What is the time complexity of searching for an element in a binary search tree
Practice Questions
Q1
What is the time complexity of searching for an element in a binary search tree (BST) in the average case?
O(1)
O(log n)
O(n)
O(n log n)
Questions & Step-by-Step Solutions
What is the time complexity of searching for an element in a binary search tree (BST) in the average case?
Step 1: Understand what a binary search tree (BST) is. A BST is a data structure where each node has at most two children, and the left child is less than the parent node, while the right child is greater.
Step 2: Know that searching in a BST involves comparing the target value with the values in the nodes, starting from the root.
Step 3: Realize that in a balanced BST, the height of the tree is minimized, which means the number of levels is kept low.
Step 4: Each time you compare the target value with a node, you can decide to go left or right, effectively halving the number of nodes you need to check.
Step 5: Since the height of a balanced BST is log(n) (where n is the number of nodes), the average time complexity for searching is O(log n).
