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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 ]
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
A Range Query Tree is a complete binary tree that has a static structure, meaning that its content can be changed but not its size. The values of the underlying array over which the associative operation needs to be performed are stored in the leaves of the tree and the number of values have to be padded to the next power of two with the identity value for the associative operation used.
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 ...
A binary heap is defined as a binary tree with two additional constraints: [3] Shape property: a binary heap is a complete binary tree; that is, all levels of the tree, except possibly the last one (deepest) are fully filled, and, if the last level of the tree is not complete, the nodes of that level are filled from left to right.
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 search tree. The Stern–Brocot tree was introduced independently by Moritz Stern and Achille Brocot .
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.