What is the maximum number of nodes at level 'l' of a binary tree?
Practice Questions
Q1
What is the maximum number of nodes at level 'l' of a binary tree?
l
2^l
2^(l+1) - 1
l^2
Questions & Step-by-Step Solutions
What is the maximum number of nodes at level 'l' 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 'l', the number of nodes can double compared to the previous level. This is because each node can have two children.
Step 4: Realize that at level 0 (the root), there is 1 node (2^0 = 1). At level 1, there can be 2 nodes (2^1 = 2). At level 2, there can be 4 nodes (2^2 = 4), and so forth.
Step 5: Conclude that the maximum number of nodes at any level 'l' is given by the formula 2^l, where 'l' is the level number.
