The minimal spanning tree algorithm is considered a greedy algorithm that,when taking the best action at each stage,will
A)sometimes fail to produce a feasible solution.
B)always produce a feasible,but not necessarily optimal,solution.
C)always produce an optimal solution.
D)always produce an optimal,but not necessarily feasible,solution.

Question

Quizplus · Accepted Answer

The minimal spanning tree algorithm is a well-known greedy algorithm that always produces an optimal solution, which means the resulting tree will have the smallest possible weight or cost among all possible spanning trees. This can be proven mathematically using the Cut Property that states that, for any cut in the graph, the edge with the minimum weight crossing the cut must be part of the minimal spanning tree. Therefore, the greedy algorithm that adds edges to the tree in increasing order of weight guarantees that the selected edges form a valid tree and one that is optimal.

The Minimal Spanning Tree Algorithm Is Considered a Greedy Algorithm