A subset of nodes S of an undirected graph is called indepen- dant if for any u, ve S if u v then (u, v) E. Given a tree of n nodes (with undirected edges) design an O(n) algorithm to find the maximum sized independant set of nodes. Argue that your solution is correct and analyse its time complexity. (Hint: Think of some special type of nodes which must occur in some maximal independant set.)