B tree (computer Science)
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A B-tree is a multiway, non-linear data structure used to represent hierarchical relationships among data items, where each node can have multiple children and elements. It maintains balanced properties to minimize disk access, ensuring that all leaves are at the same level and nodes contain a defined number of children. The document illustrates the insertion process into a B-tree of order 4 with a specific set of elements.
B tree (computer Science)
- 2. A tree is non-linear data structure in which items are arranged in a sorted sequence. It used to represent hierarchical relationship existing amongst several data items.
- 3. B tree is a multiway tree. If its have N order then in each node of B tree can contain N-1 element in a node and node n way
- 4. B tree is also know as the balance sort tree. Its not a binary tree to reduce disk access several condition of the tree must be true. •The height of the tree must be kept to minimum .
- 5. •There must be no empty sub tree above the leaves of the tree •The leaves of the tree must all be on the same level. •All nodes except the leaves must have at least same minimum number of children.
- 6. The B tree of order M has following properties:- Each node has a maximum of M children and a minimum of M/2 children or any no. from 2 to the maximum
- 7. Each node has one fewer keys then children with a maximum m-1 key. When a new key is to be insert into a full node, the is split into two node and the key with the median value is inserted in the parent node. In case the parent node is the root a new root is created.
- 8. Lets consume B tree of the following element:- 7,16,13,9,11,5,17,23,21 with order 4. Solutions- (4-1)=3 step1:- 6,7,13
- 9. Step 2:- _7_ 5,6 9,11,13
- 10. Step 3:- 7, 11 5, 6 13,17,239
- 11. Step 4:- 7, 11, 17 5,6 9 21,23 13