Java Implementation of Kruskal's Algorithm using disjoing sets
Kruskal's algorithm: Start with T = ∅. Consider edges in ascending order of weight. Insert edge e into T unless doing so would create a cycle

• Works on UN-directed graphs
• Algorithm still works on edges with identical weight
  Edges are sorted by weight first. Depending on the order they are entered into the edge list in the constructor, you may get different Minimum Spanning Trees (but all still optimal solutions)

##PseudoCode

##Detailed Implementation

##Code Notes Current code runs on this sample graph It produces this Minimum Spanning Tree

• Requires distinct nodes named with consecutive integers. If they really do have the same "name", convert them to integer ID's to use this algorithm
  Example graph has 8 nodes numbered 1-8 (array ignores the 0th index)
• You must hardcode the graph structure in constructor as a list of edges
• graphEdges is indexed from 1 to make it more human-readable. In the constructor:
  graphEdges=new ArrayList<Edge>(); //creates empty ArrayList
  graphEdges.add(new Edge(0, 0, 0)); //adds dummy edge before any actual edges
  The 0th index is ignored because the loop starts @ 1
• DisjointSet nodeSet = new DisjointSet(nodeCount+1); also skips the 0th index by creating a Disjoint Set 1 larger than the number of nodes
• Make sure nodeCount is accurate. There's no error checking between nodeCount & the actual edge list
• outputMessage is a string that records the steps the algorithm takes. It's printed to the screen & to a file once complete
• My implementation has early termination. If a graph has N nodes the MST has (N-1) edges
  Hence && mstEdges.size()<(nodeCount-1) in my loop
• The Edge class simply packages an edge's weight & 2 vertices together as 1 object

####Sources

• Disjoint Sets by Mark Allen Weiss Author of Data Structures and Algorithm Analysis in Java (3rd Edition), 2011
  He also has other helpful Java Data Structures implementations