Question

Illustrate the process of sorting the array [72, 62, 86, 39, 80, 10, 85, 50] using quicksort. Please provide every step of how the array changes and the pivot of partitioning.

Answer 1

The quicksort process involves choosing a pivot, partitioning the array based on that pivot, and then recursively sorting the sub-arrays. The example array is sorted through a series of steps, with each pivot leading to elements being moved into their correct positions.

Step-by-step explanation:

Illustrating QuickSort with an Array Example

To illustrate the quicksort algorithm, we'll sort the array [72, 62, 86, 39, 80, 10, 85, 50]. The process of sorting using quicksort involves repeatedly partitioning the array and sorting the subsections.

1. Select a pivot element from the array. In this example, we'll choose the last element, 50, as the pivot.
2. Partition the array into two sections: elements less than the pivot and elements greater than the pivot. After partitioning, the array looks like [39, 10, 50, 62, 86, 72, 80, 85], with 50 now in its correct sorted position.
3. Recursively apply the above steps to the sub-arrays to the left and right of the pivot. The left sub-array is [39, 10], and the right sub-array is [62, 86, 72, 80, 85].
4. For the left sub-array [39, 10], choose 39 as the pivot. After partitioning, we get [10, 39]. Both 10 and 39 are now in their final positions.
5. For the right sub-array [62, 86, 72, 80, 85], choose 85 as the pivot. After partitioning, we get [62, 72, 80, 85, 86]. The pivot, 85, is now in its final position.
6. Repeat the process for any remaining sub-arrays. In this case, [62, 72, 80] is the only one that needs sorting. Choose 80 as the pivot and you'll end up with [62, 72, 80] sorted.
7. The entire array is now sorted: [10, 39, 50, 62, 72, 80, 85, 86].

At each step, elements are moved around the pivot, ensuring that by the end of the process, the entire array is sorted.