10.2.1. Finding and Removing the Maximum

Try these first

1. 1.

   What is the maximum element in a max heap?

   Hint

   Think about the structure of the max heap.

2. 2.

   Which operation has a logarithmic time complexity in a heap?

   Hint

   Recall how the height of a heap relates to its size.

3. 3.

   Where is the maximum value located in a max heap?

   • Root
   • Leaf
   • Middle

   Hint

   Think about the properties that define the max heap.

4. 4.

   True or False: Sifting down is the process used to adjust the heap after removing the maximum element.

   • True
   • False

   Hint

   Recall the steps involved in the maximum removal.

5. 5.

   Given a max heap represented as an array: [50, 30, 20, 15, 10, 5], remove the maximum. Show the array after each step of restoring the heap property.

   Hint

   Keep track of the largest child when performing sift down.

6. 6.

   Create a max heap from the following numbers: 15, 30, 10, 8, 25, and explain the process step by step.

   Hint

   Always fix the heap property after each insertion.