What is the maximum number of nodes in a Red-Black tree of height h?
Practice Questions
Q1
What is the maximum number of nodes in a Red-Black tree of height h?
2^h
2^(h+1)-1
h^2
h!
Questions & Step-by-Step Solutions
What is the maximum number of nodes in a Red-Black tree of height h?
Step 1: Understand what a Red-Black tree is. It is a type of binary search tree with specific properties that help keep it balanced.
Step 2: Know that the height (h) of a tree is the number of edges on the longest path from the root to a leaf.
Step 3: Realize that in a Red-Black tree, every node can be either red or black, and there are rules about how these colors can be arranged.
Step 4: Understand that the maximum number of nodes in a Red-Black tree occurs when the tree is as full as possible.
Step 5: The maximum number of nodes in a binary tree of height h is given by the formula 2^(h+1) - 1. This is because each level of the tree can have twice as many nodes as the level above it.
Step 6: Apply the formula to find the maximum number of nodes in a Red-Black tree of height h, which is 2^(h+1) - 1.
