5. (4 points) Given a tree T = (V, E), a subset S CV of vertices is said to be a vertex cover of G iff for every edge (u, v) E E, at least one of u, v belongs to the subset S. A minimum vertex cover of T is a vertex cover with minimum cardinality (i.e., smallest vertex cover). Design an algorithm for finding a minimum vertex cover of a given tree T = (V, E). Give pseudocode, discuss running time, and argue that your algorithm always outputs a minimum vertex cover for any given tree