### Understanding Quadratic Probing in Hash Tables **Hashing Table Size: 7** Elements to Insert: 12, 5, 19, 2, 23 **Instructions:** Use Quadratic Probing if there is a collision. Provide the answer in the form of the order of inserted elements. **Options:** a) ``` - 19 2 23 12 - 5 ``` b) ``` - 19 2 23 - 12 5 ``` c) ``` 12 - 2 23 - 19 - 5 ``` d) ``` 12 - - 2 23 19 5 ``` ### Quadratic Probing Explained: Quadratic probing is a collision resolution technique in hash tables. It uses a quadratic function rather than linear probing to calculate the index for the next probe. The formula generally looks like this: \[ h(k, i) = (h(k) + c_1 \cdot i + c_2 \cdot i^2) \mod m \] where: - \( h(k) \) is the initial hash function. - \( c_1 \) and \( c_2 \) are constants, often both set to 1. - \( i \) is the collision count. - \( m \) is the size of the hash table. Quadratic probing helps to reduce primary clustering seen in linear probing. ### Detailed Explanation of the Options: - **Option (a)**: - The elements in the hash table would be inserted in the following order: ``` - 19 2 23 12 - 5 ``` - **Option (b)**: - The elements in the hash table would be: ``` - 19 2 23 - 12 5 ``` - **Option (c)**: - The elements in the hash table are arranged as: ``` 12 - 2 23 - 19 - 5 ``` - **Option (d)**: - The elements in the hash table appear in this order: ``` 12 - - 2 23 19 5 ``` These options show the possible arrangements of the elements in the hash table after applying quadratic probing. The given answer choices illustrate different results based on
### Understanding Quadratic Probing in Hash Tables **Hashing Table Size: 7** Elements to Insert: 12, 5, 19, 2, 23 **Instructions:** Use Quadratic Probing if there is a collision. Provide the answer in the form of the order of inserted elements. **Options:** a) ``` - 19 2 23 12 - 5 ``` b) ``` - 19 2 23 - 12 5 ``` c) ``` 12 - 2 23 - 19 - 5 ``` d) ``` 12 - - 2 23 19 5 ``` ### Quadratic Probing Explained: Quadratic probing is a collision resolution technique in hash tables. It uses a quadratic function rather than linear probing to calculate the index for the next probe. The formula generally looks like this: \[ h(k, i) = (h(k) + c_1 \cdot i + c_2 \cdot i^2) \mod m \] where: - \( h(k) \) is the initial hash function. - \( c_1 \) and \( c_2 \) are constants, often both set to 1. - \( i \) is the collision count. - \( m \) is the size of the hash table. Quadratic probing helps to reduce primary clustering seen in linear probing. ### Detailed Explanation of the Options: - **Option (a)**: - The elements in the hash table would be inserted in the following order: ``` - 19 2 23 12 - 5 ``` - **Option (b)**: - The elements in the hash table would be: ``` - 19 2 23 - 12 5 ``` - **Option (c)**: - The elements in the hash table are arranged as: ``` 12 - 2 23 - 19 - 5 ``` - **Option (d)**: - The elements in the hash table appear in this order: ``` 12 - - 2 23 19 5 ``` These options show the possible arrangements of the elements in the hash table after applying quadratic probing. The given answer choices illustrate different results based on
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Question
![### Understanding Quadratic Probing in Hash Tables
**Hashing Table Size: 7**
Elements to Insert: 12, 5, 19, 2, 23
**Instructions:** Use Quadratic Probing if there is a collision. Provide the answer in the form of the order of inserted elements.
**Options:**
a)
```
- 19 2 23 12 - 5
```
b)
```
- 19 2 23 - 12 5
```
c)
```
12 - 2 23 - 19 - 5
```
d)
```
12 - - 2 23 19 5
```
### Quadratic Probing Explained:
Quadratic probing is a collision resolution technique in hash tables. It uses a quadratic function rather than linear probing to calculate the index for the next probe. The formula generally looks like this:
\[ h(k, i) = (h(k) + c_1 \cdot i + c_2 \cdot i^2) \mod m \]
where:
- \( h(k) \) is the initial hash function.
- \( c_1 \) and \( c_2 \) are constants, often both set to 1.
- \( i \) is the collision count.
- \( m \) is the size of the hash table.
Quadratic probing helps to reduce primary clustering seen in linear probing.
### Detailed Explanation of the Options:
- **Option (a)**:
- The elements in the hash table would be inserted in the following order:
```
- 19 2 23 12 - 5
```
- **Option (b)**:
- The elements in the hash table would be:
```
- 19 2 23 - 12 5
```
- **Option (c)**:
- The elements in the hash table are arranged as:
```
12 - 2 23 - 19 - 5
```
- **Option (d)**:
- The elements in the hash table appear in this order:
```
12 - - 2 23 19 5
```
These options show the possible arrangements of the elements in the hash table after applying quadratic probing. The given answer choices illustrate different results based on](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F33d7469d-24b0-4323-9278-1b0790a1937b%2Fb61ad515-6d5b-48c0-bf8e-28bc53678bb5%2Fhthl6y7_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding Quadratic Probing in Hash Tables
**Hashing Table Size: 7**
Elements to Insert: 12, 5, 19, 2, 23
**Instructions:** Use Quadratic Probing if there is a collision. Provide the answer in the form of the order of inserted elements.
**Options:**
a)
```
- 19 2 23 12 - 5
```
b)
```
- 19 2 23 - 12 5
```
c)
```
12 - 2 23 - 19 - 5
```
d)
```
12 - - 2 23 19 5
```
### Quadratic Probing Explained:
Quadratic probing is a collision resolution technique in hash tables. It uses a quadratic function rather than linear probing to calculate the index for the next probe. The formula generally looks like this:
\[ h(k, i) = (h(k) + c_1 \cdot i + c_2 \cdot i^2) \mod m \]
where:
- \( h(k) \) is the initial hash function.
- \( c_1 \) and \( c_2 \) are constants, often both set to 1.
- \( i \) is the collision count.
- \( m \) is the size of the hash table.
Quadratic probing helps to reduce primary clustering seen in linear probing.
### Detailed Explanation of the Options:
- **Option (a)**:
- The elements in the hash table would be inserted in the following order:
```
- 19 2 23 12 - 5
```
- **Option (b)**:
- The elements in the hash table would be:
```
- 19 2 23 - 12 5
```
- **Option (c)**:
- The elements in the hash table are arranged as:
```
12 - 2 23 - 19 - 5
```
- **Option (d)**:
- The elements in the hash table appear in this order:
```
12 - - 2 23 19 5
```
These options show the possible arrangements of the elements in the hash table after applying quadratic probing. The given answer choices illustrate different results based on
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