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The term B-tree may refer to a specific design or a general class of designs. In the narrow sense, a B-tree stores keys in its internal nodes but need not store those keys in the records at the leaves. The general class includes variations such as the B+ tree, the B * tree and the B *+ tree.
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. The primary value of a B+ tree is in storing data for efficient retrieval in a block-oriented storage context — in particular, filesystems .
To turn a regular search tree into an order statistic tree, the nodes of the tree need to store one additional value, which is the size of the subtree rooted at that node (i.e., the number of nodes below it). All operations that modify the tree must adjust this information to preserve the invariant that size[x] = size[left[x]] + size[right[x]] + 1
In computer science, a 2–3–4 tree (also called a 2–4 tree) is a self-balancing data structure that can be used to implement dictionaries. The numbers mean a tree where every node with children (internal node) has either two, three, or four child nodes: a 2-node has one data element, and if internal has two child nodes;
This approach relies on the standard formula for generating any primitive Pythagorean triple from a half-angle tangent. Specifically one writes t = n / m = b / (a + c), where t is the tangent of half of the interior angle that is opposite to the side of length b. The root node of the tree is t = 1/2, which is for the primitive Pythagorean ...
A full binary tree (sometimes referred to as a proper, [15] plane, or strict binary tree) [16] [17] is a tree in which every node has either 0 or 2 children. Another way of defining a full binary tree is a recursive definition. A full binary tree is either: [11] A single vertex (a single node as the root node). A tree whose root node has two ...
To calculate the net force on a particular body, the nodes of the tree are traversed, starting from the root. If the center of mass of an internal node is sufficiently far from the body, the bodies contained in that part of the tree are treated as a single particle whose position and mass is respectively the center of mass and total mass of the internal node.
Trees can be used to represent and manipulate various mathematical structures, such as: Paths through an arbitrary node-and-edge graph (including multigraphs), by making multiple nodes in the tree for each graph node used in multiple paths; Any mathematical hierarchy; Tree structures are often used for mapping the relationships between things ...