9.2.1. Binary Tree Definition

Try these first

1. 1.

   What is a binary tree?

   Hint

   Think about the definition of tree structures.

2. 2.

   What defines a max heap?

   Hint

   Consider the relationship between parent and child nodes.

3. 3.

   What is a binary tree?

   • A structure with nodes having two children
   • A structure that can have many children
   • A linear data structure

   Hint

   Think about the limitations on node connectivity.

4. 4.

   True or False: In a max heap, each parent node must be smaller than its children.

   • True
   • False

   Hint

   Recall the definition of a max heap.

5. 5.

   Design a binary tree that fulfills the max heap property using the following numbers: [8, 3, 5, 1, 4, 2]. Explain how you achieved the arrangement and any challenges you encountered.

   Hint

   Try drawing the heap as you add nodes, ensuring each parent-child relationship holds.

6. 6.

   Given a binary tree that does not maintain the max heap property, explain how you would adjust it. Provide a specific example with steps.

   Hint

   Think about the process of comparing and swapping from the violating node upward.