- consider tree storing , entries what is the worst-case height of in the following casesa is binary search tree is an avl tree is splay tree is ( tree is red-black tree - draw an example of red-black tree that is not an avl tree - let be red-black tree and let be the position of the parent of the original node that is deleted by the standard search tree deletion algorithm prove that if has zero childrenthe removed node was red leaf - let be red-black tree and let be the position of the parent of the original node that is deleted by the standard search tree deletion algorithm prove that if has one childthe deletion has caused black deficit at pexcept for the case when the one remaining child is red leaf - let be red-black tree and let be the position of the parent of the original node that is deleted by the standard search tree deletion algorithm prove that if has two childrenthe removed node was black and had one red child creativity - explain how to use an avl tree or red-black tree to sort comparable elements in ( log ntime in the worst case - can we use splay tree to sort comparable elements in ( log ntime in the worst casewhy or why notc- repeat exercise - for the treemap class - show that any -node binary tree can be converted to any other -node binary tree using (nrotations - for key that is not found in binary search tree prove that both the greatest key less than and the least key greater than lie on the path traced by the search for - in section we claim that the find range method of binary search tree executes in ( htime where is the number of items found within the range and is the height of the tree our implementationin code fragment begins by searching for the starting keyand then repeatedly calling the after method until reaching the end of the range each call to after is guaranteed to run in (htime this suggests weaker (shbound for find rangesince it involves (scalls to after prove that this implementation achieves the stronger ( hbound