What is the average time complexity for inserting an element in a balanced binar
Practice Questions
Q1
What is the average time complexity for inserting an element in a balanced binary search tree?
O(n)
O(log n)
O(n log n)
O(1)
Questions & Step-by-Step Solutions
What is the average time complexity for inserting an element in a balanced binary search tree?
Step 1: Understand what a balanced binary search tree (BST) is. It is a tree 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 in a balanced BST, the height of the tree is kept to a minimum. This means that the tree is structured in a way that it is not too tall, which helps in keeping operations efficient.
Step 3: When you want to insert a new element, you start at the root of the tree and compare the new element with the current node's value.
Step 4: If the new element is smaller, you move to the left child; if it is larger, you move to the right child. You repeat this process until you find the correct spot for the new element.
Step 5: The maximum number of comparisons you will make is equal to the height of the tree. In a balanced BST, the height is approximately log base 2 of the number of nodes (n).
Step 6: Therefore, the average time complexity for inserting an element in a balanced binary search tree is O(log n).
