Construct a heap for the list 2, 15, 12, 10, 6, 14, 8 by successive key insertions (top-downalgorithm). (10 p.)

Sure, here are the steps to construct a heap for the list 2, 15, 12, 10, 6, 14, 8 using successive key insertions (top-down algorithm):

1. Start with an empty heap.

2. Insert the first element, 2. The heap is now: [2].

3. Insert the next element, 15. Since 15 is greater than 2, swap them. The heap is now: [15, 2].

4. Insert the next element, 12. Place it as a child of 2. The heap is now: [15, 2, 12].

5. Insert the next element, 10. Place it as a second child of 2. The heap is now: [15, 2, 12, 10].

6. Insert the next element, 6. Place it as a child of 12. The heap is now: [15, 2, 12, 10, 6].

7. Insert the next element, 14. Place it as a second child of 12. Since 14 is greater than 12, swap them. The heap is now: [15, 2, 14, 10, 6, 12].

8. Insert the last element, 8. Place it as a child of 10. The heap is now: [15, 2, 14, 10, 6, 12, 8].

So, the final heap after successive key insertions is: [15, 2, 14, 10, 6, 12, 8].