than the previously inserted oneevery node is right childso all the nodes are on one side of the root the tree is maximally unbalanced if you inserted items in descending orderevery node would be the left child of its parentthe tree would be unbalanced on the other side degenerates to (nwhen there are no branchesthe tree becomesin effecta linked list the arrangement of data is one-dimensional instead of two-dimensional unfortunatelyas with linked listyou must now search through (on the averagehalf the items to find the one you're looking for in this situation the speed of searching is reduced to ( )instead of (lognas it is for balanced tree searching through , items in such an unbalanced tree would require an average of , comparisonswhereas for balanced tree with random insertions it requires only for presorted data you might just as well use linked list in the first place data that' only partly sorted will generate trees that are only partly unbalanced if you use the tree workshop applet from to attempt to generate trees with nodesyou'll see that some of them are more unbalanced than othersas shown in figure figure partially unbalanced tree although not as bad as maximally unbalanced treethis situation is not optimal for searching times in the tree workshop applettrees can become partially unbalancedeven with randomly generated databecause the amount of data is so small that even short run of ordered numbers will have big effect on the tree alsoa very small or very large key value can cause an unbalanced tree by not allowing the insertion of many nodes on one side or the other root of for exampleallows only two more nodes to be inserted to its left with realistic amount of random data it' not likely tree would become seriously unbalanced howeverthere may be runs of sorted data that will partially unbalance tree searching partially unbalanced trees will take time somewhere between (nand (logn)depending on how badly the tree is unbalanced balance to the rescue to guarantee the quick (log nsearch times tree is capable ofwe need to ensure that our tree is always balanced (or at least almost balancedthis means that each node in tree needs to have roughly the same number of descendents on its left side as it has on its right