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 .
- The longest path from to a leaf can be traced through nodes , 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:
- What is the depth of node ?
- What is the difference between the depth and height of a node?
- How do you calculate the total number of nodes in a binary tree?
- Can a binary tree be perfectly balanced? What conditions must be met?
- 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