A tree is a connected, acyclic undirected graph. So, for each pair v and u of nodes in a tree, there is exactly one simple path connecting v and u (a simple path is one that does not repeat any node). The diameter of a tree t is the length of the longest simple path in t. For example, the tree shown below has diameter 12. A (nonempty) rooted tree is a tree (V, E) together with a node (the root) v E V. In the diagram below we have placed the tree's root at the top. The height of a rooted tree (v, V, E) is the length of the longest simple path from v to some other node u E V. For example, the rooted tree shown below has height 8. Assume that a rooted tree is represented as a label-and-pointer structure that provides the root (a label) together with a (possibly empty) list of pointers, each pointing to a rooted tree. Design a linear-time recursive algorithm that, given a non-empty rooted tree, finds the tree's diameter. Hint: Given the rooted tree G = (v, V, E), let v's neighbours be u,..., uk. Removing v and its incident edges from G leaves us with k separate rooted trees G,..., Gk, with roots u,..., uk, respectively, and these graphs can now be dealt with recursively, after which G's diameter can be calculated.