chap advanced tree structures (ashow the result (including appropriate rotationsof inserting the value into the avl tree on the left in figure (bshow the result (including appropriate rotationsof inserting the value into the avl tree on the left in figure (cshow the result (including appropriate rotationsof inserting the value into the avl tree on the left in figure (dshow the result (including appropriate rotationsof inserting the value into the avl tree on the left in figure show the splay tree that results from searching for value in the splay tree of figure ( show the splay tree that results from searching for value in the splay tree of figure ( some applications do not permit storing two records with duplicate key values in such casean attempt to insert duplicate-keyed record into tree structure such as splay tree should result in failure on insert what is the appropriate action to take in splay tree implementation when the insert routine is called with duplicate-keyed record show the result of deleting point from the - tree of figure (ashow the result of building - tree from the following points (inserted in the order givena ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( (bshow the result of deleting point from the tree you built in part ( (ashow the result of deleting from the pr quadtree of figure (bshow the result of deleting records and from the pr quadtree of figure (ashow the result of building pr quadtree from the following points (inserted in the order givenassume the tree is representing space of by units ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( (bshow the result of deleting point from the tree you built in part ( (cshow the result of deleting point from the resulting tree in part ( on averagehow many leaf nodes of pr quadtree will typically be emptyexplain why when performing region search on pr quadtreewe need only search those subtrees of an internal node whose corresponding square falls within the query circle this is most easily computed by comparing the and ranges of the query circle against the and ranges of the square corresponding to the subtree howeveras illustrated by figure the and ranges might overlap without the circle actually intersecting the square write function that accurately determines if circle and square intersect