Add Cosine Similarity Algorithm for Strings (#459)

Algorithms.Tests/Strings/Similarity/CosineSimilarityTests.cs

@@ -0,0 +1,84 @@
+using System;
+using Algorithms.Strings.Similarity;
+using NUnit.Framework;
+
+namespace Algorithms.Tests.Strings.Similarity;
+
+[TestFixture]
+public class CosineSimilarityTests
+{
+    [Test]
+    public void Calculate_IdenticalStrings_ReturnsOne()
+    {
+        var str1 = "test";
+        var str2 = "test";
+        var result = CosineSimilarity.Calculate(str1, str2);
+        Assert.That(result, Is.EqualTo(1.0).Within(1e-6), "Identical strings should have a cosine similarity of 1.");
+    }
+
+    [Test]
+    public void Calculate_CompletelyDifferentStrings_ReturnsZero()
+    {
+        var str1 = "abc";
+        var str2 = "xyz";
+        var result = CosineSimilarity.Calculate(str1, str2);
+        Assert.That(result, Is.EqualTo(0.0).Within(1e-6), "Completely different strings should have a cosine similarity of 0.");
+    }
+
+    [Test]
+    public void Calculate_EmptyStrings_ReturnsZero()
+    {
+        var str1 = "";
+        var str2 = "";
+        var result = CosineSimilarity.Calculate(str1, str2);
+        Assert.That(result, Is.EqualTo(0.0).Within(1e-6), "Empty strings should have a cosine similarity of 0.");
+    }
+
+    [Test]
+    public void Calculate_OneEmptyString_ReturnsZero()
+    {
+        var str1 = "test";
+        var str2 = "";
+        var result = CosineSimilarity.Calculate(str1, str2);
+        Assert.That(result, Is.EqualTo(0.0).Within(1e-6), "Empty string should have a cosine similarity of 0.");
+    }
+
+    [Test]
+    public void Calculate_SameCharactersDifferentCases_ReturnsOne()
+    {
+        var str1 = "Test";
+        var str2 = "test";
+        var result = CosineSimilarity.Calculate(str1, str2);
+        Assert.That(result, Is.EqualTo(1.0).Within(1e-6), "The method should be case-insensitive.");
+    }
+
+    [Test]
+    public void Calculate_SpecialCharacters_ReturnsCorrectValue()
+    {
+        var str1 = "hello!";
+        var str2 = "hello!";
+        var result = CosineSimilarity.Calculate(str1, str2);
+        Assert.That(result, Is.EqualTo(1.0).Within(1e-6), "Strings with special characters should have a cosine similarity of 1.");
+    }
+
+    [Test]
+    public void Calculate_DifferentLengthWithCommonCharacters_ReturnsCorrectValue()
+    {
+        var str1 = "hello";
+        var str2 = "hello world";
+        var result = CosineSimilarity.Calculate(str1, str2);
+        var expected = 10 / (Math.Sqrt(7) * Math.Sqrt(19)); // calculated manually
+        Assert.That(result, Is.EqualTo(expected).Within(1e-6), "Strings with different lengths but some common characters should have the correct cosine similarity.");
+    }
+
+    [Test]
+    public void Calculate_PartiallyMatchingStrings_ReturnsCorrectValue()
+    {
+        var str1 = "night";
+        var str2 = "nacht";
+        var result = CosineSimilarity.Calculate(str1, str2);
+        // Assuming the correct calculation gives an expected value
+        var expected = 3.0 / 5.0;
+        Assert.That(result, Is.EqualTo(expected).Within(1e-6), "Partially matching strings should have the correct cosine similarity.");
+    }
+}

Algorithms/Strings/Similarity/CosineSimilarity.cs

@@ -0,0 +1,136 @@
+using System;
+using System.Collections.Generic;
+
+namespace Algorithms.Strings.Similarity;
+
+public static class CosineSimilarity
+{
+    /// <summary>
+    /// Calculates the Cosine Similarity between two strings.
+    /// Cosine Similarity is a measure of similarity between two non-zero vectors of an inner product space.
+    /// It measures the cosine of the angle between the two vectors.
+    /// </summary>
+    /// <param name="left">The first string.</param>
+    /// <param name="right">The second string.</param>
+    /// <returns>
+    /// A double value between 0 and 1 that represents the similarity
+    /// of the two strings.
+    /// </returns>
+    public static double Calculate(string left, string right)
+    {
+        // Step 1: Get the vectors for the two strings
+        // Each vector represents the frequency of each character in the string.
+        var vectors = GetVectors(left.ToLowerInvariant(), right.ToLowerInvariant());
+        var leftVector = vectors.leftVector;
+        var rightVector = vectors.rightVector;
+
+        // Step 2: Calculate the intersection of the two vectors
+        // The intersection is the set of characters that appear in both strings.
+        var intersection = GetIntersection(leftVector, rightVector);
+
+        // Step 3: Calculate the dot product of the two vectors
+        // The dot product is the sum of the products of the corresponding values of the characters in the intersection.
+        var dotProduct = DotProduct(leftVector, rightVector, intersection);
+
+        // Step 4: Calculate the square magnitude of each vector
+        // The magnitude is the square root of the sum of the squares of the values in the vector.
+        var mLeft = 0.0;
+        foreach (var value in leftVector.Values)
+        {
+            mLeft += value * value;
+        }
+
+        var mRight = 0.0;
+        foreach (var value in rightVector.Values)
+        {
+            mRight += value * value;
+        }
+
+        // Step 5: Check if either vector is zero
+        // If either vector is zero (i.e., all characters are unique), the Cosine Similarity is 0.
+        if (mLeft <= 0 || mRight <= 0)
+        {
+            return 0.0;
+        }
+
+        // Step 6: Calculate and return the Cosine Similarity
+        // The Cosine Similarity is the dot product divided by the product of the magnitudes.
+        return dotProduct / (Math.Sqrt(mLeft) * Math.Sqrt(mRight));
+    }
+
+    /// <summary>
+    /// Calculates the vectors for the given strings.
+    /// </summary>
+    /// <param name="left">The first string.</param>
+    /// <param name="right">The second string.</param>
+    /// <returns>A tuple containing the vectors for the two strings.</returns>
+    private static (Dictionary<char, int> leftVector, Dictionary<char, int> rightVector) GetVectors(string left, string right)
+    {
+        var leftVector = new Dictionary<char, int>();
+        var rightVector = new Dictionary<char, int>();
+
+        // Calculate the frequency of each character in the left string
+        foreach (var character in left)
+        {
+            leftVector.TryGetValue(character, out var frequency);
+            leftVector[character] = ++frequency;
+        }
+
+        // Calculate the frequency of each character in the right string
+        foreach (var character in right)
+        {
+            rightVector.TryGetValue(character, out var frequency);
+            rightVector[character] = ++frequency;
+        }
+
+        return (leftVector, rightVector);
+    }
+
+    /// <summary>
+    /// Calculates the dot product between two vectors represented as dictionaries of character frequencies.
+    /// The dot product is the sum of the products of the corresponding values of the characters in the intersection of the two vectors.
+    /// </summary>
+    /// <param name="leftVector">The vector of the left string.</param>
+    /// <param name="rightVector">The vector of the right string.</param>
+    /// <param name="intersection">The intersection of the two vectors, represented as a set of characters.</param>
+    /// <returns>The dot product of the two vectors.</returns>
+    private static double DotProduct(Dictionary<char, int> leftVector, Dictionary<char, int> rightVector, HashSet<char> intersection)
+    {
+        // Initialize the dot product to 0
+        double dotProduct = 0;
+
+        // Iterate over each character in the intersection of the two vectors
+        foreach (var character in intersection)
+        {
+            // Calculate the product of the corresponding values of the characters in the left and right vectors
+            dotProduct += leftVector[character] * rightVector[character];
+        }
+
+        // Return the dot product
+        return dotProduct;
+    }
+
+    /// <summary>
+    /// Calculates the intersection of two vectors, represented as dictionaries of character frequencies.
+    /// </summary>
+    /// <param name="leftVector">The vector of the left string.</param>
+    /// <param name="rightVector">The vector of the right string.</param>
+    /// <returns>A HashSet containing the characters that appear in both vectors.</returns>
+    private static HashSet<char> GetIntersection(Dictionary<char, int> leftVector, Dictionary<char, int> rightVector)
+    {
+        // Initialize a HashSet to store the intersection of the two vectors.
+        var intersection = new HashSet<char>();
+
+        // Iterate over each key-value pair in the left vector.
+        foreach (var kvp in leftVector)
+        {
+            // If the right vector contains the same key, add it to the intersection.
+            if (rightVector.ContainsKey(kvp.Key))
+            {
+                intersection.Add(kvp.Key);
+            }
+        }
+
+        return intersection;
+    }
+}

README.md

@@ -178,6 +178,7 @@ find more than one implementation for the same objective but using different alg
     * [A181391 Van Eck's](./Algorithms/Sequences/VanEcksSequence.cs)
   * [String](./Algorithms/Strings)
     * [Similarity](./Algorithms/Strings/Similarity/)
+      * [Cosine Similarity](./Algorithms/Strings/Similarity/CosineSimilarity.cs)
       * [Hamming Distance](./Algorithms/Strings/Similarity/HammingDistance.cs)
       * [Jaro Similarity](./Algorithms/Strings/Similarity/JaroSimilarity.cs)
       * [Jaro-Winkler Distance](./Algorithms/Strings/Similarity/JaroWinklerDistance.cs)