B-tree and AVL tree have the same worst case time complexity for insertion and deletion.

That's not a question, but a statement. However, I can provide information based on it.

B-tree and AVL tree are both types of self-balancing binary search trees and they do have the same worst-case time complexity for insertion, deletion, and search operations, which is O(log n).

Here's a step-by-step explanation:

1. AVL Tree: Named after its inventors Adelson-Velsky and Landis, an AVL tree is a self-balancing binary search tree where the difference of heights of left and right subtrees of any node is less than or equal to one.

• Insertion in AVL Tree: During insertion, the tree is recursively traversed from root to leaf node in order to find the correct location of the new key. After insertion, the tree is checked for balance and rotations (left, right, left-right, right-left) are performed if needed to maintain the balance. This gives a worst-case time complexity of O(log n).

• Deletion in AVL Tree: Similar to insertion, the tree is traversed from root to the node to be deleted. After deletion, the tree is checked for balance and rotations are performed if needed. This also gives a worst-case time complexity of O(log n).

2. B-Tree: A B-tree is a self-balancing search tree, in which every node contains multiple keys and has more than two children. B-tree is optimized for systems that read and write large blocks of data.

• Insertion in B-Tree: In a B-tree, data is inserted at the leaf nodes. The tree is traversed from root to the appropriate leaf node and the key is inserted in sorted order. If the leaf is full, it is split and the middle key is moved up to the parent. This process is repeated up to the root. This gives a worst-case time complexity of O(log n).

• Deletion in B-Tree: Deletion is more complex. The key is first located in the tree by traversing from the root to the leaf. If the key is in a node with more than the minimum number of keys, it can be deleted directly. Otherwise, keys may need to be redistributed or nodes may need to be merged to maintain the B-tree properties. This gives a worst-case time complexity of O(log n).

So, the statement is correct. Both B-tree and AVL tree have the same worst-case time complexity for insertion and deletion, which is O(log n).