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The function Join on two AVL trees t 1 and t 2 and a key k will return a tree containing all elements in t 1, t 2 as well as k. It requires k to be greater than all keys in t 1 and smaller than all keys in t 2. If the two trees differ by height at most one, Join simply create a new node with left subtree t 1, root k and right subtree t 2.
An AVL tree is a kind of balanced binary search tree in which the two children of each internal node must have heights that differ by at most one. [7] The height of an external node is zero, and the height of any internal node is always one plus the maximum of the heights of its two children.
The degree of a tree is the maximum degree of a node in the tree. Distance The number of edges along the shortest path between two nodes. Level The level of a node is the number of edges along the unique path between it and the root node. [4] This is the same as depth. Width The number of nodes in a level. Breadth The number of leaves. Forest
The black height of a red–black tree is the number of black nodes in any path from the root to the leaves, which, by requirement 4, is constant (alternatively, it could be defined as the black depth of any leaf node). [16]: 154–165 The black height of a node is the black height of the subtree rooted by it. In this article, the black height ...
This means that for every LLRB tree, there is a unique corresponding 2–3–4 tree, and vice versa. If we impose the additional requirement that a node may not have two red children, LLRB trees become isomorphic to 2–3 trees, since 4-nodes are now prohibited. Sedgewick remarks that the implementations of LLRB 2–3 trees and LLRB 2–3–4 ...
The size of an internal node is the sum of sizes of its two children, plus one: (size[n] = size[n.left] + size[n.right] + 1). Based on the size, one defines the weight to be weight[n] = size[n] + 1. [a] Weight has the advantage that the weight of a node is simply the sum of the weights of its left and right children. Binary tree rotations.
The White House said Clinton, Soros and the 17 other recipients of the prestigious award are “individuals who have made exemplary contributions to the prosperity, values, or security of the ...
Height - Length of the path from the root to the deepest node in the tree. A (rooted) tree with only one node (the root) has a height of zero. In the example diagram, the tree has height of 2. Sibling - Nodes that share the same parent node. A node p is an ancestor of a node q if it exists on the path from q to the root. The node q is then ...