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Signum Framework Tutorials Part 2 – Southwind Logic

, 15 Nov 2012 LGPL3
In this part, we will focus on writing business logic, LINQ queries and explain inheritance
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using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using Signum.Utilities;
using System.Collections;
using Signum.Utilities.Properties;
using System.Xml.Linq;

namespace Signum.Utilities.DataStructures
{
    public class DirectedEdgedGraph<T, E> : IEnumerable<T>
    {
        Dictionary<T, Dictionary<T, E>> adjacency;
        public IEqualityComparer<T> Comparer { get; private set; }

        public DirectedEdgedGraph()
            : this(EqualityComparer<T>.Default)
        {
        }

        public DirectedEdgedGraph(IEqualityComparer<T> comparer)
        {
            this.Comparer = comparer;
            this.adjacency = new Dictionary<T, Dictionary<T, E>>(comparer);
        }

        public IEnumerable<T> Nodes
        {
            get { return adjacency.Keys; }
        }

        public IEnumerable<Edge<T>> Edges
        {
            get { return adjacency.SelectMany(k => k.Value.Select(n => new Edge<T>(k.Key, n.Key))); }
        }

        public IEnumerable<Edge<T, E>> EdgesWithValue
        {
            get { return adjacency.SelectMany(k => k.Value.Select(n => new Edge<T, E>(k.Key, n.Key, n.Value))); }
        }

        public int Count
        {
            get { return adjacency.Count; }
        }

        public int EdgesCount
        {
            get { return adjacency.Sum(k => k.Value.Count); }
        }

        public bool Contains(T node)
        {
            return adjacency.ContainsKey(node);
        }

        public bool Connected(T from, T to)
        {
            return Get(from).ContainsKey(to);
        }

        public bool TryConnected(T from, T to)
        {
            return TryGet(from).TryCS(hs => hs.ContainsKey(to)) ?? false;
        }

        public void Add(T from)
        {
            TryGetOrAdd(from);
        }

        public void Add(T from, T to, E value)
        {
            var f = TryGetOrAdd(from);
            TryGetOrAdd(to);
            f[to] = value;

        }

        public void Add(T from, params KeyValuePair<T, E>[] elements)
        {
            var f = TryGetOrAdd(from);
            foreach (var item in elements)
            {
                TryGetOrAdd(item.Key);
                f[item.Key] = item.Value;
            }
        }

        public void Add(T from, IEnumerable<KeyValuePair<T, E>> elements)
        {
            var f = TryGetOrAdd(from);
            foreach (var item in elements)
            {
                TryGetOrAdd(item.Key);
                f[item.Key] = item.Value;
            }
        }

        public bool Remove(T from, T to)
        {
            var dic = adjacency.TryGetC(from);
            if (dic == null)
                return false;

            return dic.Remove(to);
        }

        public bool Remove(Edge<T> edge)
        {
            return Remove(edge.From, edge.To);
        }

        public void RemoveAll(IEnumerable<Edge<T>> edges)
        {
            foreach (var edge in edges)
                Remove(edge.From, edge.To);
        }

        public bool RemoveFullNode(T node)
        {
            if (!adjacency.ContainsKey(node))
                return false;

            return RemoveFullNode(node, InverseRelatedTo(node));
        }

        /// <summary>
        /// Unsafe but fast
        /// </summary>
        public bool RemoveFullNode(T node, IEnumerable<T> inverseRelated)
        {
            if (!adjacency.ContainsKey(node))
                return false;

            adjacency.Remove(node);
            foreach (var n in inverseRelated)
                Remove(n, node);

            return true;
        }

        public static void RemoveFullNodeSymetric(DirectedEdgedGraph<T, E> original, DirectedEdgedGraph<T, E> inverse, T node)
        {
            var from = inverse.RelatedTo(node).Keys;
            var to = original.RelatedTo(node).Keys;

            original.RemoveFullNode(node, from);
            inverse.RemoveFullNode(node, to);
        }

        Dictionary<T, E> TryGet(T node)
        {
            return adjacency.TryGetC(node);
        }

        Dictionary<T, E> Get(T node)
        {
            var result = adjacency.TryGetC(node);
            if (result == null)
                throw new InvalidOperationException("The node {0} is not in the graph".Formato(node));
            return result;
        }

        Dictionary<T, E> TryGetOrAdd(T node)
        {
            return adjacency.GetOrCreate(node, () => new Dictionary<T, E>(Comparer));
        }

        public Dictionary<T, E> TryRelatedTo(T node)
        {
            return TryGet(node) ?? new Dictionary<T, E>();
        }

        public Dictionary<T, E> RelatedTo(T node)
        {
            return Get(node);
        }

        /// <summary>
        /// Costly
        /// </summary>
        public IEnumerable<T> InverseRelatedTo(T node)
        {
            return this.Where(n => Connected(n, node));
        }

        public HashSet<T> IndirectlyRelatedTo(T node)
        {
            HashSet<T> set = new HashSet<T>();
            IndirectlyRelatedTo(node, set);
            return set;
        }

        void IndirectlyRelatedTo(T node, HashSet<T> set)
        {
            foreach (var item in RelatedTo(node))
                if (set.Add(item.Key))
                    IndirectlyRelatedTo(item.Key, set);
        }

        public HashSet<T> IndirectlyRelatedTo(T node, Func<KeyValuePair<T, E>, bool> condition)
        {
            HashSet<T> set = new HashSet<T>();
            IndirectlyRelatedTo(node, set, condition);
            return set;
        }

        void IndirectlyRelatedTo(T node, HashSet<T> set, Func<KeyValuePair<T, E>, bool> condition)
        {
            foreach (var item in RelatedTo(node).Where(condition))
                if (set.Add(item.Key))
                    IndirectlyRelatedTo(item.Key, set, condition);
        }

        public void DepthExplore(T node, Func<T, bool> condition, Action<T> preAction, Action<T> postAction)
        {
            if (condition != null && !condition(node))
                return;

            if (preAction != null)
                preAction(node);

            foreach (T item in RelatedTo(node).Keys)
                DepthExplore(item, condition, preAction, postAction);

            if (postAction != null)
                postAction(node);
        }

        public void BreadthExplore(T root, Func<T, bool> condition, Action<T> action)
        {
            Queue<T> queue = new Queue<T>();
            queue.Enqueue(root);

            while (queue.Count > 0)
            {
                T node = queue.Dequeue();
                if (!condition(node))
                    continue;

                action(node);

                queue.EnqueueRange(RelatedTo(node).Keys);
            }
        }

        public DirectedEdgedGraph<T, E> Inverse()
        {
            DirectedEdgedGraph<T, E> result = new DirectedEdgedGraph<T, E>(Comparer);
            foreach (var item in Nodes)
            {
                result.Add(item);
                foreach (var related in RelatedTo(item))
                {
                    result.Add(related.Key, item, related.Value);
                }
            }
            return result;
        }

        public DirectedEdgedGraph<T, E> UndirectedGraph()
        {
            return this.Inverse().Do(g => g.UnionWith(this));
        }

        public void UnionWith(DirectedEdgedGraph<T, E> other)
        {
            foreach (var item in other.Nodes)
                Add(item, other.RelatedTo(item));
        }

        public DirectedEdgedGraph<T, E> Clone()
        {
            return new DirectedEdgedGraph<T, E>(Comparer).Do(g => g.UnionWith(this));
        }

        public static DirectedEdgedGraph<T, E> Generate(T root, Func<T, IEnumerable<KeyValuePair<T, E>>> expandFunction)
        {
            return Generate(root, expandFunction, EqualityComparer<T>.Default);
        }

        public static DirectedEdgedGraph<T, E> Generate(T root, Func<T, IEnumerable<KeyValuePair<T, E>>> expandFunction, IEqualityComparer<T> comparer)
        {
            DirectedEdgedGraph<T, E> result = new DirectedEdgedGraph<T, E>(comparer);
            result.Expand(root, expandFunction);
            return result;
        }

        public static DirectedEdgedGraph<T, E> Generate(IEnumerable<T> roots, Func<T, IEnumerable<KeyValuePair<T, E>>> expandFunction)
        {
            return Generate(roots, expandFunction, EqualityComparer<T>.Default);
        }

        public static DirectedEdgedGraph<T, E> Generate(IEnumerable<T> roots, Func<T, IEnumerable<KeyValuePair<T, E>>> expandFunction, IEqualityComparer<T> comparer)
        {
            DirectedEdgedGraph<T, E> result = new DirectedEdgedGraph<T, E>(comparer);
            foreach (var root in roots)
                result.Expand(root, expandFunction);
            return result;
        }

        public void Expand(T node, Func<T, IEnumerable<KeyValuePair<T, E>>> expandFunction)
        {
            if (Contains(node)) return;

            Add(node); //necesario para ciclos
            foreach (var item in expandFunction(node))
            {
                Expand(item.Key, expandFunction);
                Add(node, item.Key, item.Value);
            }
        }

        public override string ToString()
        {
            return adjacency.ToString(kvp => "{0}=>{1};".Formato(kvp.Key,
                 kvp.Value.ToString(kvp2 => "[{0}->{1}]".Formato(kvp2.Value, kvp2.Key), ",")),
                "\r\n"); ;
        }

        public string ToGraphviz()
        {
            return ToGraphviz(typeof(E).Name, a => a.ToString(), e => e.ToString());
        }

        public string ToGraphviz(string name)
        {
            return ToGraphviz(name, a => a.ToString(), e => e.ToString());
        }

        public string ToGraphviz(string name, Func<T, string> getNodeLabel, Func<E, string> getEdgeLabel)
        {
            int num = 0;
            Dictionary<T, int> nodeDic = Nodes.ToDictionary(n => n, n => num++, Comparer);

            string nodes = Nodes.ToString(e => "   {0} [ label =\"{1}\"];".Formato(nodeDic[e], getNodeLabel(e)), "\r\n");

            string edges = EdgesWithValue.ToString(e => "   {0} -> {1} [ label =\"{2}\"];".Formato(nodeDic[e.From], nodeDic[e.To], getEdgeLabel(e.Value)), "\r\n");

            return "digraph \"{0}\"\r\n{{\r\n{1}\r\n{2}\r\n}}".Formato(name, nodes, edges);
        }

        public XDocument ToDGML()
        {
            return ToDGML(
                a => a.ToString() ?? "[null]",
                a => ColorGenerator.ColorFor(a.GetType().FullName.GetHashCode()),
                e => e.ToString() ?? "[null]");
        }

        public XDocument ToDGML(Func<T, string> getNodeLabel, Func<T, string> getColor, Func<E, string> getEdgeLabel)
        {
            return ToDGML(n => new[]
            {
                new XAttribute("Label", getNodeLabel(n)),
                new XAttribute("Background", getColor(n))
            }, e=> new []
            {
                new XAttribute("Label", getEdgeLabel(e))
            });
        }
            
        public XDocument ToDGML(Func<T, XAttribute[]> getNodeAttributes, Func<E, XAttribute[]> getEdgeAttributes)
        {
            int num = 0;
            Dictionary<T, int> nodeDic = Nodes.ToDictionary(n => n, n => num++, Comparer);

            XNamespace ns = "http://schemas.microsoft.com/vs/2009/dgml";

            return new XDocument(
                new XElement(ns + "DirectedGraph",
                    new XElement(ns + "Nodes",
                        Nodes.Select(n => new XElement(ns + "Node",
                            new XAttribute("Id", nodeDic[n]),
                            getNodeAttributes(n)))),
                    new XElement(ns + "Links",
                        EdgesWithValue.Select(e => new XElement(ns + "Link",
                            new XAttribute("Source", nodeDic[e.From]),
                            new XAttribute("Target", nodeDic[e.To]),
                            getEdgeAttributes(e.Value))))
                 )
            );
        }

        public IEnumerator<T> GetEnumerator()
        {
            return adjacency.Keys.GetEnumerator();
        }

        IEnumerator IEnumerable.GetEnumerator()
        {
            return adjacency.Keys.GetEnumerator();
        }

        public IEnumerable<HashSet<T>> CompilationOrderGroups()
        {
            DirectedEdgedGraph<T, E> clone = this.Clone();
            DirectedEdgedGraph<T, E> inv = this.Inverse();

            while (clone.Count > 0)
            {
                var leaves = clone.Sinks();
                foreach (var node in leaves)
                    clone.RemoveFullNode(node, inv.RelatedTo(node).Keys);
                yield return leaves;
            }
        }

        public IEnumerable<T> CompilationOrder()
        {
            return CompilationOrderGroups().SelectMany(e => e);
        }

        /// <summary>
        /// A simple but effective linear-time heuristic constructs a vertex ordering,
        /// just as in the topological sort heuristic above, and deletes any arc going from right to left. 
        /// 
        /// This heuristic builds up the ordering from the outside in based on the in- and out-degrees of each vertex. 
        /// - Any vertex of in-degree 0 is a source and can be placed first in the ordering. 
        /// - Any vertex of out-degree 0 is a sink and can be placed last in the ordering, again without violating any constraints. 
        /// - If not, we find the vertex with the maximum difference between in- and out-degree, 
        /// and place it on the side of the permutation that will salvage the greatest number of constraints. 
        /// Delete any vertex from the DAG after positioning it and repeat until the graph is empty.
        /// </summary>
        /// <returns></returns>
        public DirectedEdgedGraph<T, E> FeedbackEdgeSet()
        {
            DirectedEdgedGraph<T, E> result = new DirectedEdgedGraph<T, E>(Comparer);

            DirectedEdgedGraph<T, E> clone = this.Clone();
            DirectedEdgedGraph<T, E> inv = this.Inverse();

            HashSet<T> head = new HashSet<T>();  // for sources
            HashSet<T> tail = new HashSet<T>();  // for sinks
            while (clone.Count > 0)
            {
                var sinks = clone.Sinks();
                if (sinks.Count() != 0)
                {
                    foreach (var sink in sinks)
                    {
                        DirectedEdgedGraph<T, E>.RemoveFullNodeSymetric(clone, inv, sink);
                        tail.Add(sink);
                    }
                    continue;
                }

                var sources = inv.Sinks();
                if (sources.Count() != 0)
                {
                    foreach (var source in sources)
                    {
                        DirectedEdgedGraph<T, E>.RemoveFullNodeSymetric(clone, inv, source);
                        head.Add(source);
                    }
                    continue;
                }

                Func<T, int> fanInOut = n => clone.RelatedTo(n).Count() - inv.RelatedTo(n).Count();

                MinMax<T> mm = clone.WithMinMaxPair(fanInOut);

                if (fanInOut(mm.Max) > -fanInOut(mm.Min))
                {
                    T node = mm.Max;
                    foreach (var n in inv.RelatedTo(node))
                        result.Add(n.Key, node, n.Value);
                    
                    DirectedEdgedGraph<T, E>.RemoveFullNodeSymetric(clone, inv, node);
                    head.Add(node);
                }
                else
                {
                    T node = mm.Min;
                    foreach (var n in clone.RelatedTo(node))
                        result.Add(node, n.Key, n.Value);
                    DirectedEdgedGraph<T, E>.RemoveFullNodeSymetric(clone, inv, node);
                    head.Add(node);
                }
            }

            return result;
        }

        HashSet<T> Sinks()
        {
            return adjacency.Where(a => a.Value.Count == 0).Select(a => a.Key).ToHashSet();
        }

        public DirectedEdgedGraph<T, E> WhereEdges(Func<Edge<T, E>, bool> condition)
        {
            DirectedEdgedGraph<T, E> result = new DirectedEdgedGraph<T, E>(Comparer);
            foreach (var item in Nodes)
                result.Add(item, RelatedTo(item).Where(to => condition(new Edge<T, E>(item, to.Key, to.Value))));
            return result;
        }

        public List<T> ShortestPath(T from, T to, Func<E, int> getWeight)
        {
            //http://en.wikipedia.org/wiki/Dijkstra's_algorithm

            Dictionary<T, int> distance = this.ToDictionary(e => e, e => int.MaxValue, Comparer);
            Dictionary<T, T> previous = new Dictionary<T, T>(Comparer);

            distance[from] = 0;
            PriorityQueue<T> queue = new PriorityQueue<T>((a, b) => distance[a].CompareTo(distance[b]));
            queue.PushAll(this);

            while (queue.Count > 0)
            {
                T u = queue.Peek();
                if (distance[u] == int.MaxValue)
                    return null;

                foreach (var v in RelatedTo(u))
                {
                    int newDist = distance[u] + getWeight(v.Value);
                    if (newDist < distance[v.Key])
                    {
                        distance[v.Key] = newDist;
                        queue.Update(v.Key);
                        previous[v.Key] = u;
                    }
                }
                queue.Pop();

                if (Comparer.Equals(u, to))
                    break;
            }

            return to.For(n => previous.ContainsKey(n), n => previous[n]).Reverse().ToList();
        }


    }

    public struct Edge<T, E>
    {
        public readonly T From;
        public readonly T To;
        public readonly E Value;

        public Edge(T from, T to, E value)
        {
            this.From = from;
            this.To = to;
            this.Value = value;
        }

        public override string ToString()
        {
            return "{0}-{1}->{2}".Formato(From, Value, To);
        }
    };
}

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About the Author

Olmo del Corral
Software Developer (Senior) Signum Software
Spain Spain
I'm Computer Scientist, one of the founders of Signum Software, and the lead developer behind Signum Framework.
 
www.signumframework.com
 
I love programming in C#, Linq, Compilers, Algorithms, Functional Programming, Computer Graphics, Maths...

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