In a binary tree, what is the maximum number of leaf nodes possible?
Practice Questions
1 question
Q1
In a binary tree, what is the maximum number of leaf nodes possible?
n
n/2
2^h
2^(h+1) - 1
The maximum number of leaf nodes in a binary tree of height h is 2^h, as each level can have twice the number of nodes as the previous level.
Questions & Step-by-step Solutions
1 item
Q
Q: In a binary tree, what is the maximum number of leaf nodes possible?
Solution: The maximum number of leaf nodes in a binary tree of height h is 2^h, as each level can have twice the number of nodes as the previous level.
Steps: 6
Step 1: Understand what a binary tree is. A binary tree is a tree data structure where each node has at most two children, referred to as the left child and the right child.
Step 2: Know what a leaf node is. A leaf node is a node that does not have any children.
Step 3: Learn about the height of a binary tree. The height of a binary tree is the number of edges on the longest path from the root node to a leaf node.
Step 4: Recognize that at each level of the binary tree, the number of nodes can double. For example, at level 0 (the root), there is 1 node; at level 1, there can be 2 nodes; at level 2, there can be 4 nodes, and so on.
Step 5: Calculate the maximum number of leaf nodes. At the maximum height h, the number of leaf nodes is 2^h because all nodes at the last level (height h) can be leaf nodes.
Step 6: Conclude that the maximum number of leaf nodes in a binary tree of height h is 2^h.
