how would the hash table look like ?linear probing and quadratic probing ? ### Closed Hashing Example#### Keys to Insert:- T0001235- T0101405- T0131735- T0001038- T0201230- T0807000- T0201203- T2374005- T4070745- T4072307#### Hashing MethodInsert these using closed hashing in the hashtable below with two probe methods:1. **Linear Probing:** \[ \text{probe(key, i)} = 2 \times i \]2. **Quadratic Probing:** \[ \text{probe(key, i)} = i^2 \]#### Hashtable Structure:- **Table of 23 Elements:** | Index | Value | Comments | |-------|-------------|------------------| | 0 | nullptr | | | 1 | T20107424 | Inserted | | 2 | nullptr | | | 3 | nullptr | | | 4 | T3290334 | Chained to T0000284 | | 5 | nullptr | | | 6 | T0314303 | Inserted | | 7 | nullptr | etc. | | 8 | ... | | | ... | ... | | | 21 | nullptr | | | 22 | nullptr | |### Explanation:This image illustrates the process of inserting keys into a hashtable using closed hashing methods. Linear and quadratic probing techniques are used to resolve collisions. Each entry in the table represents a possible storage location for the keys. Collisions are handled by computing an alternative position using the probing formulae, ensuring all keys have unique positions within the fixed size of the table.

Lets see the solution in the next steps

T4070745 T4072307 Insert this using (closed hashing) in the bashtable below 1. probe (key.i) = 2*i 2. |probe (key,i) = i**2 Table of 23 elements 0: nullpr 1: T20107424 2: nullpts 3: nullpts 4: T3290334 →- T0000284 5: nullptr 6: T0314303 7. nullotr

T4070745 T4072307 Insert this using (closed hashing) in the bashtable below 1. probe (key.i) = 2*i 2. |probe (key,i) = i**2 Table of 23 elements 0: nullpr 1: T20107424 2: nullpts 3: nullpts 4: T3290334 →- T0000284 5: nullptr 6: T0314303 7. nullotr

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

Hash Table

A hash table also called a hash map, is a data structure that maps key-value pairs. The hash table can be used in complex systems to provide fast access and compact storage. A hash table is a structure that stores data in an abstract data type kind of associative array. It keeps data in an array format, with a distinct index value for every data value. If the index of the required data is known, then the data can be accessed very easily.

Question

how would the hash table look like ?

linear probing and quadratic probing ?

### Closed Hashing Example

#### Keys to Insert:
- T0001235
- T0101405
- T0131735
- T0001038
- T0201230
- T0807000
- T0201203
- T2374005
- T4070745
- T4072307

#### Hashing Method
Insert these using closed hashing in the hashtable below with two probe methods:

1. **Linear Probing:**
\[
\text{probe(key, i)} = 2 \times i
\]

2. **Quadratic Probing:**
\[
\text{probe(key, i)} = i^2
\]

#### Hashtable Structure:
- **Table of 23 Elements:**

| Index | Value | Comments |
|-------|-------------|------------------|
| 0 | nullptr | |
| 1 | T20107424 | Inserted |
| 2 | nullptr | |
| 3 | nullptr | |
| 4 | T3290334 | Chained to T0000284 |
| 5 | nullptr | |
| 6 | T0314303 | Inserted |
| 7 | nullptr | etc. |
| 8 | ... | |
| ... | ... | |
| 21 | nullptr | |
| 22 | nullptr | |

### Explanation:

This image illustrates the process of inserting keys into a hashtable using closed hashing methods. Linear and quadratic probing techniques are used to resolve collisions. Each entry in the table represents a possible storage location for the keys. Collisions are handled by computing an alternative position using the probing formulae, ensuring all keys have unique positions within the fixed size of the table.

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