Math Problem Statement

Consider the following Binary Tree. What is the height of the tree?

Solution

To determine the height of the binary tree shown in the image:

  • Height of a binary tree is defined as the number of edges on the longest path from the root node (A) to a leaf node (nodes without children).

Looking at the tree:

  • The root node is AA.
  • The longest path from AA to a leaf can be traced through nodes ADHLA \to D \to H \to L, which has 3 edges.

Thus, the height of the tree is 3.

Would you like more details on how this is calculated or any further questions?

Here are 5 related questions to expand on this topic:

  1. What is the depth of node JJ?
  2. What is the difference between the depth and height of a node?
  3. How do you calculate the total number of nodes in a binary tree?
  4. Can a binary tree be perfectly balanced? What conditions must be met?
  5. What is the time complexity of searching an element in a binary search tree?

Tip: The depth of a node is the number of edges from the root to that node, while the height is the number of edges from the node to the deepest leaf.

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Math Problem Analysis

Mathematical Concepts

Binary Trees
Graph Theory

Formulas

Height of Binary Tree: Longest path from root to leaf

Theorems

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Suitable Grade Level

Grades 10-12