What is the worst-case time complexity for insertion in a Red-Black tree?
Practice Questions
Q1
What is the worst-case time complexity for insertion in a Red-Black tree?
O(n)
O(log n)
O(n log n)
O(1)
Questions & Step-by-Step Solutions
What is the worst-case time complexity for insertion in a Red-Black tree?
Step 1: Understand what a Red-Black tree is. It is a type of self-balancing binary search tree.
Step 2: Know that in a binary search tree, we can insert a new node by comparing it with existing nodes.
Step 3: Realize that the height of a Red-Black tree is always kept in check, specifically it is at most 2 * log(n + 1), where n is the number of nodes.
Step 4: When we insert a new node, we may need to perform some rotations and color changes to maintain the properties of the Red-Black tree.
Step 5: The operations of insertion, including finding the correct position and performing rotations, take time proportional to the height of the tree.
Step 6: Since the height of the Red-Black tree is O(log n), the time complexity for insertion is also O(log n).
