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In computer science, a k-d tree (short for k-dimensional tree) is a space-partitioning data structure for organizing points in a k-dimensional space. K-dimensional is that which concerns exactly k orthogonal axes or a space of any number of dimensions. [1] k-d trees are a useful data structure for several applications, such as:
Like heapsort, smoothsort organizes the input into a priority queue and then repeatedly extracts the maximum. Also like heapsort, the priority queue is an implicit heap data structure (a heap-ordered implicit binary tree), which occupies a prefix of the array. Each extraction shrinks the prefix and adds the extracted element to a growing sorted ...
An octree is a tree data structure in which each internal node has exactly eight children. Octrees are most often used to partition a three-dimensional space by recursively subdividing it into eight octants. Octrees are the three-dimensional analog of quadtrees. The word is derived from oct (Greek root meaning "eight") + tree.
Binary space partitioning arose from computer graphics needing to rapidly draw three-dimensional scenes composed of polygons. A simple way to draw such scenes is the painter's algorithm , which produces polygons in order of distance from the viewer, back to front, painting over the background and previous polygons with each closer object.
The Z-ordering can be used to efficiently build a quadtree (2D) or octree (3D) for a set of points. [5] [6] The basic idea is to sort the input set according to Z-order.Once sorted, the points can either be stored in a binary search tree and used directly, which is called a linear quadtree, [7] or they can be used to build a pointer based quadtree.
A tree sort is a sort algorithm that builds a binary search tree from the elements to be sorted, and then traverses the tree so that the elements come out in sorted order. [1] Its typical use is sorting elements online : after each insertion, the set of elements seen so far is available in sorted order.
A balanced binary tree is a binary tree structure in which the left and right subtrees of every node differ in height (the number of edges from the top-most node to the farthest node in a subtree) by no more than 1 (or the skew is no greater than 1). [22]
In computer science, a trie (/ ˈ t r aɪ /, / ˈ t r iː /), also known as a digital tree or prefix tree, [1] is a specialized search tree data structure used to store and retrieve strings from a dictionary or set. Unlike a binary search tree, nodes in a trie do not store their associated key.