-trees how does the use of an index improve the efficiency of the sample join operation presented in sect what advantages does -tree have over hash table implementation of an index what advantages does hash table have over -tree implementation of an index how can -tree index be created over table with millions of records and still be usablewhat challenges could this pose and how does -tree provide means to deal with those challenges starting with fig insert an item with key and draw picture of the resulting -tree starting with fig delete the item containing and draw picture of the resulting -tree when does node get coalescedwhat does that meanprovide short example different from any example in the text when does rotation correct imbalance in nodeprovide short example different from any example in the text insert the values through into an empty -tree of degree to demonstrate your understanding of the insert algorithm draw picturesbut you can combine pictures that don' require splitting at each split be sure to draw completely new picture delete the values and from the tree you constructed in the previous review question showing the rebalanced tree after each deletion programming problems write -tree class and -tree node class implement the insert and delete algorithms described in this implement lookup method as well use this implementation to efficiently run the join operation presented in sect compare the time this algorithm takes to run to the time the non-indexed joinfrom sect takes to run write the two methods recursively write the -tree class with iterativenon-recursiveimplementations of insert and delete in this case the insert and delete methods of the -tree class don' necessarily have to call insert and delete on -tree nodes since the example tables in this are rather smallafter completing exercise or run the query code again using dictionary for the index compare the amount of time taken to implement the query in this way with the -tree implementation comment on the experiment results this copy belongs to 'acha