Kruskal’s Algorithm
 Kruskal’s Algorithm is a famous greedy algorithm.
 It is used for finding the Minimum Spanning Tree (MST) of a given graph.
 To apply Kruskal’s algorithm, the given graph must be weighted, connected and undirected.
Kruskal’s Algorithm Implementation
The implementation of Kruskal’s Algorithm is explained in the following steps
Step01:
 Sort all the edges from low weight to high weight.
Step02:
 Take the edge with the lowest weight and use it to connect the vertices of graph.
 If adding an edge creates a cycle, then reject that edge and go for the next least weight edge.
Step03:
 Keep adding edges until all the vertices are connected and a Minimum Spanning Tree (MST) is obtained.
Thumb Rule to Remember
The above steps may be reduced to the following thumb rule

Kruskal’s Algorithm Time Complexity
Worst case time complexity of Kruskal’s Algorithm
= O(ElogV) or O(ElogE) 
Analysis
 The edges are maintained as min heap.
 The next edge can be obtained in O(logE) time if graph has E edges.
 Reconstruction of heap takes O(E) time.
 So, Kruskal’s Algorithm takes O(ElogE) time.
 The value of E can be at most O(V^{2}).
 So, O(logV) and O(logE) are same.
Special Case
 If the edges are already sorted, then there is no need to construct min heap.
 So, deletion from min heap time is saved.
 In this case, time complexity of Kruskal’s Algorithm = O(E + V)
Also Read Prim’s Algorithm
PRACTICE PROBLEMS BASED ON KRUSKAL’S ALGORITHM
Problem01:
Construct the minimum spanning tree (MST) for the given graph using Kruskal’s Algorithm
Solution
To construct MST using Kruskal’s Algorithm,
 Simply draw all the vertices on the paper.
 Connect these vertices using edges with minimum weights such that no cycle gets formed.
Step01:
Step02:
Step03:
Step04:
Step05:
Step06:
Step07:
Since all the vertices have been connected / included in the MST, so we stop.
Weight of the MST
= Sum of all edge weights
= 10 + 25 + 22 + 12 + 16 + 14
= 99 units
To gain better understanding about Kruskal’s Algorithm,
To practice previous years GATE problems based on Kruskal’s Algorithm,
Next Article Prim’s Algorithm Vs Kruskal’s Algorithm
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