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Add Damerau-Levenshtein Distance (#460)
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‎Algorithms.Tests/Strings/Similarity/DamerauLevenshteinDistanceTests.cs

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

‎Algorithms/Strings/Similarity/DamerauLevenshteinDistance.cs

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

‎README.md

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* [String](./Algorithms/Strings)
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* [Similarity](./Algorithms/Strings/Similarity/)
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* [Cosine Similarity](./Algorithms/Strings/Similarity/CosineSimilarity.cs)
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* [Damerau-Levenshtein Distance](./Algorithms/Strings/Similarity/DamerauLevenshteinDistance.cs)
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* [Hamming Distance](./Algorithms/Strings/Similarity/HammingDistance.cs)
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* [Jaro Similarity](./Algorithms/Strings/Similarity/JaroSimilarity.cs)
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* [Jaro-Winkler Distance](./Algorithms/Strings/Similarity/JaroWinklerDistance.cs)

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