What is the time complexity of inserting a node in a balanced binary search tree
Practice Questions
Q1
What is the 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 time complexity of inserting a node 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 number of levels in the tree is logarithmic relative to the number of nodes.
Step 3: When you want to insert a new node, you start at the root and compare the new value with the current node's value.
Step 4: Depending on whether the new value is less than or greater than the current node's value, you move to the left or right child, respectively.
Step 5: You repeat this comparison and movement down the tree until you find the correct spot for the new node.
Step 6: Since the height of a balanced BST is O(log n), the maximum number of comparisons you will make to find the right spot is also O(log n).
Step 7: Therefore, the time complexity for inserting a node in a balanced binary search tree is O(log n).
