SpanningForest.cs

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#region License
/*This file is part of Satsuma Graph Library
Copyright © 2013 Balázs Szalkai

This software is provided 'as-is', without any express or implied
warranty. In no event will the authors be held liable for any damages
arising from the use of this software.

Permission is granted to anyone to use this software for any purpose,
including commercial applications, and to alter it and redistribute it
freely, subject to the following restrictions:

   1. The origin of this software must not be misrepresented; you must not
   claim that you wrote the original software. If you use this software
   in a product, an acknowledgment in the product documentation would be
   appreciated but is not required.

   2. Altered source versions must be plainly marked as such, and must not be
   misrepresented as being the original software.

   3. This notice may not be removed or altered from any source
   distribution.*/
#endregion

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

namespace Satsuma
{
    public sealed class Prim<TCost>
        where TCost : IComparable<TCost>
    {
        public IGraph Graph { get; private set; }
        public Func<Arc, TCost> Cost { get; private set; }

        public HashSet<Arc> Forest { get; private set; }
        public Subgraph ForestGraph { get; private set; }

        public Prim(IGraph graph, Func<Arc, TCost> cost)
        {
            Graph = graph;
            Cost = cost;
            Forest = new HashSet<Arc>();
            ForestGraph = new Subgraph(graph);
            ForestGraph.EnableAllArcs(false);

            Run();
        }

        public Prim(IGraph graph, Dictionary<Arc, TCost> cost)
            : this(graph, arc => cost[arc])
        {
        }

        private void Run()
        {
            Forest.Clear();
            PriorityQueue<Node, TCost> priorityQueue = new PriorityQueue<Node, TCost>();
            HashSet<Node> processed = new HashSet<Node>();
            Dictionary<Node, Arc> parentArc = new Dictionary<Node, Arc>();

            // start with one point from each component
            var components = new ConnectedComponents(Graph, ConnectedComponents.Flags.CreateComponents);
            foreach (var c in components.Components)
            {
                Node root = c.First();
                processed.Add(root);
                foreach (var arc in Graph.Arcs(root))
                {
                    Node v = Graph.Other(arc, root);
                    parentArc[v] = arc;
                    priorityQueue[v] = Cost(arc);
                }
            }
            components = null;

            while (priorityQueue.Count != 0)
            {
                Node n = priorityQueue.Peek();
                priorityQueue.Pop();
                processed.Add(n);
                Arc arcToAdd = parentArc[n];
                Forest.Add(arcToAdd);
                ForestGraph.Enable(arcToAdd, true);

                foreach (var arc in Graph.Arcs(n))
                {
                    Node v = Graph.Other(arc, n);
                    if (processed.Contains(v)) continue;

                    TCost arcCost = Cost(arc);
                    TCost vCost;
                    bool vInPriorityQueue = priorityQueue.TryGetPriority(v, out vCost);
                    if (!vInPriorityQueue || arcCost.CompareTo(vCost) < 0)
                    {
                        priorityQueue[v] = arcCost;
                        parentArc[v] = arc;
                    }
                }
            }
        }
    }

    public sealed class Kruskal<TCost>
        where TCost : IComparable<TCost>
    {
        public IGraph Graph { get; private set; }
        public Func<Arc, TCost> Cost { get; private set; }
        public Func<Node, int> MaxDegree { get; private set; }

        public HashSet<Arc> Forest { get; private set; }
        public Subgraph ForestGraph { get; private set; }
        public Dictionary<Node, int> Degree { get; private set; }

        private IEnumerator<Arc> arcEnumerator; // Enumerates the arcs by cost increasing.
        private int arcsToGo;
        private DisjointSet<Node> components; // The components of the current spanning forest.

        public Kruskal(IGraph graph, Func<Arc, TCost> cost, Func<Node, int> maxDegree = null)
        {
            Graph = graph;
            Cost = cost;
            MaxDegree = maxDegree;

            Forest = new HashSet<Arc>();
            ForestGraph = new Subgraph(graph);
            ForestGraph.EnableAllArcs(false);
            Degree = new Dictionary<Node, int>();
            foreach (var node in Graph.Nodes()) Degree[node] = 0;

            List<Arc> arcs = Graph.Arcs().ToList();
            arcs.Sort((a, b) => Cost(a).CompareTo(Cost(b)));
            arcEnumerator = arcs.GetEnumerator();
            arcsToGo = Graph.NodeCount() - new ConnectedComponents(Graph).Count;
            components = new DisjointSet<Node>();
        }

        public Kruskal(IGraph graph, Dictionary<Arc, TCost> cost)
            : this(graph, arc => cost[arc], null)
        {
        }

        public bool Step()
        {
            if (arcsToGo <= 0 || arcEnumerator == null || !arcEnumerator.MoveNext())
            {
                arcEnumerator = null;
                return false;
            }

            AddArc(arcEnumerator.Current);
            return true;
        }

        public void Run()
        {
            while (Step()) ;
        }

        public bool AddArc(Arc arc)
        {
            var u = Graph.U(arc);
            if (MaxDegree != null && Degree[u] >= MaxDegree(u)) return false;
            DisjointSetSet<Node> x = components.WhereIs(u);

            var v = Graph.V(arc);
            if (MaxDegree != null && Degree[v] >= MaxDegree(v)) return false;
            DisjointSetSet<Node> y = components.WhereIs(v);

            if (x == y) return false; // cycle

            Forest.Add(arc);
            ForestGraph.Enable(arc, true);
            components.Union(x, y);
            Degree[u]++;
            Degree[v]++;
            arcsToGo--;
            return true;
        }
    }
}