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