What is the time complexity of different tree operations?

What is the time complexity of different tree operations?

The time complexity of tree operations varies by type of tree. For example, in a binary search tree (BST), insertion, deletion, and search operations have an average time complexity of O(log n), but in the worst case, it can be O(n) if the tree becomes unbalanced.

What about balanced trees like AVL or Red-Black trees?

For balanced trees like AVL or Red-Black trees, the time complexity for insertion, deletion, and search operations is consistently O(log n) because they maintain balance after every operation.

Are there any operations that are more complex?

Yes, some operations like finding the lowest common ancestor or performing a range query can have different complexities. For example, finding the lowest common ancestor in a BST can be done in O(h) time, where h is the height of the tree.

How does the complexity change with different types of trees?

The complexity can change significantly. For example, in a B-tree, which is used in databases, the time complexity for search, insert, and delete operations is O(log n) as well, but it can handle a large number of children per node, which optimizes disk reads.