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# Prim's Algorithm
In computer science, **Prim's algorithm** is a greedy algorithm that
finds a minimum spanning tree for a weighted undirected graph.
The algorithm operates by building this tree one vertex at a
time, from an arbitrary starting vertex, at each step adding
the cheapest possible connection from the tree to another vertex.
![Prim's Algorithm](https://upload.wikimedia.org/wikipedia/commons/f/f7/Prim%27s_algorithm.svg)
Prim's algorithm starting at vertex `A`. In the third step, edges
`BD` and `AB` both have weight `2`, so `BD` is chosen arbitrarily.
After that step, `AB` is no longer a candidate for addition
to the tree because it links two nodes that are already
in the tree.
## Minimum Spanning Tree
A **minimum spanning tree** (MST) or minimum weight spanning tree
is a subset of the edges of a connected, edge-weighted
(un)directed graph that connects all the vertices together,
without any cycles and with the minimum possible total edge
weight. That is, it is a spanning tree whose sum of edge weights
is as small as possible. More generally, any edge-weighted
undirected graph (not necessarily connected) has a minimum
spanning forest, which is a union of the minimum spanning
trees for its connected components.
![Minimum Spanning Tree](https://upload.wikimedia.org/wikipedia/commons/d/d2/Minimum_spanning_tree.svg)
A planar graph and its minimum spanning tree. Each edge is
labeled with its weight, which here is roughly proportional
to its length.
![Minimum Spanning Tree](https://upload.wikimedia.org/wikipedia/commons/c/c9/Multiple_minimum_spanning_trees.svg)
This figure shows there may be more than one minimum spanning
tree in a graph. In the figure, the two trees below the graph
are two possibilities of minimum spanning tree of the given graph.
## References
- [Minimum Spanning Tree on Wikipedia](https://en.wikipedia.org/wiki/Minimum_spanning_tree)
- [Prim's Algorithm on Wikipedia](https://en.wikipedia.org/wiki/Prim%27s_algorithm)
- [Prim's Algorithm on YouTube by Tushar Roy](https://www.youtube.com/watch?v=oP2-8ysT3QQ)