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.

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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.