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A full binary tree (sometimes referred to as a proper, [15] plane, or strict binary tree) [16] [17] is a tree in which every node has either 0 or 2 children. Another way of defining a full binary tree is a recursive definition. A full binary tree is either: [11] A single vertex (a single node as the root node). A tree whose root node has two ...
Example of a complete binary max-heap Example of a complete binary min heap. A binary heap is a heap data structure that takes the form of a binary tree. Binary heaps are a common way of implementing priority queues. [1]: 162–163 The binary heap was introduced by J. W. J. Williams in 1964 as a data structure for implementing heapsort. [2]
The root has depth zero, leaves have height zero, and a tree with only a single vertex (hence both a root and leaf) has depth and height zero. Conventionally, an empty tree (a tree with no vertices, if such are allowed) has depth and height −1. A k-ary tree (for nonnegative integers k) is a rooted tree in which each vertex has at most k ...
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
English: Analysis of data structures, tree compared to hash and array based structures, height balanced tree compared to more perfectly balanced trees, a simple height balanced tree class with test code, comparable statistics for tree performance, statistics of worst case strictly-AVL-balanced trees versus perfect full binary trees.
Let n ≥ 0 be the number of entries in the tree. Let m be the maximum number of children a node can have. Each node can have at most m−1 keys. It can be shown (by induction for example) that a B-tree of height h with all its nodes completely filled has n = m h+1 –1 entries. Hence, the best case height (i.e. the minimum height) of a B-tree is:
In a binary tree the balance factor of a node X is defined to be the height difference ():= (()) (()) [6]: 459 of its two child sub-trees rooted by node X. A node X with () < is called "left-heavy", one with () > is called "right-heavy", and one with () = is sometimes simply called "balanced".
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.