GATE CSE 2020 Q16: Worst-case time to insert n^2 elements into an AVL tree of n

What is the worst case time complexity of inserting $n^2$ elements into an AVL-tree with $n$ elements initially?

Try it: multiple choice: exactly one correct option

Wrong answer costs 1/3 mark in GATE.

Show answer and explanation

Answer: C (official GATE 2020 final answer key)

Concept used: Each AVL insertion costs $O(\log m)$ for a tree of $m$ nodes.

First step: The tree never exceeds $n + n^2$ nodes, so each insertion is $O(\log n^2) = O(\log n)$ ; multiply by $n^2$ insertions.

Full step-by-step solution

Detailed working, common mistakes and linked mock tests will be available with a free GATEiit account. Log-in is coming soon.

Share this question

Source: official GATE 2020 CS question paper and final answer key, organised by IIT Delhi. Question paper · Answer key