10.4.1. Naive Heap Construction

Try these first

1. 1.

   What is the main property of a max heap?

   Hint

   Think about how the largest value is organized in the tree.

2. 2.

   How does the time complexity of insertion in a heap compare to a simple list?

   Hint

   Consider how the elements are arranged in a list versus a heap.

3. 3.

   In a max heap, every parent node is less than or equal to its children.

   • True
   • False

   Hint

   Recall the definition of a max heap from our discussion.

4. 4.

   What is the time complexity for deleting the maximum node in a max heap?

   • O(N)
   • log(N)
   • O(1)

   Hint

   Think about the height of the heap.

5. 5.

   Given the array [1, 3, 5, 7, 9, 2, 4, 6, 8], construct a max heap using both the naive insertion method and the bottom-up method. Compare the steps taken.

   Hint

   Keep track of the number of swaps and the structure at each step.

6. 6.

   Explain why it’s more efficient to use a bottom-up heapifying approach rather than naive construction. Provide an example to illustrate your reason.

   Hint

   Focus on how many nodes are involved at different levels and how many swaps are really done.