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First, the tree is turned into a linked list by means of an in-order traversal, reusing the pointers in the tree's nodes. A series of left-rotations forms the second phase. [3] The Stout–Warren modification generates a complete binary tree, namely one in which the bottom-most level is filled strictly from left to right.
To define a binary tree, the possibility that only one of the children may be empty must be acknowledged. An artifact, which in some textbooks is called an extended binary tree, is needed for that purpose. An extended binary tree is thus recursively defined as: [11] the empty set is an extended binary tree
A trie is a type of search tree where – unlike for example a B-tree – keys are not stored in the nodes but in the path to leaves. The key is distributed across the tree structure. In a "classic" trie, each node with its child-branches represents one symbol of the alphabet of one position (character) of a key.
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.
In computer science, a B-tree is a self-balancing tree data structure that maintains sorted data and allows searches, sequential access, insertions, and deletions in logarithmic time. The B-tree generalizes the binary search tree, allowing for nodes with more than two children. [2]
In computer science, a trie (/ ˈ t r aɪ /, / ˈ t r iː /), also known as a digital tree or prefix tree, [1] is a specialized search tree data structure used to store and retrieve strings from a dictionary or set. Unlike a binary search tree, nodes in a trie do not store their associated key.
Another example is the representation of a binary tree: an arbitrary binary tree on nodes can be represented in + bits while supporting a variety of operations on any node, which includes finding its parent, its left and right child, and returning the size of its subtree, each in constant time.
In computer science, join-based tree algorithms are a class of algorithms for self-balancing binary search trees. This framework aims at designing highly-parallelized algorithms for various balanced binary search trees. The algorithmic framework is based on a single operation join. [1]