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Author: SleekPanther

README.md

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+# Reverse Delete Algorithm (Minimum Spanning Tree)
+Greedy Algorithm to find a minimum spanning tree in an undirected graph by deleting heaviest edges unless it would disconnect the graph
+
+## Problem Statement
+**Minim Spanning Tree:** a subset of nodes that touches all vertices while keeping all nodes connected and uses the sum of the edge weights in a minimum  
+A Minimum spanning tree yields a graph with **M-1** edges because adding 1 more edge would by definition create a cycle
+
+### Graph
+![](images/graph.png)
+
+### Minimum Spanning Tree
+![](images/mst.png)  
+#### Weight = 18+14+9+7+6+5+2 = 61
+
+## Reverse Delete Greedy Strategy
+**Start with all edges in the tree T. Consider edges in descending order of weight. Delete edge from T unless doing so would disconnect T**
+
+- Sort edges by weight
+- Initialize MST with all edges
+- Delete the highest weight edge
+  - If deleting the edge disconnects the graph, add it back
+  - Otherwise continue
+
+## Usage
+- Node names are consecutive integers starting from `0`
+- Create a graph: `ArrayList<Edge> graph = new ArrayList<Edge>();`
+- Graph undirected edge list, but **only add each edge once**
+  - In the graph there is an edge from `0` to `9` with weight=`9`
+  - This bidirectional edge can just be represented once: `graph.add(new Edge(0, 1, 9));`
+- Count the vertices in the graph: `int vertexCount = 8;`
+- Call the static method `ReverseDeleteMST.findMST(graph, vertexCount);`
+
+# Code Notes
+- Due to the implementation of Breadth First Search, the code creates an additional copy of the graph as an adjacency list
+- This adjacency list graph is the one where edges are deleted, the original input graph as an edge list is left in tact
+- The MST is technically built up from nothing and added to if deleting an edge in the adjacency list would disconnect the graph
+
+## References
+- [Kevin Wayne Slides](https://www.cs.princeton.edu/~wayne/kleinberg-tardos/pdf/04GreedyAlgorithmsII.pdf#page=14)
+- [University of Illinois - Minimum Spanning Trees](https://courses.engr.illinois.edu/cs473/sp2011/Lectures/12_notes.pdf)
+- [T. M. Murali Slides](http://courses.cs.vt.edu/cs5114/spring2009/lectures/lecture05-greedy-graph-algorithms.pdf#page=36)
+- [Fan Chung Graham Slides](http://www.math.ucsd.edu/~fan/teach/202/14/04mst.pdf#page=11)
+- [Reverse Delete Algorithm - GeeksForGeeks](http://www.geeksforgeeks.org/reverse-delete-algorithm-minimum-spanning-tree/) Algorithm strategy, code only briefly referenced
+- [Remove items from ArrayList with certain value - Stack Overflow](https://stackoverflow.com/a/29107463/8132253) Lambda expression to delete specific value from `ArrayList`