How ot construct the Min heap

Hey!

What I would recommend here is to start by checking out this helpful tutorial: Min Heap Binary Tree Tutorial.

In general, a min heap is structured so that each parent node is smaller than its child nodes, with the smallest element at the root. For example, as you insert each number, swap elements as needed to keep this order.

For your exact question, this would look like:

1. Insert 82, 90, 10, 12, 15, 77, 55, 23 one by one.
2. After each insertion, adjust (or “heapify”) to ensure each parent node is smaller than its children.

Hope this helps!

- Bobby

Heya,

To construct a Min-Heap from the list of values (82, 90, 10, 12, 15, 77, 55, 23), we’ll insert each element one-by-one, ensuring that the heap property is maintained at each step. The Min-Heap property requires that each parent node is less than or equal to its child nodes.

Let’s go through the insertion and rebalancing process for each element:

Step-by-Step Insertion and Heapify

1. Start with an empty Min-Heap.

2. Insert 82:

   • Heap: [82]

3. Insert 90:

   • Heap: [82, 90]
   • 90 is greater than 82, so the heap property holds.

4. Insert 10:

   • Heap: [82, 90, 10]
   • 10 is less than 82, so swap them to maintain the Min-Heap property.
   • Heap after swap: [10, 90, 82]

5. Insert 12:

   • Heap: [10, 90, 82, 12]
   • 12 is greater than 10, so no swaps are needed.

6. Insert 15:

   • Heap: [10, 90, 82, 12, 15]
   • 15 is greater than 10, so no swaps are needed.

7. Insert 77:

   • Heap: [10, 90, 82, 12, 15, 77]
   • 77 is greater than 10, so no swaps are needed.

8. Insert 55:

   • Heap: [10, 90, 82, 12, 15, 77, 55]
   • 55 is greater than 10, so no swaps are needed.

9. Insert 23:

   • Heap: [10, 90, 82, 12, 15, 77, 55, 23]
   • 23 is greater than 10, so no swaps are needed.

Final Min-Heap

After all insertions, the heap structure, arranged to meet the Min-Heap property, is:

        10
       /  \
     12    77
    /  \   / \
   23  15 90  55
            \
            82

So, the array representation of this Min-Heap is:

[10, 12, 77, 23, 15, 90, 55, 82]