encompass-cs/src/graph/DirectedGraph.cs

using System;
using System.Collections.Generic;
using System.Linq;

namespace Encompass
{
    public enum SearchSymbol
    {
        start,
        finish
    }

    public class DirectedGraph<T>
    {
        protected List<T> _vertices = new List<T>();
        protected Dictionary<T, List<T>> _edges = new Dictionary<T, List<T>>();

        public IEnumerable<T> Vertices { get { return _vertices; } }

        /*
         * GRAPH STRUCTURE METHODS
         */

        public void AddVertex(T vertex)
        {
            if (!VertexExists(vertex))
            {
                _vertices.Add(vertex);
                _edges.Add(vertex, new List<T>());
            }
        }

        public void AddVertices(params T[] vertices)
        {
            foreach (var vertex in vertices)
            {
                AddVertex(vertex);
            }
        }

        public bool VertexExists(T vertex)
        {
            return Vertices.Contains(vertex);
        }

        public void RemoveVertex(T vertex)
        {
            if (VertexExists(vertex))
            {
                foreach (var u in Neighbors(vertex))
                {
                    RemoveEdge(vertex, u);
                }

                _vertices.Remove(vertex);
            }
        }

        public void AddEdge(T v, T u)
        {
            if (VertexExists(v) && VertexExists(u))
            {
                _edges[v].Add(u);
            }
        }

        public void AddEdges(params Tuple<T, T>[] edges)
        {
            foreach (var edge in edges)
            {
                AddEdge(edge.Item1, edge.Item2);
            }
        }

        public void RemoveEdge(T v, T u)
        {
            _edges[v].Remove(u);
        }

        public IEnumerable<T> Neighbors(T vertex)
        {
            if (VertexExists(vertex))
            {
                return _edges[vertex];
            }
            else
            {
                return Enumerable.Empty<T>();
            }
        }

        /*
         * GRAPH ANALYSIS METHODS
         */

        public Dictionary<T, Dictionary<SearchSymbol, uint>> NodeDFS()
        {
            var discovered = new HashSet<T>();
            uint time = 0;
            var output = new Dictionary<T, Dictionary<SearchSymbol, uint>>();

            foreach (var vertex in Vertices)
            {
                output.Add(vertex, new Dictionary<SearchSymbol, uint>());
            }

            Action<T> dfsHelper = null;
            dfsHelper = (T v) =>
            {
                discovered.Add(v);
                time += 1;
                output[v].Add(SearchSymbol.start, time);

                foreach (var neighbor in Neighbors(v))
                {
                    if (!discovered.Contains(neighbor))
                    {
                        dfsHelper(neighbor);
                    }
                }

                time += 1;
                output[v].Add(SearchSymbol.finish, time);
            };

            foreach (var vertex in Vertices)
            {
                if (!discovered.Contains(vertex))
                {
                    dfsHelper(vertex);
                }
            }

            return output;
        }

        public IEnumerable<T> TopologicalSort()
        {
            var dfs = NodeDFS();
            var priority = new SortedList<uint, T>();
            foreach (var entry in dfs)
            {
                priority.Add(entry.Value[SearchSymbol.finish], entry.Key);
            }
            return priority.Values.Reverse();
        }

        public IEnumerable<IEnumerable<T>> StronglyConnectedComponents()
        {
            var preorder = new Dictionary<T, uint>();
            var lowlink = new Dictionary<T, uint>();
            var sccFound = new Dictionary<T, bool>();
            var sccQueue = new Stack<T>();

            var result = new List<List<T>>();

            uint preorderCounter = 0;

            foreach (var source in Vertices)
            {
                if (!sccFound.ContainsKey(source))
                {
                    var queue = new Stack<T>();
                    queue.Push(source);

                    while (queue.Count > 0)
                    {
                        var v = queue.Peek();
                        if (!preorder.ContainsKey(v))
                        {
                            preorderCounter += 1;
                            preorder[v] = preorderCounter;
                        }

                        var done = true;
                        var vNeighbors = Neighbors(v);
                        foreach (var w in vNeighbors)
                        {
                            if (!preorder.ContainsKey(w))
                            {
                                queue.Push(w);
                                done = false;
                                break;
                            }
                        }

                        if (done)
                        {
                            lowlink[v] = preorder[v];
                            foreach (var w in vNeighbors)
                            {
                                if (!sccFound.ContainsKey(w))
                                {
                                    if (preorder[w] > preorder[v])
                                    {
                                        lowlink[v] = Math.Min(lowlink[v], lowlink[w]);
                                    }
                                    else
                                    {
                                        lowlink[v] = Math.Min(lowlink[v], preorder[w]);
                                    }
                                }
                            }
                            queue.Pop();
                            if (lowlink[v] == preorder[v])
                            {
                                sccFound[v] = true;
                                var scc = new List<T>();
                                scc.Add(v);
                                while (sccQueue.Count > 0 && preorder[sccQueue.Peek()] > preorder[v])
                                {
                                    var k = sccQueue.Pop();
                                    sccFound[k] = true;
                                    scc.Add(k);
                                }
                                result.Add(scc);
                            }
                            else
                            {
                                sccQueue.Push(v);
                            }
                        }
                    }
                }
            }

            return result;
        }
    }
}