420 lines
13 KiB
C#
420 lines
13 KiB
C#
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using System;
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using System.Collections.Generic;
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using System.Linq;
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namespace MoonTools.Core.Graph
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{
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public enum SearchSymbol
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{
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start,
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finish
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}
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public class DirectedGraph<T>
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{
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private class SimpleCycleComparer : IEqualityComparer<IEnumerable<T>>
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{
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public bool Equals(IEnumerable<T> x, IEnumerable<T> y)
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{
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return x.SequenceEqual(y);
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}
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public int GetHashCode(IEnumerable<T> obj)
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{
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return obj.Aggregate(0, (current, next) => current.GetHashCode() ^ next.GetHashCode());
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}
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}
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protected List<T> _vertices = new List<T>();
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protected Dictionary<T, HashSet<T>> _neighbors = new Dictionary<T, HashSet<T>>();
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public IEnumerable<T> Vertices { get { return _vertices; } }
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/*
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* GRAPH STRUCTURE METHODS
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*/
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public void AddVertex(T vertex)
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{
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if (!VertexExists(vertex))
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{
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_vertices.Add(vertex);
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_neighbors.Add(vertex, new HashSet<T>());
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}
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}
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public void AddVertices(params T[] vertices)
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{
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foreach (var vertex in vertices)
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{
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AddVertex(vertex);
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}
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}
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public bool VertexExists(T vertex)
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{
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return Vertices.Contains(vertex);
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}
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public void RemoveVertex(T vertex)
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{
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var edgesToRemove = new List<Tuple<T, T>>();
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if (VertexExists(vertex))
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{
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foreach (var entry in _neighbors)
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{
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if (entry.Value.Contains(vertex))
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{
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edgesToRemove.Add(Tuple.Create(entry.Key, vertex));
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}
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}
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foreach (var edge in edgesToRemove)
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{
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RemoveEdge(edge.Item1, edge.Item2);
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}
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_vertices.Remove(vertex);
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_neighbors.Remove(vertex);
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}
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}
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public void AddEdge(T v, T u)
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{
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if (VertexExists(v) && VertexExists(u))
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{
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_neighbors[v].Add(u);
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}
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}
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public void AddEdges(params Tuple<T, T>[] edges)
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{
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foreach (var edge in edges)
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{
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AddEdge(edge.Item1, edge.Item2);
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}
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}
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public void RemoveEdge(T v, T u)
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{
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_neighbors[v].Remove(u);
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}
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public IEnumerable<T> Neighbors(T vertex)
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{
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if (VertexExists(vertex))
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{
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return _neighbors[vertex];
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}
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else
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{
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return Enumerable.Empty<T>();
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}
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}
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/*
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* GRAPH ANALYSIS METHODS
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*/
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public Dictionary<T, Dictionary<SearchSymbol, uint>> NodeDFS()
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{
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var discovered = new HashSet<T>();
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uint time = 0;
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var output = new Dictionary<T, Dictionary<SearchSymbol, uint>>();
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foreach (var vertex in Vertices)
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{
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output.Add(vertex, new Dictionary<SearchSymbol, uint>());
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}
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void dfsHelper(T v)
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{
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discovered.Add(v);
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time++;
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output[v].Add(SearchSymbol.start, time);
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foreach (var neighbor in Neighbors(v))
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{
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if (!discovered.Contains(neighbor))
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{
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dfsHelper(neighbor);
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}
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}
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time++;
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output[v].Add(SearchSymbol.finish, time);
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}
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foreach (var vertex in Vertices)
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{
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if (!discovered.Contains(vertex))
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{
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dfsHelper(vertex);
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}
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}
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return output;
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}
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public bool Cyclic()
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{
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return StronglyConnectedComponents().Any((scc) => scc.Count() > 1);
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}
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public IEnumerable<T> TopologicalSort()
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{
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var dfs = NodeDFS();
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var priority = new SortedList<uint, T>();
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foreach (var entry in dfs)
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{
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priority.Add(entry.Value[SearchSymbol.finish], entry.Key);
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}
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return priority.Values.Reverse();
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}
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public IEnumerable<IEnumerable<T>> StronglyConnectedComponents()
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{
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var preorder = new Dictionary<T, uint>();
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var lowlink = new Dictionary<T, uint>();
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var sccFound = new Dictionary<T, bool>();
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var sccQueue = new Stack<T>();
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var result = new List<List<T>>();
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uint preorderCounter = 0;
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foreach (var source in Vertices)
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{
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if (!sccFound.ContainsKey(source))
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{
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var queue = new Stack<T>();
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queue.Push(source);
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while (queue.Count > 0)
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{
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var v = queue.Peek();
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if (!preorder.ContainsKey(v))
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{
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preorderCounter++;
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preorder[v] = preorderCounter;
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}
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var done = true;
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var vNeighbors = Neighbors(v);
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foreach (var w in vNeighbors)
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{
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if (!preorder.ContainsKey(w))
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{
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queue.Push(w);
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done = false;
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break;
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}
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}
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if (done)
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{
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lowlink[v] = preorder[v];
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foreach (var w in vNeighbors)
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{
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if (!sccFound.ContainsKey(w))
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{
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if (preorder[w] > preorder[v])
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{
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lowlink[v] = Math.Min(lowlink[v], lowlink[w]);
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}
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else
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{
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lowlink[v] = Math.Min(lowlink[v], preorder[w]);
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}
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}
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}
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queue.Pop();
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if (lowlink[v] == preorder[v])
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{
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sccFound[v] = true;
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var scc = new List<T>
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{
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v
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};
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while (sccQueue.Count > 0 && preorder[sccQueue.Peek()] > preorder[v])
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{
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var k = sccQueue.Pop();
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sccFound[k] = true;
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scc.Add(k);
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}
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result.Add(scc);
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}
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else
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{
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sccQueue.Push(v);
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}
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}
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}
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}
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}
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return result;
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}
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public IEnumerable<IEnumerable<T>> SimpleCycles()
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{
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void unblock(T thisnode, HashSet<T> blocked, Dictionary<T, HashSet<T>> B)
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{
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var stack = new Stack<T>();
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stack.Push(thisnode);
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while (stack.Count > 0)
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{
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var node = stack.Pop();
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if (blocked.Contains(thisnode))
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{
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blocked.Remove(thisnode);
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if (B.ContainsKey(node))
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{
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foreach (var n in B[node])
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{
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if (!stack.Contains(n))
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{
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stack.Push(n);
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}
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}
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B[node].Clear();
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}
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}
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}
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}
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List<List<T>> result = new List<List<T>>();
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var subGraph = Clone();
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var sccs = new Stack<IEnumerable<T>>();
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foreach (var scc in StronglyConnectedComponents())
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{
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sccs.Push(scc);
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}
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while (sccs.Count > 0)
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{
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var scc = new Stack<T>(sccs.Pop());
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var startNode = scc.Pop();
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var path = new Stack<T>();
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path.Push(startNode);
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var blocked = new HashSet<T>
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{
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startNode
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};
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var closed = new HashSet<T>();
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var B = new Dictionary<T, HashSet<T>>();
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var stack = new Stack<Tuple<T, Stack<T>>>();
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stack.Push(Tuple.Create(startNode, new Stack<T>(subGraph.Neighbors(startNode))));
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while (stack.Count > 0)
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{
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var entry = stack.Peek();
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var thisnode = entry.Item1;
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var neighbors = entry.Item2;
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if (neighbors.Count > 0)
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{
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var nextNode = neighbors.Pop();
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if (nextNode.Equals(startNode))
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{
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var resultPath = new List<T>();
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foreach (var v in path)
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{
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resultPath.Add(v);
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}
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result.Add(resultPath);
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foreach (var v in path)
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{
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closed.Add(v);
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}
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}
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else if (!blocked.Contains(nextNode))
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{
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path.Push(nextNode);
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stack.Push(Tuple.Create(nextNode, new Stack<T>(subGraph.Neighbors(nextNode))));
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closed.Remove(nextNode);
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blocked.Add(nextNode);
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continue;
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}
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}
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if (neighbors.Count == 0)
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{
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if (closed.Contains(thisnode))
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{
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unblock(thisnode, blocked, B);
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}
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else
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{
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foreach (var neighbor in subGraph.Neighbors(thisnode))
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{
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if (!B.ContainsKey(neighbor))
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{
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B[neighbor] = new HashSet<T>();
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}
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B[neighbor].Add(thisnode);
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}
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}
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stack.Pop();
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path.Pop();
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}
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}
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subGraph.RemoveVertex(startNode);
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var H = subGraph.SubGraph(scc.ToArray());
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var HSccs = H.StronglyConnectedComponents();
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foreach (var HScc in HSccs)
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{
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sccs.Push(HScc);
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}
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}
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return result.Distinct(new SimpleCycleComparer());
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}
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public DirectedGraph<T> Clone()
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{
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var clone = new DirectedGraph<T>();
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clone.AddVertices(Vertices.ToArray());
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foreach (var v in Vertices)
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{
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foreach (var n in Neighbors(v))
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{
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clone.AddEdge(v, n);
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}
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}
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return clone;
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}
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public DirectedGraph<T> SubGraph(params T[] subVertices)
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{
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var subGraph = new DirectedGraph<T>();
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subGraph.AddVertices(subVertices.ToArray());
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foreach (var v in Vertices)
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{
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if (Vertices.Contains(v))
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{
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var neighbors = Neighbors(v);
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foreach (var u in neighbors)
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{
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if (subVertices.Contains(u))
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{
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subGraph.AddEdge(v, u);
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}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
return subGraph;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|