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In computer science, a range tree is an ordered tree data structure to hold a list of points. It allows all points within a given range to be reported efficiently, and is typically used in two or higher dimensions. Range trees were introduced by Jon Louis Bentley in 1979. Similar data structures were discovered independently by Lueker, Lee and Wong, and Willard. The range tree is an alternative to the ''k''-d tree. Compared to ''k''-d trees, range trees offer faster query times of (in Big O notation) but worse storage of , where ''n'' is the number of points stored in the tree, ''d'' is the dimension of each point and ''k'' is the number of points reported by a given query. Bernard Chazelle improved this to query time and space complexity . == Description == A range tree on a set of 1-dimensional points is a balanced binary search tree on those points. The points stored in the tree are stored in the leaves of the tree; each internal node stores the largest value contained in its left subtree. A range tree on a set of points in ''d''-dimensions is a recursively defined multi-level binary search tree. Each level of the data structure is a binary search tree on one of the ''d''-dimensions. The first level is a binary search tree on the first of the ''d''-coordinates. Each vertex ''v'' of this tree contains an associated structure that is a (''d''−1)-dimensional range tree on the last (''d''−1)-coordinates of the points stored in the subtree of ''v''. 抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Range tree」の詳細全文を読む スポンサード リンク
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