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Some authors use the term complete to refer instead to a perfect binary tree as defined above, in which case they call this type of tree (with a possibly not filled last level) an almost complete binary tree or nearly complete binary tree. [20] [21] A complete binary tree can be efficiently represented using an array. [19] A complete binary ...
In computer science, a scapegoat tree is a self-balancing binary search tree, invented by Arne Andersson [2] in 1989 and again by Igal Galperin and Ronald L. Rivest in 1993. [1] It provides worst-case O ( log n ) {\displaystyle {\color {Blue}O(\log n)}} lookup time (with n {\displaystyle n} as the number of entries) and O ( log n ...
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.
To construct a tango tree, we simulate a complete binary search tree called the reference tree, which is simply a traditional binary search tree containing all the elements. This tree never shows up in the actual implementation, but is the conceptual basis behind the following pieces of a tango tree.
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 computer science, an optimal binary search tree (Optimal BST), sometimes called a weight-balanced binary tree, [1] is a binary search tree which provides the smallest possible search time (or expected search time) for a given sequence of accesses (or access probabilities). Optimal BSTs are generally divided into two types: static and dynamic.
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.
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 binary search tree. The Stern–Brocot tree was introduced independently by Moritz Stern and Achille Brocot .