How many leaf nodes can a binary tree with n internal nodes have?

Practice Questions

Q1
How many leaf nodes can a binary tree with n internal nodes have?
  1. n + 1
  2. n
  3. 2n
  4. n - 1

Questions & Step-by-Step Solutions

How many leaf nodes can a binary tree with n internal nodes have?
  • Step 1: Understand what a binary tree is. A binary tree is a tree data structure where each node has at most two children.
  • Step 2: Identify what internal nodes are. Internal nodes are nodes that have at least one child (they are not leaf nodes).
  • Step 3: Recognize what leaf nodes are. Leaf nodes are nodes that do not have any children (they are the end points of the tree).
  • Step 4: Know the relationship between internal nodes and leaf nodes in a binary tree. For every internal node, it can create new leaf nodes.
  • Step 5: Realize that in a binary tree, if you have 'n' internal nodes, you can always have one more leaf node than the number of internal nodes.
  • Step 6: Therefore, if there are 'n' internal nodes, the total number of leaf nodes will be 'n + 1'.
  • Binary Tree Structure – Understanding the relationship between internal nodes and leaf nodes in a binary tree.
  • Node Count Relationship – The formula relating internal nodes to leaf nodes in binary trees.
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