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A rapidly exploring random tree (RRT) is an algorithm designed to efficiently search nonconvex, high-dimensional spaces by randomly building a space-filling tree. The tree is constructed incrementally from samples drawn randomly from the search space and is inherently biased to grow towards large unsearched areas of the problem.
When a directed rooted tree has an orientation away from the root, it is called an arborescence [3] or out-tree; [11] when it has an orientation towards the root, it is called an anti-arborescence or in-tree. [11] The tree-order is the partial ordering on the vertices of a tree with u < v if and only if the unique path from the root to v passes ...
A B+ tree consists of a root, internal nodes and leaves. [1] The root may be either a leaf or a node with two or more children. A B+ tree can be viewed as a B-tree in which each node contains only keys (not key–value pairs), and to which an additional level is added at the bottom with linked leaves.
If the tree is fairly balanced, this amounts to O(log n) space for a tree containing n elements. In the worst case, when the tree takes the form of a chain, the height of the tree is n so the algorithm takes O(n) space. A second problem is that all traversals must begin at the root when nodes have pointers only to their children.
Cartesian trees are defined using binary trees, which are a form of rooted tree. To construct the Cartesian tree for a given sequence of distinct numbers, set its root to be the minimum number in the sequence, [1] and recursively construct its left and right subtrees from the subsequences before and after this number, respectively. As a base ...
In computer science, a priority search tree is a tree data structure for storing points in two dimensions. It was originally introduced by Edward M. McCreight. [1] It is effectively an extension of the priority queue with the purpose of improving the search time from O(n) to O(s + log n) time, where n is the number of points in the tree and s is the number of points returned by the search.
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Since the data elements in each node are ordered, a search function will be directed to the correct subtree and eventually to the correct node which contains the item. Let T be a 2–3 tree and d be the data element we want to find. If T is empty, then d is not in T and we're done. Let t be the root of T. Suppose t is a leaf.