Problem: In this problem, we would like to re-implement a selection sort to sort an array of numbers with some improvements. Selection Sort divides the input list into two parts: the sublist of elements already sorted and the unsorted sublist of elements remaining to be sorted. - find the smallest element in the unsorted sublist - swap this element with the leftmost unsorted element, it equivalents to move this element from the unsorted sublist to the sorted one, - continue to proceed all elements in the unsorted sublist. Question 1:  ▪ Propose a recursive algorithm (pseudo-code) for the above Selection Sort (combined with iteration if necessary).  ▪ Implement the proposed pseudo-code using C/C++  ▪ Calculate the complexity of your program (Best scenario, Worst scenario, Average). Justify your answer.

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Counting sort

The counting sort algorithm sorts an array’s contents by counting the repetition of each element that occurs in the array. A counting sort algorithm is a stable algorithm that works the best when the range of elements in the array is small, say for example from 0 to 9. The count which is the number of repetitions of an element in the array is mapped to an index of an auxiliary array, which is then saved in an auxiliary array. The counting sort algorithm has a stable time complexity of the order of O(size of array + size of auxiliary array). Let’s discuss the algorithm in detail as follows.