10.3. Heap Representation

Try these first

1. 1.

   What is the height of a heap?

   Hint

   Think about the path traveled from the top to the bottom of the heap.

2. 2.

   What operation removes the maximum element from a max heap?

   Hint

   Consider which operation focuses on the root element being the maximum.

3. 3.

   What property must be satisfied in a max heap?

   • All nodes are equal
   • The root is the smallest element
   • The root is greater than its children

   Hint

   Think about how a max heap is defined.

4. 4.

   True or False: The height of a heap increases with the number of elements.

   • True
   • False

   Hint

   Consider how levels in a tree increase with additional nodes.

5. 5.

   Given a max heap represented as an array, describe how you would implement insert and delete operations, including complexities.

   Hint

   Consider the implications of maintaining heap properties during the operations.

6. 6.

   Explain how the logarithmic time complexity of heap operations reflects upon their height and number of nodes.

   Hint

   Think about the nature of binary trees and their properties.