Suppose we are sorting an array of eight integers using quicksort, and we have just finished the first partitioning with the array looking like this: 2 5 1 7 9 12 11 10, which statement is correct?

a. The pivot could be 7, but it is not 9.
b. The pivot could be 9 but not 7.
c. The pivot could be either 7 or 9.
d. Neither 7 nor 9 is the pivot.

Since we are trying to sort an array of eight integers using quick sort, from the first partitioning it shows that the pivot or the central point can either be 7 or 9. When you look at the array, it is only 7 and 9 that are placed correctly in the sorted array. Every element to the left of 7 and 9 are smaller and every element on the right of 7 and 9 are integers higher than them. Hence this shows that the pivot lies between 7 or 9.

MrRoyal MrRoyal · Answer 2 · 2021-10-26T18:46:27+02:00

The pivot element of an array is the middle element of the array.

The pivot element could be either 7 or 9

From the question, we have:

[tex]\mathbf{n = 8}[/tex]

So, the pivot element is:

[tex]\mathbf{Pivot = \frac{n +1}{2}}[/tex]

So, we have:

[tex]\mathbf{Pivot = \frac{8 +1}{2}}[/tex]

[tex]\mathbf{Pivot = \frac{9}{2}}[/tex]

Divide 9 by 2

[tex]\mathbf{Pivot = 4.5}[/tex]

So, the pivot element is the 4.5th element.

The 4.5th element is between the 4th and 5th element (i.e. 7 or 9)

This means that, the pivot element could be either 7 or 9

Hence, the correct option is (c).