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In computer science, the segment tree is a data structure used for storing information about intervals or segments. It allows querying which of the stored segments contain a given point. A similar data structure is the interval tree. A segment tree for a set I of n intervals uses O(n log n) storage and can be built in O(n log n) time.
A more difficult subset of the problem consists of executing range queries on dynamic data; that is, data that may mutate between each query. In order to efficiently update array values, more sophisticated data structures like the segment tree or Fenwick tree are necessary.
A similar data structure is the segment tree. ... Interval trees solve this problem. This article describes two alternative designs for an interval tree, ...
Range minimum query reduced to the lowest common ancestor problem.. Given an array A[1 … n] of n objects taken from a totally ordered set, such as integers, the range minimum query RMQ A (l,r) =arg min A[k] (with 1 ≤ l ≤ k ≤ r ≤ n) returns the position of the minimal element in the specified sub-array A[l …
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.
A 1-dimensional range tree on a set of n points is a binary search tree, which can be constructed in () time. Range trees in higher dimensions are constructed recursively by constructing a balanced binary search tree on the first coordinate of the points, and then, for each vertex v in this tree, constructing a (d−1)-dimensional range tree on the points contained in the subtree of v.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
In computational geometry, Klee's measure problem is the problem of determining how efficiently the measure of a union of (multidimensional) rectangular ranges can be computed. Here, a d -dimensional rectangular range is defined to be a Cartesian product of d intervals of real numbers , which is a subset of R d .