Question

Having the following list of integer numbers, do the following: 7, 1, 5, 18, 14, 7, 2, 21, 3. Apply Lomuto-partition quicksort to sort the list in ascending order.

a. 1, 2, 3, 5, 7, 7, 14, 18, 21

b. 21, 18, 14, 7, 7, 5, 3, 2, 1

c. 21, 18, 14, 7, 7, 5, 3, 2, 1

d. 1, 3, 2, 5, 7, 7, 14, 18, 21

Answer 1

Using the Lomuto partition scheme of the quicksort algorithm, the list of integers is sorted into the ascending order: 1, 2, 3, 5, 7, 7, 14, 18, 21, corresponding to answer option (a).

Step-by-step explanation:

The question asks to sort a list of integer numbers using the Lomuto partition scheme of the quicksort algorithm. Quicksort is efficient for sorting and is a divide-and-conquer algorithm. In the Lomuto partition scheme, the last element is typically chosen as the pivot, and the data is re-arranged so that all elements less than the pivot come before it, and all elements greater than the pivot come after it. This process is repeated recursively for the subarrays.

Let's apply the Lomuto partition scheme to the given list: 7, 1, 5, 18, 14, 7, 2, 21, 3.

1. Choose the last element (3) as the pivot.
2. Rearrange the array so that all elements less than 3 are before it, and all others are after it.
3. Since there's only one element less than 3 (1, 2), we swap 3 with the second element.
4. Now the partially sorted array is: 1, 2, 3.
5. Continue recursively with the subarrays (7, 5, 18, 14, 7) and (21).
6. After completing the sorting process using Lomuto partition, the sorted array in ascending order will be: 1, 2, 3, 5, 7, 7, 14, 18, 21.

Thus, the correct answer to the question matches option (a).