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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.
A full binary tree (sometimes referred to as a proper, [15] plane, or strict binary tree) [16] [17] is a tree in which every node has either 0 or 2 children. Another way of defining a full binary tree is a recursive definition. A full binary tree is either: [11] A single vertex (a single node as the root node). A tree whose root node has two ...
A Fenwick tree or binary indexed tree (BIT) is a data structure that stores an array of values and can efficiently compute prefix sums of the values and update the values. It also supports an efficient rank-search operation for finding the longest prefix whose sum is no more than a specified value.
Bagwell [1] presented a time and space efficient solution for tries named Array Mapped Tree (AMT). The Hash array mapped trie (HAMT) is based on AMT. The compact trie node representation uses a bitmap to mark every valid branch – a bitwise trie with bitmap.
To turn a regular search tree into an order statistic tree, the nodes of the tree need to store one additional value, which is the size of the subtree rooted at that node (i.e., the number of nodes below it). All operations that modify the tree must adjust this information to preserve the invariant that size[x] = size[left[x]] + size[right[x]] + 1
To split a tree into two trees, those smaller than key x, and those larger than key x, we first draw a path from the root by inserting x into the tree. After this insertion, all values less than x will be found on the left of the path, and all values greater than x will be found on the right.
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 ...
A binary search tree is said to be weight-balanced if half the nodes are on the left of the root, and half on the right. An α-weight-balanced node is defined as meeting a relaxed weight balance criterion: