Search results
Results from the WOW.Com Content Network
When inserting a node into an AVL tree, you initially follow the same process as inserting into a Binary Search Tree. If the tree is empty, then the node is inserted as the root of the tree. 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.
To insert a value, we start at the root of the 2–3–4 tree: If the current node is a 4-node: Remove and save the middle value to get a 3-node. Split the remaining 3-node up into a pair of 2-nodes (the now missing middle value is handled in the next step). If this is the root node (which thus has no parent):
To insert into a 3-node, more work may be required depending on the location of the 3-node. If the tree consists only of a 3-node, the node is split into three 2-nodes with the appropriate keys and children. Insertion of a number in a 2–3 tree for 3 possible cases. If the target node is a 3-node whose parent is a 2-node, the key is inserted ...
The query algorithm visits one node per level of the tree, so O(log n) nodes in total. On the other hand, at a node v, the segments in I are reported in O(1 + k v) time, where k v is the number of intervals at node v, reported. The sum of all the k v for all nodes v visited, is k, the number of reported segments. [5]
Deletion from an AVL tree may be carried out by rotating the node to be deleted down into a leaf node, and then pruning off that leaf node directly. Since at most log n nodes are rotated during the rotation into the leaf, and each AVL rotation takes constant time, the deletion process in total takes O(log n) time.
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.
Image credits: Genie_noteC #5. I cut open all my product containers and use every last drop. It's more about not wasting stuff, but it's also frugal. You would be surprised how much product can be ...
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: