review questions answer these short answermultiple choiceand true/false questions to test your mastery of the what is the balance of node in an avl tree how does the balance of node relate to its height how does an avl tree make use of the balance of node what is pivot node what is bad child in relationship to avl trees what is the path stack and when is it necessary after doing right rotationwhere is the pivot node and the bad child in the subtree that was originally rooted at the pivot why is the balance of the root of subtree always after code for case is executed in the two subcases for case what node becomes the root node of the subtree rooted at the pivot after executing the algorithm on each of the subcases why does the avl tree insert algorithm always completes in (log ntimedo case by case analysis to justify your answer for each of the three cases involved in inserting value what is the purpose of the rotate string in the recursive insert splay tree implementation why does it seem that the recursive splay tree insert and lookup implementation operates faster than the avl tree implementation programming problems write an avl tree implementation that maintains balances in each node and implements insert iteratively write test program to thoroughly test your program on some randomly generated data write an avl tree implementation that maintains balances in each node and implements insert recursively write test program to thoroughly test your program on some randomly generated data write an avl tree implementation that maintains heights in each node and implements insert recursively write test program to thoroughly test your program on some randomly generated data write an avl tree implementation that maintains heights in each node and implements insert iteratively write test program to thoroughly test your program on some randomly generated data complete programming problem then implement the delete operation for avl trees finallywrite test program to thoroughly test your data structure as values are inserted and deleted from your tree you should test your code to make sure it maintains all heights correctly and the ordering of all values in the tree this copy belongs to 'acha