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A complete binary tree is a binary tree in which every level, except possibly the last, is completely filled, and all nodes in the last level are as far left as possible. It can have between 1 and 2 h nodes at the last level h . [ 19 ]
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A min-max heap is a complete binary tree containing alternating min (or even) and max (or odd) levels. Even levels are for example 0, 2, 4, etc, and odd levels are respectively 1, 3, 5, etc. We assume in the next points that the root element is at the first level, i.e., 0. Example of Min-max heap
In number theory, the Stern–Brocot tree is an infinite complete binary tree in which the vertices correspond one-for-one to the positive rational numbers, whose values are ordered from the left to the right as in a search tree. The Stern–Brocot tree was introduced independently by Moritz Stern and Achille Brocot .
The NIST Dictionary of Algorithms and Data Structures [1] is a reference work maintained by the U.S. National Institute of Standards and Technology.It defines a large number of terms relating to algorithms and data structures.
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.
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.
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.