What is the worst-case time complexity for inserting a node in a binary search t
Practice Questions
Q1
What is the worst-case time complexity for inserting a node in a binary search tree?
O(n)
O(log n)
O(n log n)
O(1)
Questions & Step-by-Step Solutions
What is the worst-case time complexity for inserting a node in a binary search tree?
Step 1: Understand what a binary search tree (BST) is. A BST is a tree 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 inserting a node means placing it in the correct position according to the BST rules.
Step 3: Consider the structure of the tree. In a balanced BST, the height of the tree is log(n), where n is the number of nodes. This allows for efficient insertion.
Step 4: However, in the worst-case scenario, the tree can become unbalanced, resembling a linked list. This happens when nodes are inserted in a sorted order.
Step 5: In this unbalanced case, to insert a new node, you may have to traverse all the way down the tree, which takes O(n) time, where n is the number of nodes in the tree.
Step 6: Therefore, the worst-case time complexity for inserting a node in a binary search tree is O(n).
