What is the average time complexity of inserting a node in a balanced binary sea
Practice Questions
Q1
What is the average time complexity of inserting a node 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 of inserting a node in a balanced binary search tree?
Step 1: Understand what a balanced binary search tree is. It is a type of tree data structure where the left and right subtrees of every node differ in height by at most one.
Step 2: Know that in a binary search tree, each node has a value, and the left child has a smaller value while the right child has a larger value.
Step 3: When inserting a new node, you start at the root and compare the value of the new node with the current node's value.
Step 4: If the new node's value is smaller, you move to the left child; if it's larger, you move to the right child.
Step 5: You repeat this process until you find the correct spot for the new node, which takes time proportional to the height of the tree.
Step 6: In a balanced binary search tree, the height is approximately log base 2 of the number of nodes (n), so the time to insert is O(log n).
