Which of the following is true about the height of a binary tree with n nodes?

Practice Questions

Q1
Which of the following is true about the height of a binary tree with n nodes?
  1. Height = n
  2. Height = log n
  3. Height <= n
  4. Height = n/2

Questions & Step-by-Step Solutions

Which of the following is true about the height of a binary tree with n nodes?
  • Step 1: Understand what a binary tree is. A binary tree is a structure where each node has at most two children.
  • Step 2: Know what 'height' means. The height of a tree is the number of edges on the longest path from the root to a leaf.
  • Step 3: Consider the case of a skewed tree. A skewed tree is one where all nodes are either to the left or to the right, forming a straight line.
  • Step 4: In a skewed tree with n nodes, the height is n - 1 because there are n nodes but only n - 1 edges connecting them.
  • Step 5: Therefore, the maximum height of a binary tree with n nodes is n - 1, which means the height can be at most n.
  • Step 6: Conclude that the height of a binary tree with n nodes is less than or equal to n.
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