What is the time complexity of deleting a node from an AVL tree?
Practice Questions
Q1
What is the time complexity of deleting a node from an AVL tree?
O(n)
O(log n)
O(n log n)
O(1)
Questions & Step-by-Step Solutions
What is the time complexity of deleting a node from an AVL tree?
Step 1: Understand what an AVL tree is. An AVL tree is a type of binary search tree that is balanced, meaning the heights of the two child subtrees of any node differ by at most one.
Step 2: Know that deleting a node from a binary search tree involves finding the node, removing it, and then rearranging the tree to maintain the binary search tree properties.
Step 3: Realize that in an AVL tree, after deleting a node, we may need to perform rotations to keep the tree balanced.
Step 4: Understand that finding a node in a balanced binary search tree takes O(log n) time because the tree height is logarithmic relative to the number of nodes.
Step 5: Recognize that the rotations needed to maintain balance after deletion also take O(log n) time in the worst case.
Step 6: Combine these steps to conclude that the overall time complexity for deleting a node from an AVL tree is O(log n).
