10.4. Building a Heap

Try these first

1. 1.

   What is the maximum value in a max heap, and where is it located?

   Hint

   Think about where the largest element would be in a hierarchical structure.

2. 2.

   Explain the bubble up operation when inserting into a heap.

   Hint

   Focus on the relationship between a node and its parent.

3. 3.

   What is the time complexity of inserting an element into a max heap?

   • O(1)
   • O(N)
   • O(log N)
   • O(N log N)

   Hint

   Consider the structure of heaps and how deep the tree can get.

4. 4.

   True or False: In a min heap, the maximum element is found at the root.

   • True
   • False

   Hint

   Think about the properties of both max heaps and min heaps.

5. 5.

   Given the values [7, 6, 5, 10, 14, 3, 9], build a max heap and show the resulting array representation.

   Hint

   Use the bottom-up method for efficient heap building.

6. 6.

   Consider a heap tree structure with nodes 5, 15, 10. If we insert 20 and then delete the maximum, what are the resulting elements in the heap?

   Hint

   Remember to restore the heap property after every operation.