### Understanding Hash Tables: Quadratic Probing Example#### Introduction to Hash Tables with Quadratic ProbingIn this exercise, we will explore the concept of hash tables using quadratic probing as a collision resolution technique. #### Hash Table Definition and ConfigurationThe given hash table, referred to as `valsTable`, uses the following parameters:- A hash function defined as `key % 10`- Constant coefficients `c1 = 1` and `c2 = 1`- Quadratic probing formula: `h(k, i) = (h'(k) + c1 * i + c2 * i^2) % table_size`#### Current State of `valsTable`The hash table, `valsTable`, has 10 buckets indexed from 0 to 9. The state of the table is depicted below:```valsTable:+----+----+| 0 | 10 || 1 | || 2 | || 3 | || 4 | || 5 | || 6 | || 7 | || 8 | 38 || 9 | |+----+----+```**Legend:**- ![#D9EAD3](https://via.placeholder.com/15/D9EAD3/000000?text=+) Empty-since-start- ![#FAD7D4](https://via.placeholder.com/15/FAD7D4/000000?text=+) Empty-after-removal- ![#FFD966](https://via.placeholder.com/15/FFD966/000000?text=+) Occupied#### Insertions with Quadratic ProbingWe need to determine the buckets into which each item will be inserted using the quadratic probing technique:1. **Inserting item `38` into `valsTable`**: - Calculate initial hash: `38 % 10 = 8` - `Bucket 8` is occupied - Insert into bucket: `10`2. **Inserting item `57` into `valsTable`**: - Calculate initial hash: `57 % 10 = 7` - `Bucket 7` is empty - Insert into bucket: [ ] *(Answer box for user input)*3. **Inserting item `80` into

Given Has function is key % 10 Hence when we put key in slot we put at place of key % 10 th place.…

Jump to level 1 valsTable: o 10 1 2 3 4 5 6 7 8 9 38 Empty-since-start Empty-after-removal Occupied Hash table vals Table uses quadratic probing, a hash function of key % 10, c1 = 1, and c2 = 1. Hashinsert(valsTable, item 38) inserts item 38 into bucket Ex: 10 Hashinsert(valsTable, item 57) inserts item 57 into bucket HashInsert(vals Table, item 80) inserts item 80 into bucket

Jump to level 1 valsTable: o 10 1 2 3 4 5 6 7 8 9 38 Empty-since-start Empty-after-removal Occupied Hash table vals Table uses quadratic probing, a hash function of key % 10, c1 = 1, and c2 = 1. Hashinsert(valsTable, item 38) inserts item 38 into bucket Ex: 10 Hashinsert(valsTable, item 57) inserts item 57 into bucket HashInsert(vals Table, item 80) inserts item 80 into bucket

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

### Understanding Hash Tables: Quadratic Probing Example

#### Introduction to Hash Tables with Quadratic Probing

In this exercise, we will explore the concept of hash tables using quadratic probing as a collision resolution technique.

#### Hash Table Definition and Configuration

The given hash table, referred to as `valsTable`, uses the following parameters:
- A hash function defined as `key % 10`
- Constant coefficients `c1 = 1` and `c2 = 1`
- Quadratic probing formula: `h(k, i) = (h'(k) + c1 * i + c2 * i^2) % table_size`

#### Current State of `valsTable`

The hash table, `valsTable`, has 10 buckets indexed from 0 to 9. The state of the table is depicted below:

```
valsTable:
+----+----+
| 0 | 10 |
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 | |
| 7 | |
| 8 | 38 |
| 9 | |
+----+----+
```

**Legend:**
- ![#D9EAD3](https://via.placeholder.com/15/D9EAD3/000000?text=+) Empty-since-start
- ![#FAD7D4](https://via.placeholder.com/15/FAD7D4/000000?text=+) Empty-after-removal
- ![#FFD966](https://via.placeholder.com/15/FFD966/000000?text=+) Occupied

#### Insertions with Quadratic Probing

We need to determine the buckets into which each item will be inserted using the quadratic probing technique:

1. **Inserting item `38` into `valsTable`**:
- Calculate initial hash: `38 % 10 = 8`
- `Bucket 8` is occupied
- Insert into bucket: `10`

2. **Inserting item `57` into `valsTable`**:
- Calculate initial hash: `57 % 10 = 7`
- `Bucket 7` is empty
- Insert into bucket: [ ] *(Answer box for user input)*

3. **Inserting item `80` into

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