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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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# Kruskal's Algorithm Kruskal's algorithm is a minimum-spanning-tree algorithm which finds an edge of the least possible weight that connects any two trees in the forest. It is a greedy algorithm in graph theory as it finds a minimum spanning tree for a connected weighted graph adding increasing cost arcs at each step. This means it finds a subset of the edges that forms a tree that includes every vertex, where the total weight of all the edges in the tree is minimized. If the graph is not connected, then it finds a minimum spanning forest (a minimum spanning tree for each connected component). ![Kruskal Algorithm](https://upload.wikimedia.org/wikipedia/commons/5/5c/MST_kruskal_en.gif) ![Kruskal Demo](https://upload.wikimedia.org/wikipedia/commons/b/bb/KruskalDemo.gif) A demo for Kruskal's algorithm based on Euclidean distance. ## 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) - [Kruskal's Algorithm on Wikipedia](https://en.wikipedia.org/wiki/Kruskal%27s_algorithm) - [Kruskal's Algorithm on YouTube by Tushar Roy](https://www.youtube.com/watch?v=fAuF0EuZVCk&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) - [Kruskal's Algorithm on YouTube by Michael Sambol](https://www.youtube.com/watch?v=71UQH7Pr9kU&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)