletion
+                dp_matrix[i][j - 1] + 1,  # Insertion
+                dp_matrix[i - 1][j - 1] + cost,  # Substitution
+            )
+
+            # Calculate Transposition
+            if (
+                i > 1
+                and j > 1
+                and first_string[i - 1] == second_string[j - 2]
+                and first_string[i - 2] == second_string[j - 1]
+            ):
+                dp_matrix[i][j] = min(dp_matrix[i][j], dp_matrix[i - 2][j - 2] + cost)
+
+    return dp_matrix[len(first_string)][len(second_string)]
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()