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A B-tree insertion example with each iteration. The nodes of this B-tree have at most 3 children (Knuth order 3). All insertions start at a leaf node. To insert a new element, search the tree to find the leaf node where the new element should be added. Insert the new element into that node with the following steps:
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insert efficient, with new records added at the end of the file, providing chronological order; retrieval efficient when the handle to the memory is the address of the memory; search inefficient, as searching has to be linear; deletion is accomplished by marking selected records as "deleted"
This implementation is a hybrid between the basic bitmap index (without compression) and the list of Row Identifiers (RID-list). Overall, the index is organized as a B+tree. When the column cardinality is low, each leaf node of the B-tree would contain long list of RIDs. In this case, it requires less space to represent the RID-lists as bitmaps.
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.
Demonstrates the process of removing an element with two children from a binary search tree. Created by Derrick Coetzee in Illustrator. To replace Image:Binary_search_tree_delete.png and en:Image:Binary_search_tree_delete.png. Date: 31 December 2005 (original upload date) Source: No machine-readable source provided.
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