What is the maximum number of nodes at level 'h' of a binary tree?
Practice Questions
Q1
What is the maximum number of nodes at level 'h' of a binary tree?
h
2^h
2^(h+1) - 1
h^2
Questions & Step-by-Step Solutions
What is the maximum number of nodes at level 'h' of a binary tree?
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: Identify what 'level' means in a binary tree. The level of a node is defined by its distance from the root node. The root node is at level 0, its children are at level 1, and so on.
Step 3: Recognize that at each level of a binary tree, the number of nodes can double compared to the previous level. For example, at level 0 (the root), there is 1 node. At level 1, there can be 2 nodes (the children of the root). At level 2, there can be 4 nodes (the children of the nodes at level 1).
Step 4: Generalize this pattern. At level 'h', the maximum number of nodes is 2 raised to the power of 'h'. This is because each node can have 2 children, leading to exponential growth.
Step 5: Conclude that the formula for the maximum number of nodes at level 'h' is 2^h.
