Consider the following problem:
You are given a pointer to the root r of a binary tree, where each vertex v has pointers v. lc and v. rc to the left and right child, and a value V al(v) > 0 . The value NIL represents a null pointer, showing that v has no child of that type. You wish to find the path from r to some leaf that maximizes the total values of vertices along that path.
(a) Give an algorithm to find the maximum sum of vertices along such a path along with a proof of correctneess and runtime analysis

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