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The B *+ tree combines the main B+ tree and B * tree features together. [ 15 ] B-trees can be turned into order statistic trees to allow rapid searches for the Nth record in key order, or counting the number of records between any two records, and various other related operations.
Database tables and indexes may be stored on disk in one of a number of forms, including ordered/unordered flat files, ISAM, heap files, hash buckets, or B+ trees. Each form has its own particular advantages and disadvantages. The most commonly used forms are B-trees and ISAM.
The order or branching factor b of a B+ tree measures the capacity of interior nodes, i.e. their maximum allowed number of direct child nodes. This value is constant over the entire tree. For a b-order B+ tree with h levels of index: [citation needed] The maximum number of records stored is =
In computer science, tree traversal (also known as tree search and walking the tree) is a form of graph traversal and refers to the process of visiting (e.g. retrieving, updating, or deleting) each node in a tree data structure, exactly once. Such traversals are classified by the order in which the nodes are visited.
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
The restrictions make insertion and deletion a little more complicated -- but, in return, the B-tree can guarantee very fast searches. Some nodes in some n-ary trees have only 1 or 2 children. B-trees are constructed so every internal node has at least L children. Some n-ary trees do not have all the leaves on the same level.
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A 2–3 tree is a B-tree of order 3. [1] Nodes on the outside of the tree have no children and one or two data elements. [2] [3] 2–3 trees were invented by John Hopcroft in 1970. [4] 2–3 trees are required to be balanced, meaning that each leaf is at the same level.