Given the array [19, 87, 11, 12, 2, 58], arrange the iterations in the correct order until the array is sorted according to Quick Sort. Assume that the pivot element is selected to be the first element of any subarray, and that all subarray operations at a given level happen simultaneously.

Note: The options only show what the array looks like after the pivot and rearrangement has happened on any given recursive step.
What number(s), if any, are NEVER the pivot element in the previous problem?

To determine which numbers are **never** selected as pivot elements in the quicksort process, let's first understand the quicksort steps for the given array \([19, 87, 11, 12, 2, 58]\), assuming the first element of any subarray is always chosen as the pivot.

### Step-by-Step Quicksort Process:

1. **Initial Array:** \([19, 87, 11, 12, 2, 58]\)
   - Pivot = 19
   - Partitioning: Elements less than 19 go to the left, and elements greater go to the right.
   - **Result:** \([11, 12, 2, 19, 87, 58]\)

2. **Subarrays after first partition:**
   - Left Subarray: \([11, 12, 2]\)
   - Right Subarray: \([87, 58]\)

3. **Left Subarray \([11, 12, 2]\)**
   - Pivot = 11
   - Partitioning: \([2, 11, 12]\)

4. **Right Subarray \([87, 58]\)**
   - Pivot = 87
   - Partitioning: \([58, 87]\)

5. **Subarrays after second partition:**
   - Left Subarray of \([2, 11, 12]\): \([2]\) (no further action, since it has one element)
   - Right Subarray of \([2, 11, 12]\): \([12]\) (no further action, since it has one element)
   - Left Subarray of \([58, 87]\): \([58]\) (no further action, since it has one element)
   - Right Subarray of \([58, 87]\): None (no elements remain)

### Conclusion:
Throughout the quicksort process:

- **19** was the pivot in the first partition.
- **11** was the pivot in the left subarray of the first partition.
- **87** was the pivot in the right subarray of the first partition.

However, **12**, **2**, and **58** were never selected as pivot elements.

### Answer:
The numbers **12**, **2**, and **58** are **never** the pivot element in the quicksort process for this array.

---

Would you like further details or have any questions? 

Here are five related questions to consider:

1. How does the choice of the first element as the pivot affect the quicksort efficiency?
2. What would be the quicksort process if the pivot were chosen as the last element?
3. How would the process differ if you selected the median as the pivot?
4. Can quicksort's efficiency be affected by the initial order of the array?
5. What are the advantages and disadvantages of using quicksort over other sorting algorithms?

**Tip:** Quicksort performs better on average when the pivot is selected such that it roughly splits the array into two equal parts.

Explore the quicksort algorithm with a detailed step-by-step example. Learn how to apply quicksort to sort arrays efficiently, focusing on pivot selection strategies and partitioning. Suitable for advanced learners and anyone interested in sorting algorithms.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation