design variation of algorithm treesearch for performing the operation findal(kin an ordered dictionary implemented with binary search tree tand show that it runs in time ( )where is the height of and is the size of the collection returned - describe how to perform an operation removeall( )which removes all the entries whose keys equal in an ordered dictionary implemented with binary search tree tand show that this method runs in time ( )where is the height of and is the size of the iterator returned - draw schematic of an avl tree such that single remove operation could require ohm(logntrinode restructurings (or rotationsfrom leaf to the root in order to restore the height-balance property - show how to perform an operationremoveall( )which removes all entries with keys equal to kin dictionary implemented with an avl tree in time (slogn)where is the number of entries in the dictionary and is the size of the iterator returned - if we maintain reference to the position of the left-most internal node of an avl treethen operation first (section can be performed in ( time describe how the implementation of the other dictionary methods needs to be modified to maintain reference to the left-most position - show that any -node binary tree can be converted to any other -node binary tree using (nrotations - let be an ordered dictionary with entries implemented by means of an avl tree show how to implement the following operation on in time (logn )where is the size of the iterator returnedfindallinrange( , )return an iterator of all the entries in with key such that < <