cycle detector

src/graph/DirectedGraph.cs

@@ -1,4 +1,5 @@
 using System;
+using System.Collections;
 using System.Collections.Generic;
 using System.Linq;
 
@@ -12,8 +13,21 @@ namespace Encompass
 
     public class DirectedGraph<T>
     {
+        private class SimpleCycleComparer : IEqualityComparer<IEnumerable<T>>
+        {
+            public bool Equals(IEnumerable<T> x, IEnumerable<T> y)
+            {
+                return Enumerable.SequenceEqual(x, y);
+            }
+
+            public int GetHashCode(IEnumerable<T> obj)
+            {
+                return obj.Aggregate(0, (current, next) => current.GetHashCode() ^ next.GetHashCode());
+            }
+        }
+
         protected List<T> _vertices = new List<T>();
-        protected Dictionary<T, List<T>> _edges = new Dictionary<T, List<T>>();
+        protected Dictionary<T, List<T>> _neighbors = new Dictionary<T, List<T>>();
 
         public IEnumerable<T> Vertices { get { return _vertices; } }
 
@@ -26,7 +40,7 @@ namespace Encompass
             if (!VertexExists(vertex))
             {
                 _vertices.Add(vertex);
-                _edges.Add(vertex, new List<T>());
+                _neighbors.Add(vertex, new List<T>());
             }
         }
 
@@ -45,14 +59,25 @@ namespace Encompass
 
         public void RemoveVertex(T vertex)
         {
+            var edgesToRemove = new List<Tuple<T, T>>();
+
             if (VertexExists(vertex))
             {
-                foreach (var u in Neighbors(vertex))
+                foreach (var entry in _neighbors)
                 {
-                    RemoveEdge(vertex, u);
+                    if (entry.Value.Contains(vertex))
+                    {
+                        edgesToRemove.Add(Tuple.Create(entry.Key, vertex));
+                    }
+                }
+
+                foreach (var edge in edgesToRemove)
+                {
+                    RemoveEdge(edge.Item1, edge.Item2);
                 }
 
                 _vertices.Remove(vertex);
+                _neighbors.Remove(vertex);
             }
         }
 
@@ -60,7 +85,7 @@ namespace Encompass
         {
             if (VertexExists(v) && VertexExists(u))
             {
-                _edges[v].Add(u);
+                _neighbors[v].Add(u);
             }
         }
 
@@ -74,14 +99,14 @@ namespace Encompass
 
         public void RemoveEdge(T v, T u)
         {
-            _edges[v].Remove(u);
+            _neighbors[v].Remove(u);
         }
 
         public IEnumerable<T> Neighbors(T vertex)
         {
             if (VertexExists(vertex))
             {
-                return _edges[vertex];
+                return _neighbors[vertex];
             }
             else
             {
@@ -226,5 +251,163 @@ namespace Encompass
 
             return result;
         }
+
+        public IEnumerable<IEnumerable<T>> SimpleCycles()
+        {
+            Action<T, HashSet<T>, Dictionary<T, HashSet<T>>> unblock = null;
+            unblock = (T thisnode, HashSet<T> blocked, Dictionary<T, HashSet<T>> B) =>
+            {
+                var stack = new Stack<T>();
+                stack.Push(thisnode);
+
+                while (stack.Count > 0)
+                {
+                    var node = stack.Pop();
+                    if (blocked.Contains(thisnode))
+                    {
+                        blocked.Remove(thisnode);
+                        if (B.ContainsKey(node))
+                        {
+                            foreach (var n in B[node])
+                            {
+                                if (!stack.Contains(n))
+                                {
+                                    stack.Push(n);
+                                }
+                            }
+                            B[node].Clear();
+                        }
+                    }
+                }
+            };
+
+            List<List<T>> result = new List<List<T>>();
+            var subGraph = Clone();
+
+            var sccs = new Stack<IEnumerable<T>>();
+            foreach (var scc in StronglyConnectedComponents())
+            {
+                sccs.Push(scc);
+            }
+
+            while (sccs.Count > 0)
+            {
+                var scc = new Stack<T>(sccs.Pop());
+                var startNode = scc.Pop();
+                var path = new Stack<T>();
+                path.Push(startNode);
+                var blocked = new HashSet<T>();
+                blocked.Add(startNode);
+                var closed = new HashSet<T>();
+                var B = new Dictionary<T, HashSet<T>>();
+                var stack = new Stack<Tuple<T, Stack<T>>>();
+                stack.Push(Tuple.Create(startNode, new Stack<T>(subGraph.Neighbors(startNode))));
+
+                while (stack.Count > 0)
+                {
+                    var entry = stack.Peek();
+                    var thisnode = entry.Item1;
+                    var neighbors = entry.Item2;
+
+                    if (neighbors.Count > 0)
+                    {
+                        var nextNode = neighbors.Pop();
+
+                        if (nextNode.Equals(startNode))
+                        {
+                            var resultPath = new List<T>();
+                            foreach (var v in path)
+                            {
+                                resultPath.Add(v);
+                            }
+                            result.Add(resultPath);
+                            foreach (var v in path)
+                            {
+                                closed.Add(v);
+                            }
+                        }
+                        else if (!blocked.Contains(nextNode))
+                        {
+                            path.Push(nextNode);
+                            stack.Push(Tuple.Create(nextNode, new Stack<T>(subGraph.Neighbors(nextNode))));
+                            closed.Remove(nextNode);
+                            blocked.Add(nextNode);
+                            continue;
+                        }
+                    }
+
+                    if (neighbors.Count == 0)
+                    {
+                        if (closed.Contains(thisnode))
+                        {
+                            unblock(thisnode, blocked, B);
+                        }
+                        else
+                        {
+                            foreach (var neighbor in subGraph.Neighbors(thisnode))
+                            {
+                                if (!B.ContainsKey(neighbor))
+                                {
+                                    B[neighbor] = new HashSet<T>();
+                                }
+                                B[neighbor].Add(thisnode);
+                            }
+                        }
+
+                        stack.Pop();
+                        path.Pop();
+                    }
+                }
+
+                subGraph.RemoveVertex(startNode);
+                var H = subGraph.SubGraph(scc.ToArray());
+                var HSccs = H.StronglyConnectedComponents();
+                foreach (var HScc in HSccs)
+                {
+                    sccs.Push(HScc);
+                }
+            }
+
+            return result.Distinct(new SimpleCycleComparer());
+        }
+
+        public DirectedGraph<T> Clone()
+        {
+            var clone = new DirectedGraph<T>();
+            clone.AddVertices(Vertices.ToArray());
+
+            foreach (var v in Vertices)
+            {
+                foreach (var n in Neighbors(v))
+                {
+                    clone.AddEdge(v, n);
+                }
+            }
+
+            return clone;
+        }
+
+        public DirectedGraph<T> SubGraph(params T[] subVertices)
+        {
+            var subGraph = new DirectedGraph<T>();
+            subGraph.AddVertices(subVertices.ToArray());
+
+            foreach (var v in Vertices)
+            {
+                if (Vertices.Contains(v))
+                {
+                    var neighbors = Neighbors(v);
+                    foreach (var u in neighbors)
+                    {
+                        if (subVertices.Contains(u))
+                        {
+                            subGraph.AddEdge(v, u);
+                        }
+                    }
+                }
+            }
+
+            return subGraph;
+        }
     }
 }

test/DirectedGraphTest.cs

@@ -77,6 +77,26 @@ namespace Tests
             Assert.That(myGraph.Neighbors(2), Does.Not.Contain(3));
             Assert.That(myGraph.Neighbors(2), Does.Contain(4));
         }
+
+        [Test]
+        public void RemoveVertex()
+        {
+            var myGraph = new DirectedGraph<int>();
+            myGraph.AddVertices(1, 2, 3, 4);
+            myGraph.AddEdges(
+                Tuple.Create(1, 2),
+                Tuple.Create(2, 3),
+                Tuple.Create(2, 4),
+                Tuple.Create(3, 4)
+            );
+
+            myGraph.RemoveVertex(2);
+
+            myGraph.Vertices.Should().NotContain(2);
+            myGraph.Neighbors(1).Should().NotContain(2);
+            myGraph.Neighbors(3).Should().Contain(4);
+        }
+
         [Test]
         public void NodeDFS()
         {
@@ -212,5 +232,119 @@ namespace Tests
             result.Should().ContainEquivalentOf(sccC);
             Assert.That(result.Count, Is.EqualTo(3));
         }
+
+        [Test]
+        public void Clone()
+        {
+            var myGraph = new DirectedGraph<int>();
+            myGraph.AddVertices(1, 2, 3, 4);
+            myGraph.AddEdges(
+                Tuple.Create(1, 1),
+                Tuple.Create(1, 2),
+                Tuple.Create(2, 3),
+                Tuple.Create(2, 1),
+                Tuple.Create(3, 4)
+            );
+
+            var clone = myGraph.Clone();
+            Assert.That(clone, Is.Not.EqualTo(myGraph));
+            clone.Vertices.Should().BeEquivalentTo(1, 2, 3, 4);
+            clone.Neighbors(1).Should().BeEquivalentTo(1, 2);
+            clone.Neighbors(2).Should().BeEquivalentTo(3, 1);
+            clone.Neighbors(3).Should().BeEquivalentTo(4);
+        }
+
+        [Test]
+        public void SubGraph()
+        {
+            var myGraph = new DirectedGraph<int>();
+            myGraph.AddVertices(1, 2, 3, 4);
+            myGraph.AddEdges(
+                Tuple.Create(1, 1),
+                Tuple.Create(1, 2),
+                Tuple.Create(2, 3),
+                Tuple.Create(2, 1),
+                Tuple.Create(3, 4)
+            );
+
+            var subGraph = myGraph.SubGraph(1, 2, 3);
+            subGraph.Vertices.Should().BeEquivalentTo(1, 2, 3);
+            subGraph.Neighbors(1).Should().BeEquivalentTo(1, 2);
+            subGraph.Neighbors(2).Should().BeEquivalentTo(1, 3);
+            subGraph.Neighbors(3).Should().NotContain(4);
+        }
+
+        [Test]
+        public void SimpleCyclesSimple()
+        {
+            var myGraph = new DirectedGraph<int>();
+            myGraph.AddVertices(0, 1, 2);
+            myGraph.AddEdges(
+                Tuple.Create(0, 0),
+                Tuple.Create(0, 1),
+                Tuple.Create(0, 2),
+                Tuple.Create(1, 2),
+                Tuple.Create(2, 0),
+                Tuple.Create(2, 1),
+                Tuple.Create(2, 2)
+            );
+
+            var result = myGraph.SimpleCycles();
+
+            var cycleA = new int[] { 0 };
+            var cycleB = new int[] { 0, 1, 2 };
+            var cycleC = new int[] { 0, 2 };
+            var cycleD = new int[] { 1, 2 };
+            var cycleE = new int[] { 2 };
+
+            result.Should().ContainEquivalentOf(cycleA);
+            result.Should().ContainEquivalentOf(cycleB);
+            result.Should().ContainEquivalentOf(cycleC);
+            result.Should().ContainEquivalentOf(cycleD);
+            result.Should().ContainEquivalentOf(cycleE);
+            result.Should().HaveCount(5);
+        }
+
+        [Test]
+        public void SimpleCyclesComplex()
+        {
+            var myGraph = new DirectedGraph<int>();
+            myGraph.AddVertices(0, 1, 2, 3, 4, 5, 6, 7, 8, 9);
+            myGraph.AddEdges(
+                Tuple.Create(0, 1),
+                Tuple.Create(1, 2),
+                Tuple.Create(2, 3),
+                Tuple.Create(3, 0),
+                Tuple.Create(0, 3),
+                Tuple.Create(3, 4),
+                Tuple.Create(4, 5),
+                Tuple.Create(5, 0),
+                Tuple.Create(0, 1),
+                Tuple.Create(1, 6),
+                Tuple.Create(6, 7),
+                Tuple.Create(7, 8),
+                Tuple.Create(8, 0),
+                Tuple.Create(8, 9)
+            );
+
+            var result = myGraph.SimpleCycles();
+            var cycleA = new int[] { 0, 3 };
+            var cycleB = new int[] { 0, 1, 2, 3, 4, 5 };
+            var cycleC = new int[] { 0, 1, 2, 3 };
+            var cycleD = new int[] { 0, 3, 4, 5 };
+            var cycleE = new int[] { 0, 1, 6, 7, 8 };
+
+            foreach (var cycle in result)
+            {
+                Console.WriteLine(string.Join(", ", cycle));
+            }
+
+            result.Should().ContainEquivalentOf(cycleA);
+            result.Should().ContainEquivalentOf(cycleB);
+            result.Should().ContainEquivalentOf(cycleC);
+            result.Should().ContainEquivalentOf(cycleD);
+            result.Should().ContainEquivalentOf(cycleE);
+            result.Should().HaveCount(5);
+        }
     }
 }