avl-tree

Is the computational complexity of TreeSet methods in Java, same as that of an AVLTree? Specifically, I want to know the computational complexity of the following methods: 1.add 2.remove 3.first 4.last 5. floor 6. higher Java Doc for method description: http://docs.oracle.com/javase/6/docs/api/java/util/TreeSet.html For an AVL Tree, there are all O(logn)? Whats the complexity of the above TreeSet Methods? Operations which work on a single element are all O(ln n) comparisons except first and last which are O(1) comparisons or O(ln N) node search time. comparator(), iterator(), clear(), first(),

Is there such a sequence of numbers (1-7, all numbers used, only once each), that would form equal AVL and splay tree? Well, in the interests of science, I implemented both AVL and splay trees in Python based on their respective Wikipedia articles. Assuming I didn't make a mistake somewhere, my finding is that there are no permutations of {1, ..., 7} that produce the same AVL and splay tree . I conjecture the same is true for all sets of size k > 3. As to the fundamental reasons for this, I have no idea. If someone would like to vet my code, here it is: ##################### # Class

It is well known that deletion from an AVL tree may cause several nodes to eventually be unbalanced. My question is, what is the minimum sized AVL tree such that 2 rotations are required (I'm assuming a left-right or right-left rotation is 1 rotation)? I currently have an AVL tree with 12 nodes where deletion would cause 2 rotations. My AVL tree is inserting in this order: 8, 5, 9, 3, 6, 11, 2, 4, 7, 10, 12, 1. If you delete the 10, 9 becomes unbalanced and a rotation occurs. In doing so, 8 becomes unbalanced and another rotation occurs. Is there a smaller tree where 2 rotations are necessary

I have used kd-tree algoritham and make tree. But i found that tree is not balanced so my question is if we used kd-tree algoritham then that tree is always balanced if not then how can we make it balance ?. We can use another algoritham likes AVL or Red-Black for balancing kd tree ? I have some sample data for that i used kd-tree algoritham but that tree is not balanced. (14,31), (15,32), (17,42), (16,44), (18,52), (16,62) This is a fairly broad topic and the questions themselves are kind of general. Hopefully this will give you some useful insights and material to work with: Kd tree is not