What is the worst-case time complexity for inserting an element into a Red-Black
Practice Questions
Q1
What is the worst-case time complexity for inserting an element into a Red-Black tree?
O(log n)
O(n)
O(n log n)
O(1)
Questions & Step-by-Step Solutions
What is the worst-case time complexity for inserting an element into 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, elements are arranged in a way that for any node, all elements in the left subtree are smaller, and all elements in the right subtree are larger.
Step 3: Recognize that Red-Black trees maintain balance through specific properties, which help keep the tree height low.
Step 4: Realize that the height of a Red-Black tree is always O(log n), where n is the number of nodes in the tree.
Step 5: Understand that inserting an element involves finding the correct position in the tree, which takes O(log n) time due to the height of the tree.
Step 6: After inserting, the tree may need to be rebalanced, but this rebalancing also takes O(log n) time.
Step 7: Combine the time for finding the position and the time for rebalancing, which both are O(log n).
