Which Design technique is used in Quicksort and Selection Sort? Explain the technique and sort following list using Quicksort and Selection sort. 5 , 3 , 8, 1, 4 , 6, 2 ,7

 Quicksort is a divide and conquer algorithm that uses a pivot element to partition the array into two subarrays. It then recursively sorts the subarrays on either side of the pivot.

The pivot selection and partitioning steps can be implemented in several ways, but a common technique is the "Hoare partition scheme". In this scheme, we choose the first element of the array as the pivot, and then use two pointers (one from the start of the array and one from the end) to scan the array and swap elements that are on the wrong side of the pivot. This process continues until the pointers meet or cross, at which point the pivot is correctly positioned and the partitioning is complete.

Here is an example of how to sort the given list using Quicksort:

1. Choose the first element (5) as the pivot.
2. Use the Hoare partition scheme to partition the array into two subarrays: [3, 1, 4, 2] and [8, 6, 7].
3. Recursively sort the subarrays [3, 1, 4, 2] and [8, 6, 7].
4. The sorted array is [1, 2, 3, 4, 5, 6, 7, 8].

Selection sort is a simple sorting algorithm that repeatedly selects the smallest element from the unsorted portion of the array and places it at the end of the sorted portion. It does this by finding the minimum element in the unsorted portion of the array, swapping it with the element at the first position of the unsorted portion, and then moving the end of the sorted portion one element forward.

Here is an example of how to sort the given list using Selection sort:

1. Find the minimum element in the array (1). Swap it with the element at the first position (5). The array is now [1, 3, 8, 5, 4, 6, 2, 7].
2. Find the minimum element in the unsorted portion of the array (2). Swap it with the element at the second position (3). The array is now [1, 2, 8, 5, 4, 6, 3, 7].
3. Find the minimum element in the unsorted portion of the array (3). Swap it with the element at the third position (8). The array is now [1, 2, 3, 5, 4, 6, 8, 7].
4. Repeat this process until the entire array is sorted. The sorted array is [1, 2, 3, 4, 5, 6, 7, 8].