9.4.2. Maintaining Heap Properties

Try these first

1. 1.

   What are the two main properties of a heap?

   Hint

   Think about how the tree is structured and how the values are arranged.

2. 2.

   Explain what happens when you insert an element into a heap.

   Hint

   Focus on the order of insertion.

3. 3.

   What is the primary use of a heap?

   • Sorting
   • Implementing a priority queue
   • Searching data

   Hint

   Recall how jobs are prioritized.

4. 4.

   In a max heap, the value of a parent node is always ____ its child nodes.

   • True
   • False

   Hint

   Think about the structure maintained in heaps.

5. 5.

   Given a series of insertions: 7, 5, 12, 10, construct the heap and explain each step.

   Hint

   Build the max heap step by step, ensuring you bubble up where needed.

6. 6.

   Explain why heaps achieve O(log N) time complexity for insertion and deletion operations.

   Hint

   Think about the structure of trees and how many levels there are.