What is the average time complexity for insertion in a Red-Black tree?
Practice Questions
Q1
What is the average 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 average 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, each node has at most two children, and the left child is less than the parent, while the right child is greater.
Step 3: Realize that a Red-Black tree maintains balance through specific properties, which helps keep the tree height low.
Step 4: Remember that the height of a balanced tree is proportional to the logarithm of the number of nodes, which is expressed as log(n).
Step 5: When inserting a new node, the tree may need to be restructured to maintain its properties, but this restructuring is done in a way that keeps the time complexity low.
Step 6: Conclude that the average time complexity for insertion in a Red-Black tree is O(log n) because the height of the tree is logarithmic in relation to the number of nodes.
