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:
```csharp
[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:
```csharp
[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:
```csharp
[3, 4, 6, 5, 8, 9, 10, 7]
```