Kruskal's Algorithm Explained with Simple Animations

Welcome to our exploration of Minimum Spanning Trees!Let's start with a weighted graph example. Each edge has a weight representing its cost or distance.A Minimum Spanning Tree is a special subset of edges that connects all vertices while minimizing the total weight.There are three key properties of a Minimum Spanning Tree that we need to understand.To begin finding the Minimum Spanning Tree, we first sort all edges by their weights from lowest to highest.This sorted list of edges will be the foundation for Kruskal's algorithm as we build our Minimum Spanning Tree.Now that we understand what a Minimum Spanning Tree is and how to prepare our edges, we're ready to move forward.In Kruskal's algorithm, we use a data structure called Union-Find to efficiently detect cycles.Initially, each vertex is in its own set, represented by these separate circles.The Find operation determines which set a vertex belongs to. Initially, each vertex is its own representative.When we perform a Union operation, we merge two sets by connecting their representatives.Path compression optimizes future operations by making all nodes in a set point directly to their representative.When we try to add an edge between vertices in the same set, Union-Find helps us detect that this would create a cycle.Let's see how Union-Find handles merging larger sets.When we merge two larger sets, all vertices in both sets become part of the same connected component.With path compression and union by rank, both Find and Union operations become extremely efficient, taking nearly constant time.Now let's build our minimum spanning tree by adding edges one by one, starting with the lowest weight.Let's examine the key properties of our completed minimum spanning tree.And those are the key takeaways from Kruskal's Algorithm for finding a minimum spanning tree.Thanks for learning about minimum spanning trees with Spark.E!