Consider the following statements. S1. Kruskal’s algorithm might produce a non-minimal spanning tree. S2. Kruskal’s algorithm can efficiently implemented using the disjoint-set data structure. Options S1 is true but S2 is false Both S1 and S2 are false Both S1 and S2 are true S2 is true but S1 is false
Question
Consider the following statements. S1. Kruskal’s algorithm might produce a non-minimal spanning tree. S2. Kruskal’s algorithm can efficiently implemented using the disjoint-set data structure.
Options S1 is true but S2 is false
Both S1 and S2 are false
Both S1 and S2 are true
S2 is true but S1 is false
Solution
S2 is true but S1 is false
Explanation:
S1: Kruskal’s algorithm always produces a minimal spanning tree. This is because it selects the edges in increasing order of their weights and ensures no cycles are formed. Hence, S1 is false.
S2: Kruskal’s algorithm can indeed be efficiently implemented using the disjoint-set data structure. This data structure helps to keep track of a partition of a set into disjoint subsets and supports operations like union and find. It is used in Kruskal's algorithm to decide whether an edge will form a cycle or not. Hence, S2 is true.
Similar Questions
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
Consider the following graph:Which one of the following is NOT the sequence of edges added to the minimum spanning tree using Kruskal's algorithm?Marks : 1Negative Marks : 0Answer here(b,e)(e,f)(b,c)(a,c)(f,g)(c,d)(b,e)(e,f)(a,c)(b,c)(f,g)(c,d)(b,e)(e,f)(a,c)(f,g)(b,c)(c,d)(b,e)(a,c)(e,f)(b,c)(f,g)(c,d)
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)
Constructing a minimum spanning tree for a graph G is to start with one connected component, add a vertex to have one connected component and no cycles, and end up with one connected componentQuestion 1Select one:a.Greedy Methodb.BFSc.Kruskals Algorithmd.Prims’s Algorithme.DFS
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.