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If the tree is not empty, then we go down the root, and recursively go down the tree searching for the location to insert the new node. This traversal is guided by the comparison function. In this case, the node always replaces a NULL reference (left or right) of an external node in the tree i.e., the node is either made a left-child or a right ...
But I agree, it would be interesting to state an algorithm how to do it. A simple one might be to create an empty tree, then walk the original unbalanced tree in-order, and insert each node into the new tree, using the AVL-insert. That should take O(n*log n). --Allefant 14:24, 24 November 2006 (UTC)
Weak AVL rule: all rank differences are 1 or 2, and all leaf nodes have rank 0. Note that weak AVL tree generalizes the AVL tree by allowing for 2,2 type node. A simple proof shows that a weak AVL tree can be colored in a way that represents a red-black tree. So in a sense, weak AVL tree combines the properties of AVL tree and red-black tree.
That node is the "next" node, and after it come its descendants on the right. It is also possible to discover the parent of a node from a threaded binary tree, without explicit use of parent pointers or a stack, although it is slower. To see this, consider a node k with right child r.
To insert a new element, search the tree to find the leaf node where the new element should be added. Insert the new element into that node with the following steps: If the node contains fewer than the maximum allowed number of elements, then there is room for the new element. Insert the new element in the node, keeping the node's elements ordered.
Most operations on a binary search tree (BST) take time directly proportional to the height of the tree, so it is desirable to keep the height small. A binary tree with height h can contain at most 2 0 +2 1 +···+2 h = 2 h+1 −1 nodes. It follows that for any tree with n nodes and height h: + And that implies:
This is loosely similar to AVL trees, in that the actual rotations depend on 'balances' of nodes, but the means of determining the balance differs greatly. Since AVL trees check the balance value on every insertion/deletion, it is typically stored in each node; scapegoat trees are able to calculate it only as needed, which is only when a ...
Unlike the balance information in AVL trees (using information about the height of subtrees) and red–black trees (which store a fictional "color" bit), the bookkeeping information in a WBT is an actually useful property for applications: the number of elements in a tree is equal to the size of its root, and the size information is exactly the ...