The runtime complexity of Kruskal's algorithm for finding the Minimum Spanning Tree is:OptionsO(V log V)O(V^2) O(E^2)O(E log E)
Question
The runtime complexity of Kruskal's algorithm for finding the Minimum Spanning Tree is:
Options:
- O(V log V)
- O(V^2)
- O(E^2)
- O(E log E)
Solution
The runtime complexity of Kruskal's algorithm for finding the Minimum Spanning Tree is O(E log E).
Here's why:
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Sorting of edges takes O(E log E) time. In Kruskal's algorithm, the first step is to sort all the edges from low weight to high.
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After sorting, we iterate through every edge and apply the find-union algorithm. The find and union operations can take at most O(log V) time. So for all edges, it can be O(E log V).
However, even if we sum up the two parts, we get O(E log E + E log V) time complexity. The value of E can be at most O(V^2), so O(log
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