From cb60c4ebd395e73e9a0714b7300efb884c84104f Mon Sep 17 00:00:00 2001
From: Evan Hemsley <evan@moonside.games>
Date: Sat, 15 Jun 2019 14:47:55 -0700
Subject: [PATCH] started on directed graph implementation

---
 src/encompass-cs.csproj    |   1 +
 src/graph/DirectedGraph.cs | 230 +++++++++++++++++++++++++++++++++++++
 test/DirectedGraphTest.cs  | 216 ++++++++++++++++++++++++++++++++++
 test/test.csproj           |   2 +
 4 files changed, 449 insertions(+)
 create mode 100644 src/graph/DirectedGraph.cs
 create mode 100644 test/DirectedGraphTest.cs

diff --git a/src/encompass-cs.csproj b/src/encompass-cs.csproj
index a625a72..72e33ce 100644
--- a/src/encompass-cs.csproj
+++ b/src/encompass-cs.csproj
@@ -15,5 +15,6 @@
     <Content Include="Engine.cs" />
     <Content Include="attributes\Mutates.cs" />
     <Content Include="exceptions\IllegalComponentMutationException.cs" />
+    <Content Include="graph\DirectedGraph.cs" />
   </ItemGroup>
 </Project>
\ No newline at end of file
diff --git a/src/graph/DirectedGraph.cs b/src/graph/DirectedGraph.cs
new file mode 100644
index 0000000..9aba493
--- /dev/null
+++ b/src/graph/DirectedGraph.cs
@@ -0,0 +1,230 @@
+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;
+        }
+    }
+}
diff --git a/test/DirectedGraphTest.cs b/test/DirectedGraphTest.cs
new file mode 100644
index 0000000..a7e2652
--- /dev/null
+++ b/test/DirectedGraphTest.cs
@@ -0,0 +1,216 @@
+using NUnit.Framework;
+using FluentAssertions;
+
+using System;
+using System.Linq;
+
+using Encompass;
+using System.Collections.Generic;
+
+namespace Tests
+{
+    public class DirectedGraphTest
+    {
+        [Test]
+        public void AddVertex()
+        {
+            var myGraph = new DirectedGraph<int>();
+            myGraph.AddVertex(4);
+
+            Assert.That(myGraph.Vertices, Does.Contain(4));
+        }
+
+        [Test]
+        public void AddVertices()
+        {
+            var myGraph = new DirectedGraph<int>();
+            myGraph.AddVertices(4, 20, 69);
+
+            Assert.IsTrue(myGraph.VertexExists(4));
+            Assert.IsTrue(myGraph.VertexExists(20));
+            Assert.IsTrue(myGraph.VertexExists(69));
+        }
+
+        [Test]
+        public void AddEdge()
+        {
+            var myGraph = new DirectedGraph<int>();
+            myGraph.AddVertices(5, 6);
+            myGraph.AddEdge(5, 6);
+
+            Assert.That(myGraph.Neighbors(5), Does.Contain(6));
+        }
+
+        [Test]
+        public void AddEdges()
+        {
+            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)
+            );
+
+            Assert.That(myGraph.Neighbors(1), Does.Contain(2));
+            Assert.That(myGraph.Neighbors(2), Does.Contain(3));
+            Assert.That(myGraph.Neighbors(2), Does.Contain(4));
+            Assert.That(myGraph.Neighbors(3), Does.Contain(4));
+            Assert.That(myGraph.Neighbors(1), Does.Not.Contain(4));
+        }
+
+        [Test]
+        public void RemoveEdge()
+        {
+            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.RemoveEdge(2, 3);
+
+            Assert.That(myGraph.Neighbors(2), Does.Not.Contain(3));
+            Assert.That(myGraph.Neighbors(2), Does.Contain(4));
+        }
+        [Test]
+        public void NodeDFS()
+        {
+            var myGraph = new DirectedGraph<char>();
+            myGraph.AddVertices('a', 'b', 'c', 'd');
+            myGraph.AddEdges(
+                Tuple.Create('a', 'b'),
+                Tuple.Create('a', 'c'),
+                Tuple.Create('b', 'd')
+            );
+
+            var result = myGraph.NodeDFS();
+
+            Assert.That(result['a'][SearchSymbol.start], Is.EqualTo(1));
+            Assert.That(result['a'][SearchSymbol.finish], Is.EqualTo(8));
+
+            Assert.That(result['b'][SearchSymbol.start], Is.EqualTo(2));
+            Assert.That(result['b'][SearchSymbol.finish], Is.EqualTo(5));
+
+            Assert.That(result['c'][SearchSymbol.start], Is.EqualTo(6));
+            Assert.That(result['c'][SearchSymbol.finish], Is.EqualTo(7));
+
+            Assert.That(result['d'][SearchSymbol.start], Is.EqualTo(3));
+            Assert.That(result['d'][SearchSymbol.finish], Is.EqualTo(4));
+        }
+
+        [Test]
+        public void TopologicalSortSimple()
+        {
+            var simpleGraph = new DirectedGraph<char>();
+            simpleGraph.AddVertices('a', 'b', 'c', 'd');
+            simpleGraph.AddEdges(
+                Tuple.Create('a', 'b'),
+                Tuple.Create('a', 'c'),
+                Tuple.Create('b', 'a'),
+                Tuple.Create('b', 'd')
+            );
+
+            Assert.That(simpleGraph.TopologicalSort(), Is.EqualTo(new char[] { 'a', 'c', 'b', 'd' }));
+        }
+
+        [Test]
+        public void TopologicalSortComplex()
+        {
+            var complexGraph = new DirectedGraph<char>();
+            complexGraph.AddVertices('a', 'b', 'c', 'd', 'e', 'f', 'g', 't', 'm');
+            complexGraph.AddEdges(
+                Tuple.Create('a', 'b'),
+                Tuple.Create('a', 'c'),
+                Tuple.Create('a', 'd'),
+                Tuple.Create('b', 'f'),
+                Tuple.Create('b', 'g'),
+                Tuple.Create('c', 'g'),
+                Tuple.Create('e', 't'),
+                Tuple.Create('t', 'm')
+            );
+
+            Assert.That(
+                complexGraph.TopologicalSort(),
+                Is.EqualTo(new char[] { 'e', 't', 'm', 'a', 'd', 'c', 'b', 'g', 'f' })
+            );
+        }
+
+        [Test]
+        public void StronglyConnectedComponentsSimple()
+        {
+            var simpleGraph = new DirectedGraph<int>();
+            simpleGraph.AddVertices(1, 2, 3);
+            simpleGraph.AddEdges(
+                Tuple.Create(1, 2),
+                Tuple.Create(2, 3),
+                Tuple.Create(3, 2),
+                Tuple.Create(2, 1)
+            );
+
+            var result = simpleGraph.StronglyConnectedComponents();
+            var scc = new int[] { 1, 2, 3 };
+
+            result.Should().ContainEquivalentOf(scc);
+            Assert.That(result.Count, Is.EqualTo(1));
+        }
+
+        [Test]
+        public void StronglyConnectedComponentsMedium()
+        {
+            var mediumGraph = new DirectedGraph<int>();
+            mediumGraph.AddVertices(1, 2, 3, 4);
+            mediumGraph.AddEdges(
+                Tuple.Create(1, 2),
+                Tuple.Create(1, 3),
+                Tuple.Create(1, 4),
+                Tuple.Create(4, 2),
+                Tuple.Create(3, 4),
+                Tuple.Create(2, 3)
+            );
+
+            var result = mediumGraph.StronglyConnectedComponents();
+            var sccA = new int[] { 2, 3, 4 };
+            var sccB = new int[] { 1 };
+
+            result.Should().ContainEquivalentOf(sccA);
+            result.Should().ContainEquivalentOf(sccB);
+            Assert.That(result.Count, Is.EqualTo(2));
+        }
+
+        [Test]
+        public void StronglyConnectedComponentsComplex()
+        {
+            var complexGraph = new DirectedGraph<int>();
+            complexGraph.AddVertices(1, 2, 3, 4, 5, 6, 7, 8);
+            complexGraph.AddEdges(
+                Tuple.Create(1, 2),
+                Tuple.Create(2, 3),
+                Tuple.Create(2, 8),
+                Tuple.Create(3, 4),
+                Tuple.Create(3, 7),
+                Tuple.Create(4, 5),
+                Tuple.Create(5, 3),
+                Tuple.Create(5, 6),
+                Tuple.Create(7, 4),
+                Tuple.Create(7, 6),
+                Tuple.Create(8, 1),
+                Tuple.Create(8, 7)
+            );
+
+            var result = complexGraph.StronglyConnectedComponents();
+            var sccA = new int[] { 3, 4, 5, 7 };
+            var sccB = new int[] { 1, 2, 8 };
+            var sccC = new int[] { 6 };
+
+            result.Should().ContainEquivalentOf(sccA);
+            result.Should().ContainEquivalentOf(sccB);
+            result.Should().ContainEquivalentOf(sccC);
+            Assert.That(result.Count, Is.EqualTo(3));
+        }
+    }
+}
diff --git a/test/test.csproj b/test/test.csproj
index 7b887e7..e69bcea 100644
--- a/test/test.csproj
+++ b/test/test.csproj
@@ -5,6 +5,7 @@
     <IsPackable>false</IsPackable>
   </PropertyGroup>
   <ItemGroup>
+    <PackageReference Include="FluentAssertions" Version="5.7.0" />
     <PackageReference Include="nunit" Version="3.11.0" />
     <PackageReference Include="NUnit3TestAdapter" Version="3.11.0" />
     <PackageReference Include="Microsoft.NET.Test.Sdk" Version="15.9.0" />
@@ -13,5 +14,6 @@
   <ItemGroup>
     <ProjectReference Include="..\src\encompass-cs.csproj" />
     <Content Include="EngineTest.cs" />
+    <Content Include="DirectedGraphTest.cs" />
   </ItemGroup>
 </Project>
\ No newline at end of file