Both Quicksort and Selection sort use the divide-and-conquer technique. Divide-and-conquer involves dividing a large problem into smaller subproblems, solving those subproblems, and then combining the solutions to the subproblems to find a solution to the original problem.
In the case of Quicksort, the large problem is an unsorted list of numbers. The algorithm divides the list into two smaller sublists: one containing the numbers smaller than a chosen pivot value, and the other containing the numbers larger than the pivot value. The algorithm then recursively applies the same process to each of the sublists until the list is fully sorted.
To sort the given list of numbers using Quicksort, we first choose a pivot value. We can choose any value from the list as the pivot, but for the sake of this example, we'll choose the first value, 5. Next, we divide the list into two sublists: one containing the numbers smaller than 5 (1, 3, 4, 2) and the other containing the numbers larger than 5 (8, 6, 7). We then recursively apply the Quicksort algorithm to each of the sublists to fully sort them. The resulting sorted list is: 1, 2, 3, 4, 5, 6, 7, 8.
Selection sort is a different sorting algorithm that also uses the divide-and-conquer technique. In this algorithm, the list is divided into two parts: a sorted sublist and an unsorted sublist. The algorithm repeatedly finds the smallest element in the unsorted sublist, removes it, and appends it to the sorted sublist until all of the elements have been sorted.
To sort the given list of numbers using Selection sort, we first divide the list into two parts: a sorted sublist (empty to start) and an unsorted sublist (the original list). We then find the smallest element in the unsorted sublist (1) and append it to the sorted sublist. This gives us a new sorted sublist (1) and a new unsorted sublist (5, 3, 8, 4, 6, 2, 7). We repeat this process until all of the elements have been sorted, resulting in the sorted list: 1, 2, 3, 4, 5, 6, 7, 8.
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