G4G0-2/Data Structures/GPT Answers to Past Paper/Question 8.md

Consider a Min Heap with These Elements: [4, 5, 6, 7, 8, 9, 10]. Insert 3 into This Min Heap.

In a min heap, the root node contains the smallest element, and every parent node is less than its children. When we insert a new element into a min heap, we follow these steps:

1. Insert the element at the end of the heap (maintaining the complete binary tree property).
2. Bubble up (or sift up) the inserted element to restore the heap property by comparing it with its parent and swapping if necessary.

Given Min Heap:

The given min heap is represented as an array:

[4, 5, 6, 7, 8, 9, 10]

This corresponds to the following binary tree:

        4
      /   \
     5     6
    / \   / \
   7   8 9  10

Step 1: Insert 3 into the Heap

First, insert 3 at the end of the heap:

[4, 5, 6, 7, 8, 9, 10, 3]

This corresponds to the following binary tree:

        4
      /   \
     5     6
    / \   / \
   7   8 9  10
  /
 3

Step 2: Bubble Up

Now, we need to bubble up the element 3 to restore the heap property. We compare 3 with its parent and swap if necessary:

• The parent of 3 is 7 (index 3). Since 3 < 7, we swap them.

After the swap, the heap becomes:

        4
      /   \
     5     6
    / \   / \
   3   8 9  10
  /
 7

Now, we continue the bubbling up process:

• The parent of 3 is 5 (index 1). Since 3 < 5, we swap them.

After the swap, the heap becomes:

        4
      /   \
     3     6
    / \   / \
   5   8 9  10
  /
 7

Finally, we compare 3 with its parent 4 (index 0):

• Since 3 < 4, we swap them.

After the swap, the heap becomes:

        3
      /   \
     4     6
    / \   / \
   5   8 9  10
  /
 7

Final Array Representation:

The final min heap as an array is:

[3, 4, 6, 5, 8, 9, 10, 7]