- for each node in tree tlet pre(vbe the rank of in preorder traversal of tlet post(vbe the rank of in postorder traversal of tlet depth (vbe the depth of vand let desc(vbe the number of descendents of vnot counting itself derive formula defining post(vin terms of desc( )depth( )and pre( )for each node in - let be tree whose nodes store strings give an efficient algorithm that computes and printsfor every node of tthe string stored at and the height of the subtree rooted at - design algorithms for the following operations for binary tree tpreordernext( )return the node visited after node in preorder traversal of inordernext( )return the node visited after node in an inorder traversal of postordernext( )return the node visited after node in postorder traversal of what are the worst-case running times of your algorithmsc- give an ( )-time algorithm for computing the depth of all the nodes of tree twhere is the number of nodes of - the indented parenthetic representation of tree is variation of the parenthetic representation of (see figure that uses indentation and line breaks as illustrated in figure give an algorithm that prints this representation of tree