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@dxzmpk/js-algorithms-data-structures

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Algorithms and data-structures implemented on JavaScript

github.com/dxzmpk/javascript-algorithms

dxzmpk/javascript-algorithms

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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&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) - [Prim's Algorithm on YouTube by Michael Sambol](https://www.youtube.com/watch?v=cplfcGZmX7I&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)