[6 marks Diameter of a tree The diameter of a tree is the length of the longest simple path between nodes of the tree. Design an efficient divide and conquer algorithm to compute the diameter of a rooted binary tree. Your algorithm may use the following operations on trees that each have time complexity (1). RooT(T) Returns the root node of the tree T LEFTCHILD(T, v) Returns the node that is the left child of v in T; or 0 if v does not have a left child. RIGHTCHILD(T, v) Returns the node that is the right child of v in T; or if v does not have a right child Provide justification of the correctness and a its running time complexity