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B Tree

A B-tree is a self-balancing tree data structure that maintains sorted data and allows searches, sequential access, insertions, and deletions in logarithmic time. It is designed to work efficiently on disks or other direct-access secondary storage devices. B-trees are characterized by their ability to store large amounts of data while keeping the height of the tree relatively small.

Key Features of a B-tree Include

  • Balanced Structure: B-trees are self-balancing, which means that they automatically adjust their structure to maintain a balanced tree even after insertions and deletions.
  • Degree: A B-tree of order m is a tree that satisfies the following properties:
    • Every node has at most m children.
    • Every non-leaf node (except the root) has at least ⌈m/2⌉ children.
    • The root has at least two children if it is not a leaf node.
    • All leaves appear at the same level.
  • Multilevel Index: B-trees are often used in database and file systems as a multilevel index structure, enabling efficient data retrieval and management.
  • Disk-Based Operations: B-trees are particularly suitable for systems that read and write large blocks of data, as they minimize the number of disk accesses required for most operations.

Operations B Tree

B-trees support various operations that enable efficient management and manipulation of data stored within the structure. Some of the key operations performed on B-trees include:

  • Search: Searching for a key within the B-tree, which involves traversing the tree from the root to the leaf nodes to locate the desired key.
  • Insertion: Inserting a new key into the B-tree while maintaining the order of keys and balancing the tree, if necessary, to ensure that the B-tree properties are preserved.
  • Deletion: Removing a key from the B-tree, which may involve adjusting the structure of the tree to maintain the B-tree properties and balance.
  • Splitting and Merging Nodes: Splitting or merging nodes when a node becomes full or underfull, respectively, to ensure that each node maintains the required number of keys and children.
  • Traversal: Traversing the B-tree in various ways, such as in-order, pre-order, and post-order traversal, to access and process all the keys in the tree.
  • Range Queries: Performing range queries to retrieve a set of keys within a specified range, which can be efficiently executed using the properties of the B-tree structure.