Implementation of Damerau-Levenshtein Distance Algorithm

Algorithms.Tests/Strings/Similarity/DamerauLevenshteinDistanceTests.cs

@@ -0,0 +1,116 @@
+using Algorithms.Strings.Similarity;
+using NUnit.Framework;
+
+namespace Algorithms.Tests.Strings.Similarity;
+
+[TestFixture]
+public class DamerauLevenshteinDistanceTests
+{
+    [Test]
+    public void Calculate_IdenticalStrings_ReturnsZero()
+    {
+        var str1 = "test";
+        var str2 = "test";
+        var result = DamerauLevenshteinDistance.Calculate(str1, str2);
+        Assert.That(result, Is.EqualTo(0), "Identical strings should have a Damerau-Levenshtein distance of 0.");
+    }
+
+    [Test]
+    public void Calculate_CompletelyDifferentStrings_ReturnsLengthOfLongestString()
+    {
+        var str1 = "abc";
+        var str2 = "xyz";
+        var result = DamerauLevenshteinDistance.Calculate(str1, str2);
+        Assert.That(result, Is.EqualTo(3),"Completely different strings should have a Damerau-Levenshtein distance equal to the length of the longest string.");
+    }
+
+    [Test]
+    public void Calculate_OneEmptyString_ReturnsLengthOfOtherString()
+    {
+        var str1 = "test";
+        var str2 = "";
+        var result = DamerauLevenshteinDistance.Calculate(str1, str2);
+        Assert.That(result, Is.EqualTo(4),"One empty string should have a Damerau-Levenshtein distance equal to the length of the other string.");
+    }
+
+    [Test]
+    public void Calculate_BothEmptyStrings_ReturnsZero()
+    {
+        var str1 = "";
+        var str2 = "";
+        var result = DamerauLevenshteinDistance.Calculate(str1, str2);
+        Assert.That(result, Is.EqualTo(0), "Both empty strings should have a Damerau-Levenshtein distance of 0.");
+    }
+
+    [Test]
+    public void Calculate_DifferentLengths_ReturnsCorrectValue()
+    {
+        var str1 = "short";
+        var str2 = "longer";
+        var result = DamerauLevenshteinDistance.Calculate(str1, str2);
+        Assert.That(result, Is.EqualTo(6), "Strings of different lengths should return the correct Damerau-Levenshtein distance.");
+    }
+
+    [Test]
+    public void Calculate_SpecialCharacters_ReturnsCorrectValue()
+    {
+        var str1 = "hello!";
+        var str2 = "hello?";
+        var result = DamerauLevenshteinDistance.Calculate(str1, str2);
+        Assert.That(result, Is.EqualTo(1), "Strings with special characters should return the correct Damerau-Levenshtein distance.");
+    }
+
+    [Test]
+    public void Calculate_DifferentCases_ReturnsCorrectValue()
+    {
+        var str1 = "Hello";
+        var str2 = "hello";
+        var result = DamerauLevenshteinDistance.Calculate(str1, str2);
+        Assert.That(result, Is.EqualTo(1), "Strings with different cases should return the correct Damerau-Levenshtein distance.");
+    }
+
+    [Test]
+    public void Calculate_CommonPrefixes_ReturnsCorrectValue()
+    {
+        var str1 = "prefix";
+        var str2 = "pre";
+        var result = DamerauLevenshteinDistance.Calculate(str1, str2);
+        Assert.That(result, Is.EqualTo(3), "Strings with common prefixes should return the correct Damerau-Levenshtein distance.");
+    }
+
+    [Test]
+    public void Calculate_CommonSuffixes_ReturnsCorrectValue()
+    {
+        var str1 = "suffix";
+        var str2 = "fix";
+        var result = DamerauLevenshteinDistance.Calculate(str1, str2);
+        Assert.That(result, Is.EqualTo(3), "Strings with common suffixes should return the correct Damerau-Levenshtein distance.");
+    }
+
+    [Test]
+    public void Calculate_Transpositions_ReturnsCorrectValue()
+    {
+        var str1 = "abcd";
+        var str2 = "acbd";
+        var result = DamerauLevenshteinDistance.Calculate(str1, str2);
+        Assert.That(result, Is.EqualTo(1), "Strings with transpositions should return the correct Damerau-Levenshtein distance.");
+    }
+
+    [Test]
+    public void Calculate_RepeatedCharacters_ReturnsCorrectValue()
+    {
+        var str1 = "aaa";
+        var str2 = "aaaaa";
+        var result = DamerauLevenshteinDistance.Calculate(str1, str2);
+        Assert.That(result, Is.EqualTo(2), "Strings with repeated characters should return the correct Damerau-Levenshtein distance.");
+    }
+
+    [Test]
+    public void Calculate_UnicodeCharacters_ReturnsCorrectValue()
+    {
+        var str1 = "こんにちは";
+        var str2 = "こんばんは";
+        var result = DamerauLevenshteinDistance.Calculate(str1, str2);
+        Assert.That(result, Is.EqualTo(2), "Strings with Unicode characters should return the correct Damerau-Levenshtein distance.");
+    }
+}

Algorithms/Strings/Similarity/DamerauLevenshteinDistance.cs

@@ -0,0 +1,104 @@
+using System;
+
+namespace Algorithms.Strings.Similarity;
+
+public static class DamerauLevenshteinDistance
+{
+    /// <summary>
+    /// Calculates the Damerau-Levenshtein distance between two strings.
+    /// The Damerau-Levenshtein distance is a string metric for measuring the difference between two sequences.
+    /// It is calculated as the minimum number of operations needed to transform one sequence into the other.
+    /// The possible operations are insertion, deletion, substitution, and transposition.
+    /// </summary>
+    /// <param name="left">The first string.</param>
+    /// <param name="right">The second string.</param>
+    /// <returns>The Damerau-Levenshtein distance between the two strings.</returns>
+    public static int Calculate(string left, string right)
+    {
+        // Get the lengths of the input strings.
+        var leftSize = left.Length;
+        var rightSize = right.Length;
+
+        // Initialize a matrix of distances between the two strings.
+        var distances = InitializeDistanceArray(leftSize, rightSize);
+
+        // Iterate over each character in the left string.
+        for (var i = 1; i < leftSize + 1; i++)
+        {
+            // Iterate over each character in the right string.
+            for (var j = 1; j < rightSize + 1; j++)
+            {
+                // Calculate the cost of the current operation.
+                // If the characters at the current positions are the same, the cost is 0.
+                // Otherwise, the cost is 1.
+                var cost = left[i - 1] == right[j - 1] ? 0 : 1;
+
+                // Calculate the minimum distance by considering three possible operations:
+                // deletion, insertion, and substitution.
+                distances[i, j] = Math.Min(
+                    Math.Min( // deletion
+                        distances[i - 1, j] + 1, // delete the character from the left string
+                        distances[i, j - 1] + 1), // insert the character into the right string
+                    distances[i - 1, j - 1] + cost); // substitute the character in the left string with the character in the right string
+
+                // If the current character in the left string is the same as the character
+                // two positions to the left in the right string and the current character
+                // in the right string is the same as the character one position to the right
+                // in the left string, then we can also consider a transposition operation.
+                if (i > 1 && j > 1 && left[i - 1] == right[j - 2] && left[i - 2] == right[j - 1])
+                {
+                    distances[i, j] = Math.Min(
+                        distances[i, j], // current minimum distance
+                        distances[i - 2, j - 2] + cost); // transpose the last two characters
+                }
+            }
+        }
+
+        // Return the distance between the two strings.
+        return distances[leftSize, rightSize];
+    }
+
+    /// <summary>
+    /// Initializes a matrix of distances between two string representations.
+    ///
+    /// This method creates a matrix of distances where the dimensions are one larger
+    /// than the input strings. The first row of the matrix represents the distances
+    /// when the left string is empty, and the first column represents the distances
+    /// when the right string is empty. The values in the first row and first column
+    /// are the lengths of the corresponding strings.
+    ///
+    /// The matrix is used by the Damerau-Levenshtein algorithm to calculate the
+    /// minimum number of single-character edits (insertions, deletions, or substitutions)
+    /// required to change one word into the other.
+    /// The matrix is initialized with dimensions one larger than the input strings.
+    /// The first row of the matrix represents the distances when the left string is empty.
+    /// The first column of the matrix represents the distances when the right string is empty.
+    /// The values in the first row and first column are the lengths of the corresponding strings.
+    /// Initializes a matrix of distances between two strings representations.
+    /// </summary>
+    /// <param name="leftSize">The size of the left string.</param>
+    /// <param name="rightSize">The size of the right string.</param>
+    /// <returns>A matrix of distances.</returns>
+    private static int[,] InitializeDistanceArray(int leftSize, int rightSize)
+    {
+        // Initialize a matrix of distances with dimensions one larger than the input strings.
+        var matrix = new int[leftSize + 1, rightSize + 1];
+
+        // Set the values in the first row to the lengths of the left string.
+        // This represents the distance when the left string is empty.
+        for (var i = 1; i < leftSize + 1; i++)
+        {
+            matrix[i, 0] = i;
+        }
+
+        // Set the values in the first column to the lengths of the right string.
+        // This represents the distance when the right string is empty.
+        for (var i = 1; i < rightSize + 1; i++)
+        {
+            matrix[0, i] = i;
+        }
+
+        // Return the initialized matrix of distances.
+        return matrix;
+    }
+}

README.md

@@ -179,6 +179,7 @@ find more than one implementation for the same objective but using different alg
   * [String](./Algorithms/Strings)
     * [Similarity](./Algorithms/Strings/Similarity/)
       * [Cosine Similarity](./Algorithms/Strings/Similarity/CosineSimilarity.cs)
+      * [Damerau-Levenshtein Distance](./Algorithms/Strings/Similarity/DamerauLevenshteinDistance.cs)
       * [Hamming Distance](./Algorithms/Strings/Similarity/HammingDistance.cs)
       * [Jaro Similarity](./Algorithms/Strings/Similarity/JaroSimilarity.cs)
       * [Jaro-Winkler Distance](./Algorithms/Strings/Similarity/JaroWinklerDistance.cs)