Question

ANSWER ASAP, DATA STRUCTURES QUESTION

In this question, you will work with a min-heap (binary heap) implemented using an array. Insert the values (in order): 9, 3, 7, 4, 8, 2, 6, 5, 10, 2, 1 into an initially empty binary heap tree. Show

Answer 1

The resulting binary heap tree after inserting the given values: 1, 2, 2, 5, 3, 6, 7, 9, 10, 8, 4.

Step-by-step explanation:

To insert the given values into an initially empty binary heap tree, we start by adding the values to the array in the order given: 9, 3, 7, 4, 8, 2, 6, 5, 10, 2, 1.

After inserting each value, we need to ensure that the heap property is maintained. This means that for any given node, the value of that node is less than or equal to the values of its children.

Here is the step-by-step process:

1. Insert 9 into the array.
2. Insert 3 into the array and compare it with its parent (9). Since 3 is smaller, we swap them.
3. Insert 7 into the array and compare it with its parent (9). Since 7 is smaller, we swap them.
4. Insert 4 into the array and compare it with its parent (9). Since 4 is smaller, we swap them.
5. Insert 8 into the array and compare it with its parent (9). Since 8 is smaller, we swap them.
6. Insert 2 into the array and compare it with its parent (9). Since 2 is smaller, we swap them.
7. Insert 6 into the array and compare it with its parent (9). Since 6 is smaller, we swap them.
8. Insert 5 into the array and compare it with its parent (9). Since 5 is smaller, we swap them.
9. Insert 10 into the array and compare it with its parent (9). Since 10 is greater, we leave it as is.
10. Insert 2 into the array and compare it with its parent (3). Since 2 is smaller, we swap them.
11. Insert 1 into the array and compare it with its parent (3). Since 1 is smaller, we swap them.

The resulting binary heap tree after inserting the given values is: 1