Search results
Results from the WOW.Com Content Network
A weight-balanced tree is a binary search tree that stores the sizes of subtrees in the nodes. That is, a node has fields key, of any ordered type; value (optional, only for mappings) left, right, pointer to node; size, of type integer. By definition, the size of a leaf (typically represented by a nil pointer) is zero.
English: Analysis of data structures, tree compared to hash and array based structures, height balanced tree compared to more perfectly balanced trees, a simple height balanced tree class with test code, comparable statistics for tree performance, statistics of worst case strictly-AVL-balanced trees versus perfect full binary trees.
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 ...
For another example, consider the recursive data structure of a binary tree with nodes that are either sentinel nodes of type or which are leaves containing a value of some type . We can represent this type algebraically as T ( X ) = 1 + X × T 2 ( X ) {\displaystyle T(X)=1+X\times T^{2}(X)} .
A binary search of a sorted table with N records, for example, can be done in roughly ⌈ log 2 N ⌉ comparisons. If the table had 1,000,000 records, then a specific record could be located with at most 20 comparisons: ⌈ log 2 (1,000,000) ⌉ = 20. Large databases have historically been kept on disk drives.
Order-statistic trees can be further amended with bookkeeping information to maintain balance (e.g., tree height can be added to get an order statistic AVL tree, or a color bit to get a red–black order statistic tree). Alternatively, the size field can be used in conjunction with a weight-balancing scheme at no additional storage cost. [4]
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:
A rope is a type of binary tree where each leaf (end node) holds a string of manageable size and length (also known as a weight), and each node further up the tree holds the sum of the lengths of all the leaves in its left subtree. A node with two children thus divides the whole string into two parts: the left subtree stores the first part of ...