4. Let T be an arbitrary rooted tree, where each vertex is labeled with a positive integer. A subset S of the nodes of T is heap-ordered if it satisfies two properties: S contains a node that is an ancestor of every other node in S. For any node v in S, the label of v is larger than the labels of any ancestor of v in S. A heap-ordered subset of nodes in a tree. (a) Describe an algorithm to find the largest heap-ordered subset S of nodes in T that has the heap property in O(n) time.