Math Problem Statement

Select the tree that is not a full binary tree. A full binary tree is defined as a tree in which every node has either 0 or 2 children.

Solution

The question asks to select the tree that is not a full binary tree. A full binary tree is a tree in which every node has either 0 or 2 children. No node in a full binary tree should have just one child.

Let's analyze the four diagrams:

  • A: This tree is a full binary tree because every internal node has exactly two children.
  • B: This tree is also a full binary tree because all internal nodes have two children.
  • C: This tree is not a full binary tree. One of its nodes has only one child, violating the rule.
  • D: This tree is a full binary tree with all internal nodes having two children.

Thus, the tree in Option C is not a full binary tree.

Would you like a further breakdown or have any questions about full binary trees?

Here are five follow-up questions you may find useful:

  1. What is the difference between a full binary tree and a complete binary tree?
  2. How can you determine the number of nodes in a full binary tree if the height is known?
  3. What is the maximum number of nodes in a full binary tree of a given height?
  4. How can you construct a full binary tree from a given number of nodes?
  5. What are some common uses of full binary trees in computer science?

Tip: In a full binary tree, the number of leaf nodes is always one more than the number of internal nodes.

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Math Problem Analysis

Mathematical Concepts

Binary Trees
Tree Structures

Formulas

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Theorems

Full Binary Tree Property: Every node has 0 or 2 children.

Suitable Grade Level

Grades 9-12