Algorithm Design Questions
The main difference between a minimum spanning tree and a shortest path tree lies in their objectives and the problem they aim to solve.
A minimum spanning tree is a tree that connects all the vertices of a weighted graph with the minimum possible total edge weight. It is used to find the most efficient way to connect all the vertices in a graph, ensuring that there are no cycles and the total weight is minimized.
On the other hand, a shortest path tree is a tree that represents the shortest paths from a single source vertex to all other vertices in a weighted graph. It is used to find the shortest path between two specific vertices or to determine the shortest paths from a single source to all other vertices.
In summary, a minimum spanning tree focuses on connecting all vertices with minimum total weight, while a shortest path tree focuses on finding the shortest paths from a single source vertex to all other vertices.