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Add Kosaraju Algorithm (#303)
Co-authored-by: Diego Delgado <diegodm223@outlook.com> Co-authored-by: diego <diego@ibertest.es>
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‎Algorithms.Tests/Graph/KosarajuTests.cs

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using Algorithms.Graph;
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using DataStructures.Graph;
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using NUnit.Framework;
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using FluentAssertions;
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using System.Collections.Generic;
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using System.Linq;
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namespace Algorithms.Tests.Graph
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{
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public class KosarajuTests
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{
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[Test]
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public void GetRepresentativesTest()
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{
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// Create a graph with some SCC.
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var graph = new DirectedWeightedGraph<int>(10);
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var vertex1 = graph.AddVertex(1);
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var vertex2 = graph.AddVertex(2);
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var vertex3 = graph.AddVertex(3);
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var vertex4 = graph.AddVertex(4);
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var vertex5 = graph.AddVertex(5);
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var vertex6 = graph.AddVertex(6);
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var vertex7 = graph.AddVertex(7);
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graph.AddEdge(vertex1, vertex2, 1);
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graph.AddEdge(vertex2, vertex3, 1);
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graph.AddEdge(vertex3, vertex1, 1);
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graph.AddEdge(vertex3, vertex2, 1);
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graph.AddEdge(vertex2, vertex4, 1);
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graph.AddEdge(vertex4, vertex5, 1);
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graph.AddEdge(vertex5, vertex4, 1);
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graph.AddEdge(vertex5, vertex6, 1);
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// Run the agorithm and obtain the representative vertex of the SCC to which each vertex belongs.
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Dictionary<Vertex<int>,Vertex<int>> result = Kosaraju<int>.GetRepresentatives(graph);
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// Check every Vertex belongs to a SCC
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result.Should().ContainKey(vertex1);
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result.Should().ContainKey(vertex2);
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result.Should().ContainKey(vertex3);
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result.Should().ContainKey(vertex4);
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result.Should().ContainKey(vertex5);
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result.Should().ContainKey(vertex6);
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result.Should().ContainKey(vertex7);
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// There should be 4 SCC: {1,2,3}, {4,5}, {6} and {7}
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// Vertices 1, 2 and 3 are a SCC
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result[vertex1].Should().Be(result[vertex2]).And.Be(result[vertex3]);
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// Vertices 4 and 5 are another SCC
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result[vertex4].Should().Be(result[vertex5]);
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// And the should have a different representative vertex
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result[vertex1].Should().NotBe(result[vertex4]);
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// Vertices 6 and 7 are their own SCC
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result[vertex6].Should().Be(vertex6);
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result[vertex7].Should().Be(vertex7);
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}
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[Test]
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public void GetSccTest()
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{
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// Create a graph with some SCC.
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var graph = new DirectedWeightedGraph<int>(10);
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var vertex1 = graph.AddVertex(1);
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var vertex2 = graph.AddVertex(2);
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var vertex3 = graph.AddVertex(3);
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var vertex4 = graph.AddVertex(4);
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var vertex5 = graph.AddVertex(5);
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var vertex6 = graph.AddVertex(6);
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var vertex7 = graph.AddVertex(7);
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graph.AddEdge(vertex1, vertex2, 1);
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graph.AddEdge(vertex2, vertex3, 1);
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graph.AddEdge(vertex3, vertex1, 1);
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graph.AddEdge(vertex3, vertex2, 1);
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graph.AddEdge(vertex2, vertex4, 1);
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graph.AddEdge(vertex4, vertex5, 1);
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graph.AddEdge(vertex5, vertex4, 1);
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graph.AddEdge(vertex5, vertex6, 1);
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// Run the algorithm and get SCC as lists of vertices.
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var scc = Kosaraju<int>.GetScc(graph);
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// There should be 4 SCC: {1,2,3}, {4,5}, {6} and {7}
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scc.Should().HaveCount(4);
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// Vertices 1, 2 and 3 are a SCC
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scc.First(c => c.Contains(vertex1)).Should().Contain(vertex2).And.Contain(vertex3);
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// Vertices 4 and 5 are another SCC
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scc.First(c => c.Contains(vertex4)).Should().Contain(vertex5);
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// Vertices 6 and 7 are their own SCC
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scc.First(c => c.Contains(vertex6)).Should().HaveCount(1);
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scc.First(c => c.Contains(vertex7)).Should().HaveCount(1);
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}
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}
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}

‎Algorithms/Graph/Kosaraju.cs

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using System.Collections.Generic;
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using System.Linq;
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using DataStructures.Graph;
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namespace Algorithms.Graph
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{
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/// <summary>
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/// Implementation of Kosaraju-Sharir's algorithm (also known as Kosaraju's algorithm) to find the
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/// strongly connected components (SCC) of a directed graph.
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/// See https://en.wikipedia.org/wiki/Kosaraju%27s_algorithm.
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/// </summary>
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/// <typeparam name="T">Vertex data type.</typeparam>
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public static class Kosaraju<T>
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{
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/// <summary>
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/// First DFS for Kosaraju algorithm: traverse the graph creating a reverse order explore list <paramref name="reversed"/>.
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/// </summary>
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/// <param name="v">Vertex to explore.</param>
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/// <param name="graph">Graph instance.</param>
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/// <param name="visited">List of already visited vertex.</param>
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/// <param name="reversed">Reversed list of vertex for the second DFS.</param>
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public static void Visit(Vertex<T> v, IDirectedWeightedGraph<T> graph, HashSet<Vertex<T>> visited, Stack<Vertex<T>> reversed)
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{
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if (visited.Contains(v))
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{
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return;
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}
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// Set v as visited
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visited.Add(v);
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// Push v in the stack.
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// This can also be done with a List, inserting v at the begining of the list
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// after visit the neighbors.
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reversed.Push(v);
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// Visit neighbors
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foreach (var u in graph.GetNeighbors(v))
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{
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Visit(u!, graph, visited, reversed);
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}
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}
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/// <summary>
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/// Second DFS for Kosaraju algorithm. Traverse the graph in reversed order
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/// assigning a root vertex for every vertex that belong to the same SCC.
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/// </summary>
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/// <param name="v">Vertex to assign.</param>
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/// <param name="root">Root vertext, representative of the SCC.</param>
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/// <param name="graph">Graph with vertex and edges.</param>
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/// <param name="roots">
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/// Dictionary that assigns to each vertex the root of the SCC to which it corresponds.
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/// </param>
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public static void Assign(Vertex<T> v, Vertex<T> root, IDirectedWeightedGraph<T> graph, Dictionary<Vertex<T>, Vertex<T>> roots)
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{
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// If v already has a representative vertex (root) already assigned, do nothing.
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if (roots.ContainsKey(v))
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{
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return;
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}
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// Assign the root to the vertex.
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roots.Add(v, root);
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// Assign the current root vertex to v neighbors.
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foreach (var u in graph.GetNeighbors(v))
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{
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Assign(u!, root, graph, roots);
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}
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}
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/// <summary>
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/// Find the representative vertex of the SCC for each vertex on the graph.
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/// </summary>
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/// <param name="graph">Graph to explore.</param>
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/// <returns>A dictionary that assigns to each vertex a root vertex of the SCC they belong. </returns>
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public static Dictionary<Vertex<T>, Vertex<T>> GetRepresentatives(IDirectedWeightedGraph<T> graph)
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{
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HashSet<Vertex<T>> visited = new HashSet<Vertex<T>>();
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Stack<Vertex<T>> reversedL = new Stack<Vertex<T>>();
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Dictionary<Vertex<T>, Vertex<T>> representatives = new Dictionary<Vertex<T>, Vertex<T>>();
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foreach (var v in graph.Vertices)
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{
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if (v != null)
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{
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Visit(v, graph, visited, reversedL);
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}
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}
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visited.Clear();
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while (reversedL.Count > 0)
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{
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Vertex<T> v = reversedL.Pop();
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Assign(v, v, graph, representatives);
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}
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return representatives;
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}
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/// <summary>
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/// Get the Strongly Connected Components for the graph.
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/// </summary>
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/// <param name="graph">Graph to explore.</param>
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/// <returns>An array of SCC.</returns>
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public static IEnumerable<Vertex<T>>[] GetScc(IDirectedWeightedGraph<T> graph)
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{
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var representatives = GetRepresentatives(graph);
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Dictionary<Vertex<T>, List<Vertex<T>>> scc = new Dictionary<Vertex<T>, List<Vertex<T>>>();
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foreach (var kv in representatives)
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{
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// Assign all vertex (key) that have the seem root (value) to a single list.
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if (scc.ContainsKey(kv.Value))
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{
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scc[kv.Value].Add(kv.Key);
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}
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else
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{
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scc.Add(kv.Value, new List<Vertex<T>> { kv.Key });
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}
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}
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return scc.Values.ToArray();
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}
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}
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}

‎README.md

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* [BreadthFirstSearch](./Algorithms/Graph/BreadthFirstSearch.cs)
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* [DepthFirstSearch](./Algorithms/Graph/DepthFirstSearch.cs)
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* [Dijkstra Shortest Path](./Algorithms/Graph/Dijkstra/DijkstraAlgorithm.cs)
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* [Kosaraju](./Algorithms/Graph/Kosaraju.cs)
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* [Knapsack problem](./Algorithms/Knapsack)
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* [Naive solver](./Algorithms/Knapsack/NaiveKnapsackSolver.cs)
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* [Dynamic Programming solver](./Algorithms/Knapsack/DynamicProgrammingKnapsackSolver.cs)

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