Add Bellman ford algorithm (TheAlgorithms#416)

Author: Kpraful

Algorithms.Tests/Graph/BellmanFordTests.cs

@@ -0,0 +1,75 @@
+using Algorithms.Graph;
+using DataStructures.Graph;
+using NUnit.Framework;
+using FluentAssertions;
+using System.Collections.Generic;
+using System;
+
+namespace Algorithms.Tests.Graph
+{
+    public class BellmanFordTests
+    {
+        [Test]
+        public void CorrectDistancesTest()
+        {
+            var graph = new DirectedWeightedGraph<int>(10);
+
+            var vertex1 = graph.AddVertex(1);
+            var vertex2 = graph.AddVertex(2);
+            var vertex3 = graph.AddVertex(3);
+            var vertex4 = graph.AddVertex(4);
+            var vertex5 = graph.AddVertex(5);
+
+            graph.AddEdge(vertex1, vertex2, 3);
+            graph.AddEdge(vertex1, vertex5, -4);
+            graph.AddEdge(vertex1, vertex3, 8);
+            graph.AddEdge(vertex2, vertex5, 7);
+            graph.AddEdge(vertex2, vertex4, 1);
+            graph.AddEdge(vertex3, vertex2, 4);
+            graph.AddEdge(vertex4, vertex3, -5);
+            graph.AddEdge(vertex4, vertex1, 2);
+            graph.AddEdge(vertex5, vertex4, 6);
+
+            var expectedDistances = new Dictionary<Vertex<int>, double>
+            {
+                { vertex1, 0 },
+                { vertex2, 1 },
+                { vertex3, -3 },
+                { vertex4, 2 },
+                { vertex5, -4 }
+            };
+
+            var bellmanFord = new BellmanFord<int>(graph, new Dictionary<Vertex<int>, double>(), new Dictionary<Vertex<int>, Vertex<int>?>());
+
+            var calculatedDistances = bellmanFord.Run(vertex1);
+
+            foreach (var vertex in graph.Vertices)
+            {
+                if (vertex != null)
+                {
+                    calculatedDistances[vertex].Should().BeApproximately(expectedDistances[vertex], 0.001);
+                }
+            }
+        }
+
+        [Test]
+        public void NegativeWeightCycleTest()
+        {
+            var graph = new DirectedWeightedGraph<int>(3);
+
+            var vertex1 = graph.AddVertex(1);
+            var vertex2 = graph.AddVertex(2);
+            var vertex3 = graph.AddVertex(3);
+
+            graph.AddEdge(vertex1, vertex2, -1);
+            graph.AddEdge(vertex2, vertex3, -2);
+            graph.AddEdge(vertex3, vertex1, -3);
+
+            var bellmanFord = new BellmanFord<int>(graph, new Dictionary<Vertex<int>, double>(), new Dictionary<Vertex<int>, Vertex<int>?>());
+
+            Action action = () => bellmanFord.Run(vertex1);
+
+            action.Should().Throw<InvalidOperationException>().WithMessage("Graph contains a negative weight cycle.");
+        }
+    }
+}

Algorithms/Graph/BellmanFord.cs

@@ -0,0 +1,120 @@
+using System;
+using System.Collections.Generic;
+using DataStructures.Graph;
+
+namespace Algorithms.Graph
+{
+    /// <summary>
+    /// Bellman-Ford algorithm on directed weighted graph.
+    /// </summary>
+    /// <typeparam name="T">Generic type of data in the graph.</typeparam>
+    public class BellmanFord<T>
+    {
+        private readonly DirectedWeightedGraph<T> graph;
+        private readonly Dictionary<Vertex<T>, double> distances;
+        private readonly Dictionary<Vertex<T>, Vertex<T>?> predecessors;
+
+        public BellmanFord(DirectedWeightedGraph<T> graph, Dictionary<Vertex<T>, double> distances, Dictionary<Vertex<T>, Vertex<T>?> predecessors)
+        {
+            this.graph = graph;
+            this.distances = distances;
+            this.predecessors = predecessors;
+        }
+
+        /// <summary>
+        /// Runs the Bellman-Ford algorithm to find the shortest distances from the source vertex to all other vertices.
+        /// </summary>
+        /// <param name="sourceVertex">Source vertex for shortest path calculation.</param>
+        /// <returns>
+        /// A dictionary containing the shortest distances from the source vertex to all other vertices.
+        /// If a vertex is unreachable from the source, it will have a value of double.PositiveInfinity.
+        /// </returns>
+        public Dictionary<Vertex<T>, double> Run(Vertex<T> sourceVertex)
+        {
+            InitializeDistances(sourceVertex);
+            RelaxEdges();
+            CheckForNegativeCycles();
+            return distances;
+        }
+
+        private void InitializeDistances(Vertex<T> sourceVertex)
+        {
+            foreach (var vertex in graph.Vertices)
+            {
+                if (vertex != null)
+                {
+                    distances[vertex] = double.PositiveInfinity;
+                    predecessors[vertex] = null;
+                }
+            }
+
+            distances[sourceVertex] = 0;
+        }
+
+        private void RelaxEdges()
+        {
+            int vertexCount = graph.Count;
+
+            for (int i = 0; i < vertexCount - 1; i++)
+            {
+                foreach (var vertex in graph.Vertices)
+                {
+                    if (vertex != null)
+                    {
+                        RelaxEdgesForVertex(vertex);
+                    }
+                }
+            }
+        }
+
+        private void RelaxEdgesForVertex(Vertex<T> u)
+        {
+            foreach (var neighbor in graph.GetNeighbors(u))
+            {
+                if (neighbor == null)
+                {
+                    continue;
+                }
+
+                var v = neighbor;
+                var weight = graph.AdjacentDistance(u, v);
+
+                if (distances[u] + weight < distances[v])
+                {
+                    distances[v] = distances[u] + weight;
+                    predecessors[v] = u;
+                }
+            }
+        }
+
+        private void CheckForNegativeCycles()
+        {
+            foreach (var vertex in graph.Vertices)
+            {
+                if (vertex != null)
+                {
+                    CheckForNegativeCyclesForVertex(vertex);
+                }
+            }
+        }
+
+        private void CheckForNegativeCyclesForVertex(Vertex<T> u)
+        {
+            foreach (var neighbor in graph.GetNeighbors(u))
+            {
+                if (neighbor == null)
+                {
+                    continue;
+                }
+
+                var v = neighbor;
+                var weight = graph.AdjacentDistance(u, v);
+
+                if (distances[u] + weight < distances[v])
+                {
+                    throw new InvalidOperationException("Graph contains a negative weight cycle.");
+                }
+            }
+        }
+    }
+}