- 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-
- Sort all the edges from low weight to high weight.
- 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.
- 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)
- 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(V2).
- So, O(logV) and O(logE) are same.
- 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-
Construct the minimum spanning tree (MST) for the given graph using Kruskal’s Algorithm-
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.
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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