Q2 (15 Points): The catornal gett length of a full binary fras is the sum. takon over all nil loaves of the trog, of the depth of eacheat. Giventhe following binary search free. in which infernal nodes are shown as oides and external nodos lazyes, nit pointers are shown as small boxes. a Calculate the external path length. bi Is there a binary search tree on the same sel of letters, (D. G. N. G. S. T), that has lower external path length? Either give such a tree and how it is formed from the original BST or prove it does not exist c) Can the nodes in the original BST be colored red and black so as to form a proper red-black tree? If so, show how to color them; if not, prove it