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The Z-ordering can be used to efficiently build a quadtree (2D) or octree (3D) for a set of points. [4] [5] 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, [6] or they can be used to build a pointer based quadtree.
Augmented map. In computer science, the augmented map [1] is an abstract data type (ADT) based on ordered maps, which associates each ordered map an augmented value. For an ordered map with key type , comparison function on and value type , the augmented value is defined based on two functions: a base function and a combine function , where is ...
In computer science, an associative array, map, symbol table, or dictionary is an abstract data type that stores a collection of (key, value) pairs, such that each possible key appears at most once in the collection. In mathematical terms, an associative array is a function with finite domain. [1] It supports 'lookup', 'remove', and 'insert ...
Complexities below assume n items to be sorted, with keys of size k, digit size d, and r the range of numbers to be sorted. Many of them are based on the assumption that the key size is large enough that all entries have unique key values, and hence that n ≪ 2 k, where ≪ means "much less than".
The Z-order curve maps each cell of the full quadtree (and hence even the compressed quadtree) in () time to a one-dimensional line (and maps it back in () time too), creating a total order on the elements. Therefore, we can store the quadtree in a data structure for ordered sets (in which we store the nodes of the tree).
Selection algorithm. In computer science, a selection algorithm is an algorithm for finding the th smallest value in a collection of ordered values, such as numbers. The value that it finds is called the th order statistic. Selection includes as special cases the problems of finding the minimum, median, and maximum element in the collection.
In C++, associative containers are a group of class templates in the standard library of the C++ programming language that implement ordered associative arrays. [ 1] Being templates, they can be used to store arbitrary elements, such as integers or custom classes. The following containers are defined in the current revision of the C++ standard ...
Each insertion sort is (), c the size of the subarrays; there are p subarrays thus p * c = n, so the insertion phase take O(n); thus, ProxmapSort is (). Average case: Each subarray is at most size c, a constant; insertion sort for each subarray is then O(c^2) at worst – a constant. (The actual time can be much better, since c items are not ...