What is the worst-case time complexity of inserting an element in a binary searc
Practice Questions
Q1
What is the worst-case time complexity of inserting an element in a binary search tree?
O(log n)
O(n)
O(n log n)
O(1)
Questions & Step-by-Step Solutions
What is the worst-case time complexity of inserting an element in a binary search tree?
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 when you insert an element into a BST, you start at the root node and compare the new element with the current node's value.
Step 3: If the new element is less than the current node's value, you move to the left child; if it's greater, you move to the right child.
Step 4: Repeat this process until you find an empty spot (a null child) where you can insert the new element.
Step 5: In the worst-case scenario, the BST becomes unbalanced, resembling a linked list. This happens when you insert elements in sorted order (e.g., 1, 2, 3, ...).
Step 6: In this unbalanced case, you may have to traverse all n nodes to find the correct insertion point, leading to a time complexity of O(n).
