Add Traveling Salesman Problem (TSP) (#536)

Author: ngtduc693

Algorithms.Tests/Problems/TravelingSalesman/TravelingSalesmanSolverTests.cs

@@ -0,0 +1,121 @@
+using Algorithms.Problems.TravelingSalesman;
+using NUnit.Framework;
+
+namespace Algorithms.Tests.Problems.TravelingSalesman;
+
+/// <summary>
+/// Unit tests for TravelingSalesmanSolver. Covers brute-force and nearest neighbor methods, including edge cases and invalid input.
+/// </summary>
+[TestFixture]
+public class TravelingSalesmanSolverTests
+{
+    /// <summary>
+    /// Tests brute-force TSP solver on a 4-city symmetric distance matrix with known optimal route.
+    /// </summary>
+    [Test]
+    public void SolveBruteForce_KnownOptimalRoute_ReturnsCorrectResult()
+    {
+        // Distance matrix for 4 cities (symmetric, triangle inequality holds)
+        double[,] matrix =
+        {
+            { 0, 10, 15, 20 },
+            { 10, 0, 35, 25 },
+            { 15, 35, 0, 30 },
+            { 20, 25, 30, 0 }
+        };
+        var (route, distance) = TravelingSalesmanSolver.SolveBruteForce(matrix);
+        // Optimal route: 0 -> 1 -> 3 -> 2 -> 0, total distance = 80
+        Assert.That(distance, Is.EqualTo(80));
+        Assert.That(route, Is.EquivalentTo(new[] { 0, 1, 3, 2, 0 }));
+    }
+
+    /// <summary>
+    /// Tests nearest neighbor heuristic on the same matrix. May not be optimal.
+    /// </summary>
+    [Test]
+    public void SolveNearestNeighbor_Heuristic_ReturnsFeasibleRoute()
+    {
+        double[,] matrix =
+        {
+            { 0, 10, 15, 20 },
+            { 10, 0, 35, 25 },
+            { 15, 35, 0, 30 },
+            { 20, 25, 30, 0 }
+        };
+        var (route, distance) = TravelingSalesmanSolver.SolveNearestNeighbor(matrix, 0);
+        // Route: 0 -> 1 -> 3 -> 2 -> 0, total distance = 80
+        Assert.That(route.Length, Is.EqualTo(5));
+        Assert.That(route.First(), Is.EqualTo(0));
+        Assert.That(route.Last(), Is.EqualTo(0));
+        Assert.That(distance, Is.GreaterThanOrEqualTo(80)); // Heuristic may be optimal or suboptimal
+    }
+
+    /// <summary>
+    /// Tests nearest neighbor with invalid start index.
+    /// </summary>
+    [Test]
+    public void SolveNearestNeighbor_InvalidStart_ThrowsException()
+    {
+        double[,] matrix =
+        {
+            { 0, 1 },
+            { 1, 0 }
+        };
+        Assert.Throws<ArgumentOutOfRangeException>(() => TravelingSalesmanSolver.SolveNearestNeighbor(matrix, -1));
+        Assert.Throws<ArgumentOutOfRangeException>(() => TravelingSalesmanSolver.SolveNearestNeighbor(matrix, 2));
+    }
+    
+    /// <summary>
+    /// Tests nearest neighbor when no unvisited cities remain (should throw InvalidOperationException).
+    /// </summary>
+    [Test]
+    public void SolveNearestNeighbor_NoUnvisitedCities_ThrowsException()
+    {
+        // Construct a matrix where one city cannot be reached (simulate unreachable city)
+        double[,] matrix =
+        {
+            { 0, double.MaxValue, 1 },
+            { double.MaxValue, 0, double.MaxValue },
+            { 1, double.MaxValue, 0 }
+        };
+        // Start at city 0, city 1 is unreachable from both 0 and 2
+        Assert.Throws<InvalidOperationException>(() => TravelingSalesmanSolver.SolveNearestNeighbor(matrix, 0));
+    }
+
+    /// <summary>
+    /// Tests brute-force and nearest neighbor with non-square matrix.
+    /// </summary>
+    [Test]
+    public void NonSquareMatrix_ThrowsException()
+    {
+        double[,] matrix = new double[2, 3];
+        Assert.Throws<ArgumentException>(() => TravelingSalesmanSolver.SolveBruteForce(matrix));
+        Assert.Throws<ArgumentException>(() => TravelingSalesmanSolver.SolveNearestNeighbor(matrix, 0));
+    }
+
+    /// <summary>
+    /// Tests brute-force with less than two cities (invalid case).
+    /// </summary>
+    [Test]
+    public void SolveBruteForce_TooFewCities_ThrowsException()
+    {
+        double[,] matrix = { { 0 } };
+        Assert.Throws<ArgumentException>(() => TravelingSalesmanSolver.SolveBruteForce(matrix));
+    }
+
+    /// <summary>
+    /// Tests nearest neighbor with only two cities (trivial case).
+    /// </summary>
+    [Test]
+    public void SolveNearestNeighbor_TwoCities_ReturnsCorrectRoute()
+    {
+        double[,] matrix =
+        {
+            { 0, 5 },
+            { 5, 0 }
+        };
+        var (route, distance) = TravelingSalesmanSolver.SolveNearestNeighbor(matrix, 0);
+        Assert.That(route, Is.EquivalentTo(new[] { 0, 1, 0 }));
+        Assert.That(distance, Is.EqualTo(10));
+    }
+}

Algorithms.Tests/RecommenderSystem/CollaborativeFilteringTests.cs

@@ -89,5 +89,71 @@ public void PredictRating_WithOtherUserHavingRatedTargetItem_ShouldCalculateSimi
             Assert.That(predictedRating, Is.Not.EqualTo(0.0d));
             Assert.That(predictedRating, Is.EqualTo(3.5d).Within(0.01));
         }
+
+        [Test]
+        public void PredictRating_TargetUserNotExist_ThrowsOrReturnsZero()
+        {
+            Assert.Throws<KeyNotFoundException>(() => recommender!.PredictRating("item1", "nonexistentUser", testRatings));
+        }
+
+        [Test]
+        public void PredictRating_RatingsEmpty_ReturnsZero()
+        {
+            var emptyRatings = new Dictionary<string, Dictionary<string, double>>();
+            Assert.Throws<KeyNotFoundException>(() => recommender!.PredictRating("item1", "user1", emptyRatings));
+        }
+
+        [Test]
+        public void PredictRating_NoOtherUserRatedTargetItem_ReturnsZero()
+        {
+            var ratings = new Dictionary<string, Dictionary<string, double>>
+            {
+                ["user1"] = new() { ["item1"] = 5.0 },
+                ["user2"] = new() { ["item2"] = 4.0 }
+            };
+            var recommenderLocal = new CollaborativeFiltering(mockSimilarityCalculator!.Object);
+            var result = recommenderLocal.PredictRating("item2", "user1", ratings);
+            Assert.That(result, Is.EqualTo(0));
+        }
+
+        [Test]
+        public void CalculateSimilarity_EmptyDictionaries_ReturnsZero()
+        {
+            var recommenderLocal = new CollaborativeFiltering(mockSimilarityCalculator!.Object);
+            var result = recommenderLocal.CalculateSimilarity(new Dictionary<string, double>(), new Dictionary<string, double>());
+            Assert.That(result, Is.EqualTo(0));
+        }
+
+        [Test]
+        public void CalculateSimilarity_OneCommonItem_ReturnsZero()
+        {
+            var recommenderLocal = new CollaborativeFiltering(mockSimilarityCalculator!.Object);
+            var dict1 = new Dictionary<string, double> { ["item1"] = 5.0 };
+            var dict2 = new Dictionary<string, double> { ["item1"] = 5.0 };
+            var result = recommenderLocal.CalculateSimilarity(dict1, dict2);
+            Assert.That(result, Is.EqualTo(0));
+        }
+
+        [Test]
+        public void PredictRating_MultipleUsersWeightedSum_CorrectCalculation()
+        {
+            var ratings = new Dictionary<string, Dictionary<string, double>>
+            {
+                ["user1"] = new() { ["item1"] = 5.0 },
+                ["user2"] = new() { ["item1"] = 2.0 },
+                ["user3"] = new() { ["item1"] = 8.0 }
+            };
+            var mockSim = new Mock<ISimilarityCalculator>();
+            mockSim.Setup(s => s.CalculateSimilarity(It.IsAny<Dictionary<string, double>>(), ratings["user2"]))
+                .Returns(-0.5);
+            mockSim.Setup(s => s.CalculateSimilarity(It.IsAny<Dictionary<string, double>>(), ratings["user3"]))
+                .Returns(1.0);
+            var recommenderLocal = new CollaborativeFiltering(mockSim.Object);
+            var result = recommenderLocal.PredictRating("item1", "user1", ratings);
+            // weightedSum = (-0.5*2.0) + (1.0*8.0) = -1.0 + 8.0 = 7.0
+            // totalSimilarity = 0.5 + 1.0 = 1.5
+            // result = 7.0 / 1.5 = 4.666...
+            Assert.That(result, Is.EqualTo(4.666).Within(0.01));
+        }
     }
 }

Algorithms/Problems/TravelingSalesman/TravelingSalesmanSolver.cs

@@ -0,0 +1,136 @@
+namespace Algorithms.Problems.TravelingSalesman;
+
+/// <summary>
+/// Provides methods to solve the Traveling Salesman Problem (TSP) using brute-force and nearest neighbor heuristics.
+/// The TSP is a classic optimization problem in which a salesman must visit each city exactly once and return to the starting city, minimizing the total travel distance.
+/// </summary>
+public static class TravelingSalesmanSolver
+{
+    /// <summary>
+    /// Solves the TSP using brute-force search. This method checks all possible permutations of cities to find the shortest possible route.
+    /// WARNING: This approach is only feasible for small numbers of cities due to factorial time complexity.
+    /// </summary>
+    /// <param name="distanceMatrix">A square matrix where element [i, j] represents the distance from city i to city j.</param>
+    /// <returns>A tuple containing the minimal route (as an array of city indices) and the minimal total distance.</returns>
+    public static (int[] Route, double Distance) SolveBruteForce(double[,] distanceMatrix)
+    {
+        int n = distanceMatrix.GetLength(0);
+        if (n != distanceMatrix.GetLength(1))
+        {
+            throw new ArgumentException("Distance matrix must be square.");
+        }
+
+        if (n < 2)
+        {
+            throw new ArgumentException("At least two cities are required.");
+        }
+
+        var cities = Enumerable.Range(0, n).ToArray();
+        double minDistance = double.MaxValue;
+        int[]? bestRoute = null;
+
+        foreach (var perm in Permute(cities.Skip(1).ToArray()))
+        {
+            var route = new int[n + 1];
+            route[0] = 0;
+            for (int i = 0; i < perm.Length; i++)
+            {
+                route[i + 1] = perm[i];
+            }
+
+            // Ensure route ends at city 0
+            route[n] = 0;
+
+            double dist = 0;
+            for (int i = 0; i < n; i++)
+            {
+                dist += distanceMatrix[route[i], route[i + 1]];
+            }
+
+            if (dist < minDistance)
+            {
+                minDistance = dist;
+                bestRoute = (int[])route.Clone();
+            }
+        }
+
+        return (bestRoute ?? Array.Empty<int>(), minDistance);
+    }
+
+    /// <summary>
+    /// Solves the TSP using the nearest neighbor heuristic. This method builds a route by always visiting the nearest unvisited city next.
+    /// This approach is much faster but may not find the optimal solution.
+    /// </summary>
+    /// <param name="distanceMatrix">A square matrix where element [i, j] represents the distance from city i to city j.</param>
+    /// <param name="start">The starting city index.</param>
+    /// <returns>A tuple containing the route (as an array of city indices) and the total distance.</returns>
+    public static (int[] Route, double Distance) SolveNearestNeighbor(double[,] distanceMatrix, int start = 0)
+    {
+        int n = distanceMatrix.GetLength(0);
+        if (n != distanceMatrix.GetLength(1))
+        {
+            throw new ArgumentException("Distance matrix must be square.");
+        }
+
+        if (start < 0 || start >= n)
+        {
+            throw new ArgumentOutOfRangeException(nameof(start));
+        }
+
+        var visited = new bool[n];
+        var route = new List<int> { start };
+        visited[start] = true;
+        double totalDistance = 0;
+        int current = start;
+        for (int step = 1; step < n; step++)
+        {
+            double minDist = double.MaxValue;
+            int next = -1;
+            for (int j = 0; j < n; j++)
+            {
+                if (!visited[j] && distanceMatrix[current, j] < minDist)
+                {
+                    minDist = distanceMatrix[current, j];
+                    next = j;
+                }
+            }
+
+            if (next == -1)
+            {
+                throw new InvalidOperationException("No unvisited cities remain.");
+            }
+
+            route.Add(next);
+            visited[next] = true;
+            totalDistance += minDist;
+            current = next;
+        }
+
+        totalDistance += distanceMatrix[current, start];
+        route.Add(start);
+        return (route.ToArray(), totalDistance);
+    }
+
+    /// <summary>
+    /// Generates all permutations of the input array.
+    /// Used for brute-force TSP solution.
+    /// </summary>
+    private static IEnumerable<int[]> Permute(int[] arr)
+    {
+        if (arr.Length == 1)
+        {
+            yield return arr;
+        }
+        else
+        {
+            for (int i = 0; i < arr.Length; i++)
+            {
+                var rest = arr.Where((_, idx) => idx != i).ToArray();
+                foreach (var perm in Permute(rest))
+                {
+                    yield return new[] { arr[i] }.Concat(perm).ToArray();
+                }
+            }
+        }
+    }
+}