What is the worst-case time complexity for inserting an element into a binary se
Practice Questions
Q1
What is the worst-case time complexity for inserting an element into a binary search tree?
O(1)
O(log n)
O(n)
O(n log n)
Questions & Step-by-Step Solutions
What is the worst-case time complexity for inserting an element into a binary search tree?
Step 1: Understand what a binary search tree (BST) is. A BST is a data structure that stores elements in a way that for any given node, all elements in the left subtree are smaller, and all elements in the right subtree are larger.
Step 2: Know that when you insert an element into a BST, you start at the root and compare the new element with the current node's value.
Step 3: If the new element is smaller, you move to the left child; if it's larger, you move to the right child.
Step 4: Repeat this process until you find an empty spot where the new element can be inserted.
Step 5: In the worst-case scenario, the BST becomes unbalanced, resembling a linked list. This happens when each new element is either always greater or always smaller than the previous ones.
Step 6: In this unbalanced state, you may have to traverse all n elements to find the correct spot for the new element, leading to a time complexity of O(n) for insertion.
