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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.
A segment tree from the set of segments I, can be built as follows.First, the endpoints of the intervals in I are sorted. The elementary intervals are obtained from that. Then, a balanced binary tree is built on the elementary intervals, and for each node v it is determined the interval Int(v) it represen
This unsorted tree has non-unique values (e.g., the value 2 existing in different nodes, not in a single node only) and is non-binary (only up to two children nodes per parent node in a binary tree). The root node at the top (with the value 2 here), has no parent as it is the highest in the tree hierarchy.
A medial- or length-oriented tree is similar to an augmented tree, but symmetrical, with the binary search tree ordered by the medial points of the intervals. There is a maximum-oriented binary heap in every node, ordered by the length of the interval (or half of the length). Also we store the minimum and maximum possible value of the subtree ...
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.
Random binary tree; Red–black tree; Rope (data structure) Rotation distance; S. Scapegoat tree; Segment tree; Self-balancing binary search tree; Skew heap; Splay ...
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.
Patricia trees are a particular implementation of the compressed binary trie that uses the binary encoding of the string keys in its representation. [23] [15]: 140 Every node in a Patricia tree contains an index, known as a "skip number", that stores the node's branching index to avoid empty subtrees during traversal.