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The tree with the minimal weighted path length is, by definition, statically optimal. But weighted path lengths have an interesting property. Let E be the weighted path length of a binary tree, E L be the weighted path length of its left subtree, and E R be the weighted path length of its right subtree. Also let W be the sum of all the ...
The randomized binary search tree, introduced by Martínez and Roura subsequently to the work of Aragon and Seidel on treaps, [7] stores the same nodes with the same random distribution of tree shape, but maintains different information within the nodes of the tree in order to maintain its randomized structure.
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In computer science, tree traversal (also known as tree search and walking the tree) is a form of graph traversal and refers to the process of visiting (e.g. retrieving, updating, or deleting) each node in a tree data structure, exactly once. Such traversals are classified by the order in which the nodes are visited.
A perfect binary tree is a binary tree in which all interior nodes have two children and all leaves have the same depth or same level (the level of a node defined as the number of edges or links from the root node to a node). [18] A perfect binary tree is a full binary tree.
Fig. 1: A binary search tree of size 9 and depth 3, with 8 at the root. In computer science, a binary search tree (BST), also called an ordered or sorted binary tree, is a rooted binary tree data structure with the key of each internal node being greater than all the keys in the respective node's left subtree and less than the ones in its right subtree.
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:
Binary trees may also be studied with all nodes unlabeled, or with labels that are not given in sorted order. For instance, the Cartesian tree data structure uses labeled binary trees that are not necessarily binary search trees. [4] A random binary tree is a random tree drawn from a certain probability distribution on binary trees. In many ...