trees  show that if all nodes in splay tree are accessed in sequential orderthen the total access time is ( )regardless of the initial tree write program to perform random operations on splay trees count the total number of rotations performed over the sequence how does the running time compare to avl trees and unbalanced binary search treeswrite efficient functions that take only pointer to the root of binary treetand compute the number of nodes in the number of leaves in the number of full nodes in what is the running time of your routinesdesign recursive linear-time algorithm that tests whether binary tree satisfies the search tree order property at every node write recursive function that takes pointer to the root node of tree and returns pointer to the root node of the tree that results from removing all leaves from write function to generate an -node random binary search tree with distinct keys through what is the running time of your routinewrite function to generate the avl tree of height with fewest nodes what is the running time of your functionwrite function to generate perfectly balanced binary search tree of height with keys through + what is the running time of your functionwrite function that takes as input binary search treetand two keysk and which are ordered so that < and prints all elements in the tree such that <key( < do not assume any information about the type of keys except that they can be ordered (consistentlyyour program should run in ( log naverage timewhere is the number of keys printed bound the running time of your algorithm the larger binary trees in this were generated automatically by program this was done by assigning an (xycoordinate to each tree nodedrawing circle around each coordinate (this is hard to see in some pictures)and connecting each node to its parent assume you have binary search tree stored in memory (perhaps generated by one of the routines aboveand that each node has two extra fields to store the coordinates the coordinate can be computed by assigning the inorder traversal number write routine to do this for each node in the tree the coordinate can be computed by using the negative of the depth of the node write routine to do this for each node in the tree in terms of some imaginary unitwhat will the dimensions of the picture behow can you adjust the units so that the tree is always roughly two-thirds as high as it is wided prove that using this system no lines crossand that for any nodexall elements in ' left subtree appear to the left of and all elements in ' right subtree appear to the right of