What is the time complexity for deleting a node in an AVL tree?
Practice Questions
Q1
What is the time complexity for deleting a node in an AVL tree?
O(n)
O(log n)
O(n log n)
O(1)
Questions & Step-by-Step Solutions
What is the time complexity for deleting a node in 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 in 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 after deleting a node in an AVL tree, we need to check if the tree is still balanced. If it is not balanced, we perform rotations to restore balance.
Step 4: Understand that finding a node in an AVL tree takes O(log n) time because the tree is balanced, which keeps the height of the tree logarithmic relative to the number of nodes.
Step 5: Know that the balancing operations (rotations) also take O(log n) time because they involve a constant amount of work for each level of the tree.
Step 6: Combine the time taken for finding the node and the time taken for balancing. Both operations take O(log n), so the overall time complexity for deleting a node in an AVL tree is O(log n).
