1. Advanced Data Structure using C++

LECTURE NOTES OF ADVANCED DATA STRUCTURE (MT-CSE 110)
Similar to case 2 except want to keep left child and any of its children.
Case 4: Delete a parent with 2 children. E.g. delete Q.
Problem: Can’t guarantee that the parent of the node could point to both
children, since the parent may have another child of its own.
AVL Tree
In an AVL, the difference between the right and left sub‐tree can never be more
than 1, throughout the tree.
A binary search tree (BST) is an AVL tree if and only if, for every node in the tree,
the difference between maximum height of the right sub‐tree minus the
maximum height of the left sub‐tree is less than 2.
That is the difference can be ‐1, 0, or 1.
AVL Trees is An ordered tree (binary search tree) is used when we wish to store
objects with (numerical) keys in a binary tree so that lookups can be done in
order log 2N time, where N is the number of objects in the tree. But an ordered
tree that is seriously ``unbalanced,'' that is, where paths from the root to the
leaves have dramatically different lengths, will ruin the desired lookup
behavior.
The worst‐case example of an unbalanced ordered tree is the tree built by
inserting a sorted sequence of objects (we show the numerical keys only; the
objects attached with the keys are unimportant):
1 2 3 4
The tree looks like this:
1
/ \
. 2
Prepared By :­
Er. Harvinder Singh
Assist Prof., CSE, H.C.T.M (Kaithal) Page ‐ 200 ‐