Jump to level 1 numbers = (55, 11, 15, 24, 59, 79, 61, 72, 99, 96) Partition(numbers, 5, 9) is called. Assume quicksort always chooses the element at the midpoint as the pivot. What is the pivot? What is the low partition? What is the high partition? What is numbers after Partition(numbers, 5, 9) completes? ( Ex: 9 Ex: 1, 2, 3 (comma between values)
Jump to level 1 numbers = (55, 11, 15, 24, 59, 79, 61, 72, 99, 96) Partition(numbers, 5, 9) is called. Assume quicksort always chooses the element at the midpoint as the pivot. What is the pivot? What is the low partition? What is the high partition? What is numbers after Partition(numbers, 5, 9) completes? ( Ex: 9 Ex: 1, 2, 3 (comma between values)
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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Can someone solve the following problem in the 1st screenshot? For extra help, the rules and hints are provided in the 2nd screenshot with different numbers but same idea (PLEASE HELP)!!!
![### Understanding Partitioning in Sorting Algorithms
#### Expected:
**Pivot:**
```plaintext
93
```
**Low Partition:**
```plaintext
66, 86, 81, 58
```
**High Partition:**
```plaintext
93
```
**Numbers:**
```plaintext
(28, 21, 40, 10, 42, 66, 86, 81, 58, 93)
```
#### Midpoint Calculation
To find the midpoint of the array:
```plaintext
5 + (9 - 5)/2 = 5 + 2 = 7
```
Thus, the pivot is `numbers[7]`, which is:
```plaintext
93
```
#### Partitioning Steps
Since `93` is equal to the pivot and `81` is less than the pivot, the partitioning algorithm swaps `93` and `81` to place `81` in the low partition and `93` in the high partition. The new arrangement of numbers is:
```plaintext
(28, 21, 40, 10, 42, 66, 86, 81, 58, 93)
```
#### Partitions
- The **low partition** contains elements from index `5` to index `8`, which are:
```plaintext
(66, 86, 81, 58)
```
- The **high partition** contains elements from index `9` to index `9`, which is:
```plaintext
(93)
```
After `Partition(numbers, 5, 9)` completes, `numbers` is:
```plaintext
(28, 21, 40, 10, 42, 66, 86, 81, 58, 93)
```
### Diagrammatic Explanation
While textually described above, a visual representation of partitioning can further aid understanding:
1. **Step 1: Initial Array**
- (28, 21, 40, 10, 42, 66, 86, 81, 58, 93)
2. **Step 2: Midpoint Identification**
- Identified pivot = 93 at index 7
3. **Step 3: Partitioning Process**
- Elements less than pivot (Low Partition): 66, 86, 81, 58](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7daa69d8-205a-4b72-abf5-96966d755823%2Ff973a3ed-d3fc-4dfe-9c65-d15730d01f0b%2Fcqarcns_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding Partitioning in Sorting Algorithms
#### Expected:
**Pivot:**
```plaintext
93
```
**Low Partition:**
```plaintext
66, 86, 81, 58
```
**High Partition:**
```plaintext
93
```
**Numbers:**
```plaintext
(28, 21, 40, 10, 42, 66, 86, 81, 58, 93)
```
#### Midpoint Calculation
To find the midpoint of the array:
```plaintext
5 + (9 - 5)/2 = 5 + 2 = 7
```
Thus, the pivot is `numbers[7]`, which is:
```plaintext
93
```
#### Partitioning Steps
Since `93` is equal to the pivot and `81` is less than the pivot, the partitioning algorithm swaps `93` and `81` to place `81` in the low partition and `93` in the high partition. The new arrangement of numbers is:
```plaintext
(28, 21, 40, 10, 42, 66, 86, 81, 58, 93)
```
#### Partitions
- The **low partition** contains elements from index `5` to index `8`, which are:
```plaintext
(66, 86, 81, 58)
```
- The **high partition** contains elements from index `9` to index `9`, which is:
```plaintext
(93)
```
After `Partition(numbers, 5, 9)` completes, `numbers` is:
```plaintext
(28, 21, 40, 10, 42, 66, 86, 81, 58, 93)
```
### Diagrammatic Explanation
While textually described above, a visual representation of partitioning can further aid understanding:
1. **Step 1: Initial Array**
- (28, 21, 40, 10, 42, 66, 86, 81, 58, 93)
2. **Step 2: Midpoint Identification**
- Identified pivot = 93 at index 7
3. **Step 3: Partitioning Process**
- Elements less than pivot (Low Partition): 66, 86, 81, 58
![### Challenge Activity: Quicksort (3.5.1)
---
#### Problem Overview
**Given List of Numbers:**
\[ 55, 11, 15, 24, 59, 79, 61, 72, 99, 96 \]
**Operation:**
Partition(numbers, 5, 9) is called.
**Instructions:**
Assume quicksort always chooses the element at the midpoint as the pivot.
1. **What is the pivot?**
- Use the provided input field to specify the pivot value.
2. **What is the low partition?**
- Indicate the low partition by listing the values separated by commas.
3. **What is the high partition?**
- Indicate the high partition by listing the values separated by commas.
4. **What are the numbers after Partition(numbers, 5, 9) completes?**
- Provide the final arrangement of numbers after the partition operation.
---
#### Interactive Components:
- **Pivot Selector:**
An input field (preset example: Ex: 9) for selecting the pivot based on the midpoint rule.
- **Low Partition Input:**
An input field for the values in the low partition (example format: Ex: 1, 2, 3 \([comma separated values]\)).
- **High Partition Input:**
An input field for the values in the high partition.
- **Final Numbers Arrangement:**
An input area to specify the list of numbers after the partition operation.
- **Control Buttons:**
- **Check Button:** To verify the entered answers.
- **Next Button:** To proceed to the next exercise after completion.
- **Progress Tracker:**
A visual representation showing current progress through checkboxes, marking steps that have been completed.
---
### Graphical Representation
A graphical representation is provided to illustrate the step where the partitioning occurs. It is shown through:
- **Number Line:**
A graphical bar indicating steps, with section 5 highlighted to show the current focus of the partition operation.
---
#### Additional Resources:
- **Feedback Link:**
For reporting issues or providing feedback on the activity.
---
By completing this challenge, you will better understand the mechanism of the Quicksort algorithm, specifically how partitions and pivots function to sort an array of numbers.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7daa69d8-205a-4b72-abf5-96966d755823%2Ff973a3ed-d3fc-4dfe-9c65-d15730d01f0b%2Fcyafggc_processed.png&w=3840&q=75)
Transcribed Image Text:### Challenge Activity: Quicksort (3.5.1)
---
#### Problem Overview
**Given List of Numbers:**
\[ 55, 11, 15, 24, 59, 79, 61, 72, 99, 96 \]
**Operation:**
Partition(numbers, 5, 9) is called.
**Instructions:**
Assume quicksort always chooses the element at the midpoint as the pivot.
1. **What is the pivot?**
- Use the provided input field to specify the pivot value.
2. **What is the low partition?**
- Indicate the low partition by listing the values separated by commas.
3. **What is the high partition?**
- Indicate the high partition by listing the values separated by commas.
4. **What are the numbers after Partition(numbers, 5, 9) completes?**
- Provide the final arrangement of numbers after the partition operation.
---
#### Interactive Components:
- **Pivot Selector:**
An input field (preset example: Ex: 9) for selecting the pivot based on the midpoint rule.
- **Low Partition Input:**
An input field for the values in the low partition (example format: Ex: 1, 2, 3 \([comma separated values]\)).
- **High Partition Input:**
An input field for the values in the high partition.
- **Final Numbers Arrangement:**
An input area to specify the list of numbers after the partition operation.
- **Control Buttons:**
- **Check Button:** To verify the entered answers.
- **Next Button:** To proceed to the next exercise after completion.
- **Progress Tracker:**
A visual representation showing current progress through checkboxes, marking steps that have been completed.
---
### Graphical Representation
A graphical representation is provided to illustrate the step where the partitioning occurs. It is shown through:
- **Number Line:**
A graphical bar indicating steps, with section 5 highlighted to show the current focus of the partition operation.
---
#### Additional Resources:
- **Feedback Link:**
For reporting issues or providing feedback on the activity.
---
By completing this challenge, you will better understand the mechanism of the Quicksort algorithm, specifically how partitions and pivots function to sort an array of numbers.
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