What is the time complexity of inserting an element into a binary search tree (B
Practice Questions
Q1
What is the time complexity of inserting an element into a binary search tree (BST) in the average case?
O(1)
O(log n)
O(n)
O(n log n)
Questions & Step-by-Step Solutions
What is the time complexity of inserting an element into a binary search tree (BST) in the average case?
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 we insert an element into a BST, we start at the root node.
Step 3: Compare the value of the element we want to insert with the value of the current node.
Step 4: If the value is less, we move to the left child; if it's greater, we move to the right child.
Step 5: Repeat steps 3 and 4 until we find an empty spot (null) where we can insert the new element.
Step 6: In a balanced BST, the height of the tree is log(n), where n is the number of nodes. This means we will make about log(n) comparisons to find the right spot for the new element.
Step 7: Therefore, the average-case time complexity for inserting an element into a BST is O(log n).
