What is the maximum number of nodes at level 'h' in a binary tree?
Practice Questions
Q1
What is the maximum number of nodes at level 'h' in 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' in 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: Know 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. At level 2, there can be 4 nodes.
Step 4: Understand the pattern. The number of nodes at level 'h' can be calculated using the formula 2^h. This means if you raise 2 to the power of 'h', you get the maximum number of nodes at that level.
Step 5: Conclude that if 'h' is the height of the tree, then the maximum number of nodes at that level is 2^h.
