Question

Consider the problem of finding a minimum spanning tree of a weighted graph. Which one of the following algorithms does not find an optimal solution to the problem?

a) Prim's algorithm
b) Kruskal's algorithm
c) Dijkstra's algorithm
d) The reverse-delete algorithm

Answer 1

Dijkstra's algorithm is the one that does not find an optimal solution for the minimum spanning tree problem, as it is intended for shortest path problems.

Step-by-step explanation:

Among the algorithms listed for finding a minimum spanning tree of a weighted graph, Prim's algorithm, Kruskal's algorithm, and the reverse-delete algorithm are all designed to find an optimal minimum spanning tree. However, Dijkstra's algorithm is not meant for this purpose.

Dijkstra's algorithm is designed for finding the shortest paths from a single source to all other nodes in a graph, not for finding a minimum spanning tree. Consequently, Dijkstra's algorithm does not guarantee an optimal solution for the minimum spanning tree problem.