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

@@ -1,4 +1,4 @@
-# Consider a min heap with these elements: [4, 5, 6, 7, 8, 9, 10]. Insert 3 into this min heap.
+# 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:
 
@@ -8,10 +8,13 @@ In a **min heap**, the root node contains the smallest element, and every parent
 ### 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
       /   \
@@ -19,13 +22,17 @@ This corresponds to the following binary tree:
     / \   / \
    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
       /   \
@@ -35,6 +42,7 @@ This corresponds to the following binary tree:
   /
  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:
@@ -42,6 +50,7 @@ Now, we need to **bubble up** the element `3` to restore the heap property. We c
 - The parent of `3` is `7` (index 3). Since `3 < 7`, we swap them.
 
 After the swap, the heap becomes:
+
 ```
         4
       /   \
@@ -57,6 +66,7 @@ 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
       /   \
@@ -86,6 +96,7 @@ After the swap, the heap becomes:
 ### **Final Array Representation**:
 
 The final min heap as an array is:
+
 ```csharp
 [3, 4, 6, 5, 8, 9, 10, 7]
 ```