You are given an undirected tree T = (V, E). In this problem we will find the diameter of the tree in 3 different ways. a. Write the following: 1. A recursive algorithm to find the *diameter of the graph, based on the leaf pruning method discussed in lecture. 2. An iterative algorithm to find the *diameter of the graph, based on the recursive version you came up with and the leaf pruning method discussed in lecture. Compute the complexity of this version. There exists a O(ED iterative implementation of the recursion. b. Show how you can find the *diameter of the graph in 0(El) time by running BFS twice. c. Find the diameter of the graph by **rooting the tree, and a recursive call from the root asking for the diameter of each subtree hanging from each of its child. *Diameter is defined as the longest path (number of edges) between any two nodes Vi, V; EV. ** Rooting a tree is choosing a vetrex in the tree to be called a root. The neighbors of the root are called the children of the root. Recursively, the child is now a root for the fragment of the tree it resides in, after the removal of the root from the tree