Assume the array below is used to implement a hash table. Assume we wish to insert the value 34 using Quadratic Probing, in which array index would the number be inserted? 643 64 64 5489 1545 3. 4. 9 10 6479 216 215 47 15478 11 12 13 14 15 16 17 18 19 20 21 254 545 4548 548 549 22 23 24 25 26 27 28

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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### Hash Table Implementation Using Quadratic Probing

#### Overview:
In this example, we have an array being used as a hash table. The task is to insert the value `34` using the method of **Quadratic Probing**. We want to determine the correct array index for inserting this value.

#### Array Representation:
Indices are labeled from 0 to 28.

- **Index 0 to 4**: Empty
- **Index 5**: 643
- **Index 6 and 7**: 64
- **Index 8**: 5489
- **Index 9**: 1545
- **Index 10**: Empty
- **Index 11**: 6479
- **Index 12**: Empty
- **Index 13**: 216
- **Index 14**: Empty
- **Index 15**: 215
- **Index 16**: Empty
- **Index 17**: 47
- **Index 18 to 20**: Empty
- **Index 21**: 15478
- **Index 22**: 254
- **Index 23**: 545
- **Index 24**: 4548
- **Index 25**: 548
- **Index 26**: 549
- **Index 27 to 28**: Empty

#### Objective:
Find the correct index for the value `34` using quadratic probing methodology. Quadratic probing involves checking hash table slots in a quadratic sequence until an empty slot is found.

For educational purposes, quadratic probing checks indexes based on the formula:
\[ \text{Index} = (h + i^2) \% \text{TableSize} \]
where \( h \) is the initial hash index computed using the hash function, \( i \) starts from 0 and increments until an empty slot is found, and TableSize is the total number of slots in the hash table.

Assume the hash function and specific calculations based on this array setup to identify the position for `34`.

#### Conclusion:
The final position for inserting the number `34` will depend on incrementing through indices based on the initial hash and quadratic probing calculation until finding an empty slot.
Transcribed Image Text:### Hash Table Implementation Using Quadratic Probing #### Overview: In this example, we have an array being used as a hash table. The task is to insert the value `34` using the method of **Quadratic Probing**. We want to determine the correct array index for inserting this value. #### Array Representation: Indices are labeled from 0 to 28. - **Index 0 to 4**: Empty - **Index 5**: 643 - **Index 6 and 7**: 64 - **Index 8**: 5489 - **Index 9**: 1545 - **Index 10**: Empty - **Index 11**: 6479 - **Index 12**: Empty - **Index 13**: 216 - **Index 14**: Empty - **Index 15**: 215 - **Index 16**: Empty - **Index 17**: 47 - **Index 18 to 20**: Empty - **Index 21**: 15478 - **Index 22**: 254 - **Index 23**: 545 - **Index 24**: 4548 - **Index 25**: 548 - **Index 26**: 549 - **Index 27 to 28**: Empty #### Objective: Find the correct index for the value `34` using quadratic probing methodology. Quadratic probing involves checking hash table slots in a quadratic sequence until an empty slot is found. For educational purposes, quadratic probing checks indexes based on the formula: \[ \text{Index} = (h + i^2) \% \text{TableSize} \] where \( h \) is the initial hash index computed using the hash function, \( i \) starts from 0 and increments until an empty slot is found, and TableSize is the total number of slots in the hash table. Assume the hash function and specific calculations based on this array setup to identify the position for `34`. #### Conclusion: The final position for inserting the number `34` will depend on incrementing through indices based on the initial hash and quadratic probing calculation until finding an empty slot.
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