### Heap Implementation Using a Fixed Size ArrayThis tutorial will guide you through the process of implementing a heap using a fixed size array, illustrating the heap construction and removal processes in detail, and demonstrating how to sort an array using a heap.#### 1. Constructing the HeapIllustrate how the following heap would be constructed (show the content of the array, showing in detail only what happens when nodes with keys `9` and `17` are added):The nodes are inserted in the following order (key, value):- (9, -4)- (3, -6)- (11, -4)- (13, -7)- (14, -2)- (12, -8)- (33, -5)- (17, -7)- (6, -3)**Heap Construction Steps:**1. Insert (9, -4)2. Insert (3, -6)3. Insert (11, -4)4. Insert (13, -7)5. Insert (14, -2)6. Insert (12, -8)7. Insert (33, -5)8. Insert (17, -7)9. Insert (6, -3)**Detailed Illustration for Adding Nodes 9 and 17:**- Initial array with node (9, -4): `[ (9, -4) ]`- After adding node (17, -7), the array content needs reordering per heap properties. The new array will reflect the heap restructuring needed to insert node (17, -7).#### 2. Removing an Element from the HeapIllustrate what happens to the heap when invoking remove (show the details).**Heap Removal Steps:**- After removing the root of the heap, restructure the array to maintain heap properties. This involves repositioning nodes to satisfy the heap ordering rules, usually done by promoting the next largest element to the root and adjusting the tree accordingly.#### 3. Sorting an Array Using a HeapAssume that you have an array of integers. Write a code that would allow you to sort the array in ascending order (smallest to largest), using only a heap.**Pseudocode for Heap Sort:**```pythondef heapify(arr, n, i): largest = i left = 2 * i + 1 right = 2 * i + 2

The heap is a memory used by programming languages to store global variables. By default, all global…

Assume that you are implementing a heap using a fixed size array. 1- Illustrate how the following heap would be constructed (show the content of the array, show in detail only what happens when nodes DOB and 17 are added): The nodes are inserted in the following order (key, value): (9, -4), (3, -6), (11, -4), (13, -7), (14, -2), (12, -8), (33-5), (17, -7), (6, -3). 2- Illustrate what happens to the heap when invoking remove (show the details). 3- Assume that you have an array of integers, write a code that would allow you to sort the array in ascending order (smallest to largest), using only a heap.

Assume that you are implementing a heap using a fixed size array. 1- Illustrate how the following heap would be constructed (show the content of the array, show in detail only what happens when nodes DOB and 17 are added): The nodes are inserted in the following order (key, value): (9, -4), (3, -6), (11, -4), (13, -7), (14, -2), (12, -8), (33-5), (17, -7), (6, -3). 2- Illustrate what happens to the heap when invoking remove (show the details). 3- Assume that you have an array of integers, write a code that would allow you to sort the array in ascending order (smallest to largest), using only a heap.

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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Concept explainers

Heap Sort

A Heap is a type of data structure that is built on trees. It's a binary tree that's virtually complete. Except for the very bottom level, all levels of the tree must be filled in a heap. The last (bottom) level should be filled from left to right. The heap data structure is used for the efficient implementation of priority queues.Heap can be of two types:

Question

### Heap Implementation Using a Fixed Size Array

This tutorial will guide you through the process of implementing a heap using a fixed size array, illustrating the heap construction and removal processes in detail, and demonstrating how to sort an array using a heap.

#### 1. Constructing the Heap

Illustrate how the following heap would be constructed (show the content of the array, showing in detail only what happens when nodes with keys `9` and `17` are added):

The nodes are inserted in the following order (key, value):
- (9, -4)
- (3, -6)
- (11, -4)
- (13, -7)
- (14, -2)
- (12, -8)
- (33, -5)
- (17, -7)
- (6, -3)

**Heap Construction Steps:**
1. Insert (9, -4)
2. Insert (3, -6)
3. Insert (11, -4)
4. Insert (13, -7)
5. Insert (14, -2)
6. Insert (12, -8)
7. Insert (33, -5)
8. Insert (17, -7)
9. Insert (6, -3)

**Detailed Illustration for Adding Nodes 9 and 17:**
- Initial array with node (9, -4): `[ (9, -4) ]`
- After adding node (17, -7), the array content needs reordering per heap properties. The new array will reflect the heap restructuring needed to insert node (17, -7).

#### 2. Removing an Element from the Heap

Illustrate what happens to the heap when invoking remove (show the details).

**Heap Removal Steps:**
- After removing the root of the heap, restructure the array to maintain heap properties. This involves repositioning nodes to satisfy the heap ordering rules, usually done by promoting the next largest element to the root and adjusting the tree accordingly.

#### 3. Sorting an Array Using a Heap

Assume that you have an array of integers. Write a code that would allow you to sort the array in ascending order (smallest to largest), using only a heap.

**Pseudocode for Heap Sort:**
```python
def heapify(arr, n, i):
largest = i
left = 2 * i + 1
right = 2 * i + 2

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