Editing Priority queue (section)

=== Prim's algorithm for minimum spanning tree ===
Using [[Binary heap|min heap priority queue]] in [[Prim's algorithm]] to find the [[minimum spanning tree]] of a [[Connected graph|connected]] and [[undirected graph]], one can achieve a good running time. This min heap priority queue uses the min heap data structure which supports operations such as ''insert'', ''minimum'', ''extract-min'', ''decrease-key''.<ref name="CLR">{{Introduction to Algorithms |edition=3 |pages=634}} "In order to implement Prim's algorithm efficiently, we need a fast way to select a new edge to add to the tree formed by the edges in A."</ref> In this implementation, the [[weighted graph|weight]] of the edges is used to decide the priority of the [[Vertex (graph theory)|vertices]]. Lower the weight, higher the priority and higher the weight, lower the priority.<ref name="GEEKS">
{{cite web
 |url         = http://www.geeksforgeeks.org/greedy-algorithms-set-5-prims-minimum-spanning-tree-mst-2/
 |title       = Prim's Algorithm
 |date = 18 November 2012
 |publisher   = Geek for Geeks
 |access-date  = 12 September 2014
 |url-status     = live
 |archive-url  = https://web.archive.org/web/20140909020508/http://www.geeksforgeeks.org/greedy-algorithms-set-5-prims-minimum-spanning-tree-mst-2/
 |archive-date = 9 September 2014
}}
</ref>