B-Tree

B-Tree of order M is a #202112101956 that has the following Characteristics.

B-Tree could be used in:

  • database system

Characteristics

  • Root node is either a leaf or has between 2 and M children
  • Non-leaf nodes, except root, has between M/2 and M children
  • All leaves share the same depth

Details

  • Leaves are used to store data
  • Keys stored in the left leaves is smaller than the keys stored in the right leaves
  • If the leaf is full, it will split the parent node into two

Analysis

  • The depth of the B-Tree is at most \(\lceil \log_{\lceil \frac{M}{2} \rceil} N \rceil\)
  • Find operation will result in \(O(\log N)\)
  • Insertion and Deletion will result in \(O(M \log_M N)\)
  • The best choice of M is either 3 or 4
  • B-Tree will be 69% full
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#data-structure #tree