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‎README.md

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# Kruskal's Algorithm Minimum Spanning Tree (Graph MST)
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Java Implementation of Kruskal's Algorithm using **disjoing sets**
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Java Implementation of Kruskal's Algorithm using **disjoing sets**
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**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
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##PseudoCode
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![kruskal-pseudocode](https://cloud.githubusercontent.com/assets/15304528/23335535/450deca2-fb85-11e6-9fd6-ce146ddb3471.png)
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- 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
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Example graph has 8 nodes numbered 1-8 (array ignores the 0th index)
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- **You must hardcode the graph structure in constructor** as a **list of edges**
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- `graphEdges` is **indexed from 1** to make it more human-readable. In the constructor:
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`graphEdges=new ArrayList<Edge>();` //creates empty ArrayList
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`graphEdges.add(new Edge(0, 0, 0));` //adds dummy edge before any actual edges
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**The 0th index is ignored because the loop starts @ 1**
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- `DisjointSet nodeSet = new DisjointSet(nodeCount+1);` also skips the 0th index by creating a Disjoint Set **1 larger than the number of nodes**
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- **Make sure `nodeCount` is accurate**. There's no error checking between `nodeCount` & the actual edge list
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- `outputMessage` is a string that records the steps the algorithm takes. It's printed to the screen & to a file once complete
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- My implementation has **early termination**. If a graph has **N nodes** the MST has **(N-1) edges**
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Hence `&& mstEdges.size()<(nodeCount-1)` in my loop
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- The `Edge` class simply packages an edge's weight & 2 vertices together as 1 object
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####Sources
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- [Disjoint Sets by Mark Allen Weiss](http://users.cis.fiu.edu/~weiss/dsaajava3/code/DisjSets.java) Author of *Data Structures and Algorithm Analysis in Java (3rd Edition), 2011*

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