Please help with excersie 12.10

Exercise 12.10. A vertex-cover ofa tree T is a subset V ofits vertices such that, for each edge in T, at least one of its endpoints belongs to V'. For example, the set containing all the vertices ofT is a vertex-cover. The mini- mum vertex-cover ofT is a vertex-cover that contains the fewest vertices We are given a rooted tree T ofn vertices. (Ifyou want you can assume the tree to be binary, ie, each node has at most two children.) Design a dynamic programming algorithm to output the size of the minimum vertex-cover of T, and analyze its running time. Note that you should first give a recursive formulation of the dynamic programming solution, clearly explaining your notation. Then give the pseudocode and analyze its running time. (Hint: Each vertex can either be in the vertex cover or not; this will be useful in setting up your subproblems.,)