Kruskal minimum Spanning tree algorithm

2. 1. All edges are sorted by weight non-descending;
   2. Select the edge of the minimum weight to determine whether it forms a loop in the current spanning tree. If the loop is not formed, the edge is added to the tree, otherwise it is discarded.
   3. Repeat step 2 until you have a v–1 edge in the spanning tree.
4. http://blog.jobbole.com/83939/

5. Using system;using system.collections.generic;using System.Linq;      Namespace graphalgorithmtesting{class Program {static void Main (string[] args) {graph G = new Graph (9);      G.addedge (0, 1, 4);      G.addedge (0, 7, 8);      G.addedge (1, 2, 8);      G.addedge (1, 7, 11);      G.addedge (2, 3, 7);      G.addedge (2, 5, 4);      G.addedge (8, 2, 2);      G.addedge (3, 4, 9);      G.addedge (3, 5, 14);      G.addedge (5, 4, 10);      G.addedge (6, 5, 2);      G.addedge (8, 6, 6);      G.addedge (7, 6, 1);       G.addedge (7, 8, 7);      Console.WriteLine ();      Console.WriteLine ("Graph Vertex Count: {0}", G.vertexcount);      Console.WriteLine ("Graph Edge Count: {0}", G.edgecount);       Console.WriteLine ();      Console.WriteLine ("Was there cycle in graph: {0}", G.hascycle ());       Console.WriteLine ();      edge[] mst = G.kruskal ();      Console.WriteLine ("MST Edges:");      foreach (var edge in MST) {Console.WriteLine ("\t{0}", Edge);  } console.readkey ();  } class Edge {public edge (int begin, int end, int. weight) {this.        begin = BEGIN; This.        end = END; This.      Weight = Weight;      } public int Begin {get; private set;}      public int End {get; private set;}       public int Weight {get; private set;} public override string ToString () {return string.      Format ("begin[{0}], end[{1}], weight[{2}]", Begin, End, Weight);      }} class Subset {public int Parent {get; set;}    public int Rank {get; set;}  } class Graph {Private Dictionary<int, list<edge>> _adjacentedges = new Dictionary<int,       List<edge>> (); Public Graph (Int. vertexcount) {this.      Vertexcount = Vertexcount;       } public int Vertexcount {get; private set;}       Public ienumerable<int> Vertices {get {return _adjacentedges.keys;}} Public ienumerable<edge> Edges {get {return} _adjacentedges.values.selectmany (e = e); }} public int Edgecount {get {return this. Edges.count ();        }} public void Addedge (int begin, int end, int weight) {if (!_adjacentedges.containskey (begin))          {var edges = new List<edge> ();        _adjacentedges.add (begin, edges); } _adjacentedges[begin].      ADD (new Edge (begin, end, weight)); } private int Find (subset[] subsets, int i) {//Find root and make root as parent of I (Path Compressio N) if (Subsets[i]. Parent = i) subsets[i]. Parent = Find (subsets, Subsets[i].         Parent); Return subsets[i].      Parent;        } private void Union (subset[] subsets, int x, int y) {int xroot = Find (subsets, X);         int yroot = Find (subsets, y); Attach smaller rank tree under root of high rank tree//(Union by rank) if (Subsets[xroot]. Rank < Subsets[yroot]. Rank) Subsets[xroot].  Parent = Yroot;      else if (Subsets[xroot]. Rank > Subsets[yroot]. Rank) Subsets[yroot].         Parent = Xroot; If ranks is same, then make one as root and increment//it rank by one else {subsets[ Yroot].          Parent = Xroot; Subsets[xroot].        rank++;        }} public bool Hascycle () {subset[] subsets = new Subset[vertexcount]; for (int i = 0; i < subsets. Length;          i++) {Subsets[i] = new subset (); Subsets[i].          Parent = i; Subsets[i].        Rank = 0;  }//Iterate through all edges of graph, find subset of both//vertices of every edge, if both subsets is        Same,//Then there are cycle in graph. foreach (var edge in this.) Edges) {int x = Find (subsets, Edge.          Begin); int y = Find (subsets, Edge.           END);          if (x = = y) {return true;        } Union (subsets, X, y);      } return false;    }   Public edge[] Kruskal () {//This would store the resultant MST edge[] mst = new edge[vertexcount-1         ]; Step 1:sort all the edges in non-decreasing order of their weight//If We is not allowed to change the given Graph, we can create a copy of//array of edges var sortededges = this.        Edges.orderby (t = t.weight);         var enumerator = Sortededges.getenumerator (); Allocate memory for creating v ssubsets//Create V subsets with single elements subset[] subsets = new S        Ubset[vertexcount]; for (int i = 0; i < subsets. Length;          i++) {Subsets[i] = new subset (); Subsets[i].          Parent = i; Subsets[i].        Rank = 0;        }//number of edges to be taken are equal to V-1 int e = 0; while (E < VertexCount-1) {//Step 2:pick the smallest edge.          and increment the index//for next iteration Edge Nextedge; if (Enumerator. MoveNext ()) {Nextedge = enumerator.             Current;            int x = Find (subsets, Nextedge.begin);             int y = Find (subsets, Nextedge.end); If including this edge does ' t cause cycle, include it//in result and increment the index of result for NEX              T edge if (x! = y) {mst[e++] = Nextedge;            Union (subsets, X, y); } else {//else discard the Nextedge}}} return M      Qty }    }  }}

   　　

Kruskal minimum Spanning tree algorithm