**Title:** Understanding Hash Tables with Quadratic Probing**Section:** Quadratic Probing in Hash Tables### Explanation of the valsTableIn the image above, we have a hash table named `valsTable` with a size of 11. The hash table employs quadratic probing to resolve collisions. Each cell in the `valsTable` is represented in a column with the following states:- **Empty-since-start:** Cells that have never been occupied.- **Empty-after-removal:** Cells that were occupied but are now empty.- **Occupied:** Cells that are currently occupied with values.The specific table shown is as follows:| Index | State | Values ||-------|-----------|--------|| 0 | Empty | || 1 | Empty | || 2 | Empty | || 3 | Empty | || 4 | Occupied | 15 || 5 | Occupied | 82 || 6 | Occupied | 50 || 7 | Empty | || 8 | Empty | || 9 | Empty | || 10 | Occupied | 32 |### Problem StatementThe hash table `valsTable` uses quadratic probing with a hash function of `key % 11`. The constants for quadratic probing are:- `c1 = 1`- `c2 = 1`You are asked to find the specific sequence of buckets that would be probed by the function `HashSearch(valsTable, 70)`.### Steps to Solve the Problem1. **Hash Function Calculation:** - Calculate the initial hash value using the hash function. - For `key = 70` and table size `m = 11`, the initial position `h(70)` is calculated as: \[ h(70) = 70 \% 11 = 4 \]2. **Quadratic Probing Formula:** - The quadratic probing formula is: \[ h_i(key) = (h(key) + c1 \cdot i + c2 \cdot i^2) \% m \] - The sequence of probe positions for `i = 0, 1, 2, \ldots

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What is the specific sequence of buckets probed by HashSearch(vals Table, 70)?

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

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**Title:** Understanding Hash Tables with Quadratic Probing

**Section:** Quadratic Probing in Hash Tables

### Explanation of the valsTable

In the image above, we have a hash table named `valsTable` with a size of 11. The hash table employs quadratic probing to resolve collisions. Each cell in the `valsTable` is represented in a column with the following states:

- **Empty-since-start:** Cells that have never been occupied.
- **Empty-after-removal:** Cells that were occupied but are now empty.
- **Occupied:** Cells that are currently occupied with values.

The specific table shown is as follows:

| Index | State | Values |
|-------|-----------|--------|
| 0 | Empty | |
| 1 | Empty | |
| 2 | Empty | |
| 3 | Empty | |
| 4 | Occupied | 15 |
| 5 | Occupied | 82 |
| 6 | Occupied | 50 |
| 7 | Empty | |
| 8 | Empty | |
| 9 | Empty | |
| 10 | Occupied | 32 |

### Problem Statement

The hash table `valsTable` uses quadratic probing with a hash function of `key % 11`. The constants for quadratic probing are:
- `c1 = 1`
- `c2 = 1`

You are asked to find the specific sequence of buckets that would be probed by the function `HashSearch(valsTable, 70)`.

### Steps to Solve the Problem

1. **Hash Function Calculation:**
- Calculate the initial hash value using the hash function.
- For `key = 70` and table size `m = 11`, the initial position `h(70)` is calculated as:
\[
h(70) = 70 \% 11 = 4
\]

2. **Quadratic Probing Formula:**
- The quadratic probing formula is:
\[
h_i(key) = (h(key) + c1 \cdot i + c2 \cdot i^2) \% m
\]
- The sequence of probe positions for `i = 0, 1, 2, \ldots

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