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:OptionsO(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:
-
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.
-
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
Similar Questions
How does Kruskal's algorithm find the minimum spanning tree in a graph?A) By selecting the edge with the smallest weightB) By selecting the edge with the largest weightC) By selecting edges randomlyD) By selecting edges based on a priority queu
Consider the following graph: Which one of the following cannot be the sequence of edges added, in that order, to a minimum spanning tree using Kruskal’s algorithm?
Which algorithm is used to find the minimum spanning tree in a graph?A) Bellman-FordB) Kruskal'sC) Prim'sD) Dijkstra's
Kruskal’s algorithm is used to ______Select one:a.find minimum spanning treeb.find single source shortest pathc.find all pair shortest path algorithmd.traverse the graph
What is the time complexity of Kruskal’s algorithm?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.