1. Write a function (heapify) to satisfy the heap property from an array A. In order to implement the heapify function, please implement the below functions first: int getParent (int index); // Purpose: calculates the index of a node's parent node // Post: integer value returned to caller int getLeftChild (int index) ; // Purpose: calculates the index of node's left child // Post: integer value returned to caller int getRightchild (int index); // Purpose: caleulates the index of a node's right child // Post: integer value returned to the user void swap (ints iteml, ints item2); // Purpose: exchanges two values // Post: iteml - old item2 and item2 - old iteml, results // returned through reference parameter 2. Write a function to build a heap (buildHeap). 3. Test output with an array A[20] = {4,1,3,2,16,9,10,14,8,7}. 4. Create a function to insert numbers to the heap. 5. Test the insert function with inserting 20 and 17 sequentially to the heap (heapInset function should be called to insert 20 and 17- Do not use build_heap function in the heap_insert function). Function Prototypes: int getParent( int index); int getleftChi Id( int index); int getRightChild( int index); void swap( int& i tem1, int& item2); void heapify( int A[], int index, int size); void build_heap( int A[], int size): void printArray( int A[], int size); void heapInser t(int A[], int &size, int Item);// Do not use build heap function in the heap_insert function).
1. Write a function (heapify) to satisfy the heap property from an array A. In order to implement the heapify function, please implement the below functions first: int getParent (int index); // Purpose: calculates the index of a node's parent node // Post: integer value returned to caller int getLeftChild (int index) ; // Purpose: calculates the index of node's left child // Post: integer value returned to caller int getRightchild (int index); // Purpose: caleulates the index of a node's right child // Post: integer value returned to the user void swap (ints iteml, ints item2); // Purpose: exchanges two values // Post: iteml - old item2 and item2 - old iteml, results // returned through reference parameter 2. Write a function to build a heap (buildHeap). 3. Test output with an array A[20] = {4,1,3,2,16,9,10,14,8,7}. 4. Create a function to insert numbers to the heap. 5. Test the insert function with inserting 20 and 17 sequentially to the heap (heapInset function should be called to insert 20 and 17- Do not use build_heap function in the heap_insert function). Function Prototypes: int getParent( int index); int getleftChi Id( int index); int getRightChild( int index); void swap( int& i tem1, int& item2); void heapify( int A[], int index, int size); void build_heap( int A[], int size): void printArray( int A[], int size); void heapInser t(int A[], int &size, int Item);// Do not use build heap function in the heap_insert function).
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Please help with C++ question in image. Thank you.
![### Heap Algorithms and Functions
#### 1. Heapify Function
Develop a `heapify` function to maintain the heap property in an array A. Implement the following auxiliary functions first:
- **`int getParent(int index);`**
- **Purpose**: Calculates the index of a node's parent.
- **Postcondition**: Returns an integer value.
- **`int getLeftChild(int index);`**
- **Purpose**: Calculates the index of a node's left child.
- **Postcondition**: Returns an integer value.
- **`int getRightChild(int index);`**
- **Purpose**: Calculates the index of a node's right child.
- **Postcondition**: Returns an integer value.
- **`void swap(int item1, int item2);`**
- **Purpose**: Exchanges two values.
- **Postcondition**: Swaps item1 and item2 through a reference parameter.
#### 2. Build Heap Function
Implement a `buildHeap` function to construct a heap from an array.
#### 3. Test Array
Use the array `A[20] = {4,1,3,2,16,9,10,14,8,7}` to test the `buildHeap` function.
#### 4. Insert Function
Create a function for inserting numbers into the heap.
#### 5. Insert Test
Test the insert function by adding 20 and 17 sequentially to the heap. Use the `heapInsert` function to add these elements. Do not utilize `build_heap` within `heap_insert`.
#### Function Prototypes
```c
int getParent(int index);
int getLeftChild(int index);
int getRightChild(int index);
void swap(int item1, int item2);
void heapify(int A[], int index, int size);
void build_heap(int A[], int size);
void printArray(int A[], int size);
void heapInsert(int A[], int &size, int item); // Do not use build_heap in heap_insert.
```
These functions and steps will guide you in understanding how to manipulate and maintain heap structures effectively.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F620c60a1-10fe-416e-8b85-1e75a34b227e%2F5c6a8dc8-cd3b-46f1-a168-83ba860590b6%2Fldtvfp7_processed.png&w=3840&q=75)
Transcribed Image Text:### Heap Algorithms and Functions
#### 1. Heapify Function
Develop a `heapify` function to maintain the heap property in an array A. Implement the following auxiliary functions first:
- **`int getParent(int index);`**
- **Purpose**: Calculates the index of a node's parent.
- **Postcondition**: Returns an integer value.
- **`int getLeftChild(int index);`**
- **Purpose**: Calculates the index of a node's left child.
- **Postcondition**: Returns an integer value.
- **`int getRightChild(int index);`**
- **Purpose**: Calculates the index of a node's right child.
- **Postcondition**: Returns an integer value.
- **`void swap(int item1, int item2);`**
- **Purpose**: Exchanges two values.
- **Postcondition**: Swaps item1 and item2 through a reference parameter.
#### 2. Build Heap Function
Implement a `buildHeap` function to construct a heap from an array.
#### 3. Test Array
Use the array `A[20] = {4,1,3,2,16,9,10,14,8,7}` to test the `buildHeap` function.
#### 4. Insert Function
Create a function for inserting numbers into the heap.
#### 5. Insert Test
Test the insert function by adding 20 and 17 sequentially to the heap. Use the `heapInsert` function to add these elements. Do not utilize `build_heap` within `heap_insert`.
#### Function Prototypes
```c
int getParent(int index);
int getLeftChild(int index);
int getRightChild(int index);
void swap(int item1, int item2);
void heapify(int A[], int index, int size);
void build_heap(int A[], int size);
void printArray(int A[], int size);
void heapInsert(int A[], int &size, int item); // Do not use build_heap in heap_insert.
```
These functions and steps will guide you in understanding how to manipulate and maintain heap structures effectively.
Transcribed Image Text:**Sample Run:**
**Print Array A:**
4, 1, 3, 2, 16, 9, 10, 14, 8, 7,
**Parent of the node 5 is the node 2**
**Left child of the node 3 is the node 7**
**Right child of the node 3 is the node 8**
**Calling Heapify A, 1**
4, 16, 3, 2, 7, 9, 10, 14, 8, 1,
---
**Build Heap**
**Print Heap A:**
16, 14, 10, 8, 7, 9, 3, 2, 4, 1,
---
**After inserting the number 20 into the heap A:**
20, 16, 10, 8, 14, 9, 3, 2, 4, 1, 7,
---
**After inserting the number 17 into the heap A:**
(No text shown for this part)
---
*Explanation:*
The text above represents the output of a sample run illustrating the process of building and modifying a binary heap. It includes the operations of printing the initial array, determining parent and child nodes, heapifying, and inserting elements into the heap.
The heap operations demonstrate:
1. **Array Print** - Initial state of the array before any operations.
2. **Node Relationships** - Displays the parent-child relationships within the binary heap.
3. **Heapify Process** - Shows the result after an element is heapified.
4. **Build Heap** - The array after it has been structured into a heap.
5. **Insertions** - The state of the heap after inserting new elements (e.g., 20 and 17).
This sequence of operations is crucial for understanding how binary heaps are structured and modified.
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