Kruskal's Algorithm finds a minimum spanning tree.

Kruskal's Algorithm is a greedy algorithm used to find the Minimum Spanning Tree (MST) of a connected, weighted graph. It works by sorting all edges in non-decreasing order of weight and adding them one by one to the MST, ensuring no cycles are formed. The process continues until all vertices are connected. It is efficient for sparse graphs and commonly implemented using the Union-Find data structure to detect cycles.

1. Kruskal’s Algorithm: Constructing Minimum Spanning Trees Welcome to the world of Kruskal's Algorithm, a powerful tool for finding the most efficient paths within complex networks. Presented By Md. Shahan Al Munim

2. Introduction to Kruskal’s Algorithm: Kruskal's Algorithm is a classic algorithm used in graph theory to find the Minimum Spanning Tree (MST) of a connected, undirected graph.

3. Understanding Kruskal's Algorithm Greedy Approach Efficiently selects edges to build the MST Minimum Spanning Tree (MST) Connects all vertices with minimal total edge weight

4. What is a Minimum Spanning Tree? Spanning Tree Connects all vertices without cycles Minimum Lowest possible total edge weight Applications Network design, resource optimization

5. Kruskal's Algorithm Steps 1 Edge Sorting 2 Edge Selection 3 Cycle Check 4 Include or Discard 5 Repeat Until Complete

6. Pseudocode Representation Kruskal(Graph G): 1. Initialize MST = ∅ (empty set for edges of the Minimum Spanning Tree) 2. Sort all edges in G by increasing edge weight. 3. Initialize a Union-Find data structure (or Disjoint Set) to keep track of connected components. 4. For each edge (u, v) in sorted edges: a. If u and v belong to different components: i. Add edge (u, v) to MST. ii. Union(u, v) to merge the components. 5. Return MST.

7. Example Walkthrough Step 1 Sort edges by weight Step 2 Add edges, avoiding cycles Step 3 Highlight the final MST

8. Time Complexity Analysis O(E log E) Sorting Efficient for sparse graphs O(E log V) Union-Find Efficient for connecting trees O(E log E) Overall Practical for many graphs

9. Real-World Applications Network Design Telecommunications, electricity, and computer networks Clustering Analysis Grouping data points efficiently Approximation Algorithms Solving problems like the traveling salesman problem

10. Advantages and Limitations Advantages Simple and efficient for sparse graphs Intuitive and easy to implement Limitations Requires sorting of edges May not be optimal for dense graphs

11. Kruskal's Algorithm: A Powerful Tool Explore the world of Kruskal's Algorithm to understand how it efficiently connects points, optimizes resources, and solves complex problems in various fields.

12. C Code For Kruskal's Algorithm