A vertex cover of a graph G = (V, E) is a subset of vertices S ⊆ V that includes at least...

A vertex cover of a graph G = (V, E) is a subset of vertices S ⊆ V that includes at least one endpoint of every edge in E. Give a linear-time algorithm for the following task.

Input: An undirected tree T = (V, E).

Output: The size of the smallest vertex cover of T.

For instance, in the following tree, possible vertex covers include {A, B, C, D, E, F, G} and {A, C, D, F} but not {C, E, F}. The smallest vertex cover has size 3: {B, E, G}.