What is the time complexity of searching for an element in a balanced AVL tree?
Practice Questions
Q1
What is the time complexity of searching for an element in a balanced AVL tree?
O(log n)
O(n)
O(n log n)
O(1)
Questions & Step-by-Step Solutions
What is the time complexity of searching for an element in a balanced 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 in a binary search tree, searching for an element involves comparing the target value with the values of the nodes, starting from the root and moving left or right based on the comparison.
Step 3: Realize that because the AVL tree is balanced, the maximum height of the tree is logarithmic in relation to the number of nodes (n). This means the height of the tree is approximately log2(n).
Step 4: Since searching involves traversing from the root to a leaf node, the time it takes to search is proportional to the height of the tree.
Step 5: Conclude that the time complexity for searching in a balanced AVL tree is O(log n) because the height of the tree determines the number of comparisons needed.
