In a binary tree, what is the minimum number of nodes required to have a height

Practice Questions

Q1
In a binary tree, what is the minimum number of nodes required to have a height of h?
  1. h
  2. h + 1
  3. 2^h
  4. 2^(h+1) - 1

Questions & Step-by-Step Solutions

In a binary tree, what is the minimum number of nodes required to have a height of h?
  • 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: Know what height means. The height of a binary tree is the number of edges on the longest path from the root node to a leaf node.
  • Step 3: Realize that a skewed tree is a type of binary tree where all nodes are either to the left or to the right, forming a straight line.
  • Step 4: For a binary tree to have a height of h, it can be formed by having h nodes in a straight line (skewed tree).
  • Step 5: Therefore, the minimum number of nodes required to achieve a height of h is exactly h.
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