1. Advanced Data Structure using C++

LECTURE NOTES OF ADVANCED DATA STRUCTURE (MT-CSE 110)
Deletion
In the previous section, we saw that the SIZE and DEPTH properties of (2,4)‐
trees can be maintained efficiently as new items are inserted into the tree. We
now show that the same result holds as items are removed.
The deletion algorithm
Once again we'll begin with a basic algorithm that we'll adjust. We want to
DELETE a key k from T. For now, we shall assume that k is stored in a node v
whose children are all external nodes. Here are the steps we follow:
perform a SEARCH for k in T,
if it fails then we don't need to DELETE the item so we exit,
otherwise (if it succeds) then we find k in a node v with only external
children (by our assumption).
now we simply remove k from v and delete the external node child to the left of
k
B‐Tree
A B‐tree is a tree data structure that keeps data sorted and allows searches,
insertions, deletions, and sequential access in logarithmic amortized time. The
B‐tree is a generalization of a binary search tree in that more than two paths
diverge from a single node. [1] Unlike self‐balancing binary search trees, the B‐
tree is optimized for systems that read and write large blocks of data. It is most
commonly used in databases and filesystems.
Overview
In B‐trees, internal (non‐leaf) nodes can have a variable number of child nodes
within some pre‐defined range. When data is inserted or removed from a node,
its number of child nodes changes. In order to maintain the pre‐defined range,
Prepared By :­
Er. Harvinder Singh
Assist Prof., CSE, H.C.T.M (Kaithal) Page ‐ 210 ‐