CyclesDetector.cs

/***
 * Detects if a given graph is cyclic. Supports directed and undirected graphs.
 */

using System;
using System.Collections.Generic;
using Algorithms.Common;
using DataStructures.Graphs;

namespace Algorithms.Graphs
{
    /// <summary>
    /// Implements Cycles Detection in Graphs
    /// </summary>
    public static class CyclesDetector
    {
        /// <summary>
        /// [Undirected DFS Forest].
        /// Helper function used to decide whether the graph explored from a specific vertex contains a cycle.
        /// </summary>
        /// <param name="graph">The graph to explore.</param>
        /// <param name="source">The vertex to explore graph from.</param>
        /// <param name="parent">The predecessor node to the vertex we are exploring the graph from.</param>
        /// <param name="visited">A hash set of the explored nodes so far.</param>
        /// <returns>True if there is a cycle; otherwise, false.</returns>
        private static bool _isUndirectedCyclic<T>(IGraph<T> graph, T source, object parent, ref HashSet<T> visited) where T : IComparable<T>
        {
            if (!visited.Contains(source))
            {
                // Mark the current node as visited
                visited.Add(source);

                // Recur for all the vertices adjacent to this vertex
                foreach (var adjacent in graph.Neighbours(source))
                {
                    // If an adjacent node was not visited, then check the DFS forest of the adjacent for UNdirected cycles.
                    if (!visited.Contains(adjacent) && _isUndirectedCyclic<T>(graph, adjacent, source, ref visited))
                        return true;

                    // If an adjacent is visited and NOT parent of current vertex, then there is a cycle.
                    if (parent != (object)null && !adjacent.IsEqualTo((T)parent))
                        return true;
                }
            }

            return false;
        }

        /// <summary>
        /// [Directed DFS Forest]
        /// Helper function used to decide whether the graph explored from a specific vertex contains a cycle.
        /// </summary>
        /// <param name="graph">The graph to explore.</param>
        /// <param name="source">The vertex to explore graph from.</param>
        /// <param name="parent">The predecessor node to the vertex we are exploring the graph from.</param>
        /// <param name="visited">A hash set of the explored nodes so far.</param>
        /// <param name="recursionStack">A set of element that are currently being processed.</param>
        /// <returns>True if there is a cycle; otherwise, false.</returns>
        private static bool _isDirectedCyclic<T>(IGraph<T> graph, T source, ref HashSet<T> visited, ref HashSet<T> recursionStack) where T : IComparable<T>
        {
            if (!visited.Contains(source))
            {
                // Mark the current node as visited and add it to the recursion stack
                visited.Add(source);
                recursionStack.Add(source);

                // Recur for all the vertices adjacent to this vertex
                foreach (var adjacent in graph.Neighbours(source))
                {
                    // If an adjacent node was not visited, then check the DFS forest of the adjacent for directed cycles.
                    if (!visited.Contains(adjacent) && _isDirectedCyclic<T>(graph, adjacent, ref visited, ref recursionStack))
                        return true;

                    // If an adjacent is visited and is on the recursion stack then there is a cycle.
                    if (recursionStack.Contains(adjacent))
                        return true;
                }
            }

            // Remove the source vertex from the recursion stack
            recursionStack.Remove(source);
            return false;
        }


        /// <summary>
        /// Returns true if Graph has cycle.
        /// </summary>
        public static bool IsCyclic<T>(IGraph<T> Graph) where T : IComparable<T>
        {
            if (Graph == null)
                throw new ArgumentNullException();

            var visited = new HashSet<T>();
            var recursionStack = new HashSet<T>();

            if (Graph.IsDirected)
            {
                foreach (var vertex in Graph.Vertices)
                    if (_isDirectedCyclic<T>(Graph, vertex, ref visited, ref recursionStack))
                        return true;
            }
            else
            {
                foreach (var vertex in Graph.Vertices)
                    if (_isUndirectedCyclic<T>(Graph, vertex, null, ref visited))
                        return true;
            }

            return false;
        }

    }

}