Explanation
- **Kruskal’s Algorithm** is a greedy algorithm used to find the **minimum spanning tree (MST)** of a graph. It selects edges in increasing weight order, ensuring no cycles are formed, and the graph remains connected.
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Steps:
- Sort all the edges of the graph in non-decreasing order of their weight.
- Initialize a disjoint-set (union-find) structure to keep track of cycles.
- For each edge in the sorted list, if the edge connects two different sets, include it in the MST and merge the sets.
- Repeat until the MST contains
V-1edges (whereVis the number of vertices).
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Time Complexity:
- O(E log E), where
Eis the number of edges.
- O(E log E), where