9.3.1. Valid Heap Example 1

Try these first

1. 1.

   Define a heap in your own words.

   Hint

   Think about what makes heaps different from other data structures.

2. 2.

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

   Hint

   Recall how height affects performance.

3. 3.

   What property must a max-heap satisfy?

   • Each parent is less than its children
   • Each parent is greater than its children
   • Parents can be equal to children

   Hint

   Think about the requirements for retrieving the maximum element quickly.

4. 4.

   True or False: A binary tree can be a heap even if it has missing nodes.

   • True
   • False

   Hint

   Recall the shape property of heaps.

5. 5.

   Create a valid max-heap from the following numbers: 10, 20, 15, 30, 25. Describe how you would go about it.

   Hint

   Keep an eye on the relationships between the parent and child nodes.

6. 6.

   A max-heap is given as [50, 30, 20, 15, 10]. If we insert a value of 25, how does this affect the heap?

   Hint

   Think about how the insertion balances the structure.