Q.Consider a list of 10 elements: randList = [7,11,3,10,17,23,1,4,21,5]. Determine the partially sorted list after four complete passes of selection sort.

This is a plain theory question requiring the application of the Selection Sort algorithm.

Selection sort works by repeatedly finding the minimum element from the unsorted part of the list and placing it at the beginning of the unsorted part. In each pass, one element is correctly placed in its final sorted position.

Given list: randList = [7, 11, 3, 10, 17, 23, 1, 4, 21, 5]

Length of the list, $n = 10$.

Let's trace the list through four complete passes of selection sort:

Initial List: [7, 11, 3, 10, 17, 23, 1, 4, 21, 5]

Pass 1:

1. Find the minimum element in the entire list [7, 11, 3, 10, 17, 23, 1, 4, 21, 5]. The minimum element is 1.
2. Swap 1 with the element at the first position (7).
3. List after Pass 1: [1, 11, 3, 10, 17, 23, 7, 4, 21, 5] (The element 1 is now in its correct sorted position.)

Pass 2:

1. Consider the unsorted sublist starting from the second position: [11, 3, 10, 17, 23, 7, 4, 21, 5].
2. Find the minimum element in this sublist. The minimum element is 3.
3. Swap 3 with the element at the second position (11).
4. List after Pass 2: [1, 3, 11, 10, 17, 23, 7, 4, 21, 5] (The elements 1, 3 are now in their correct sorted positions.)

Pass 3:

1. Consider the unsorted sublist starting from the third position: [11, 10, 17, 23, 7, 4, 21, 5].
2. Find the minimum element in this sublist. The minimum element is 4.
3. Swap 4 with the element at the third position (11).
4. List after Pass 3: [1, 3, 4, 10, 17, 23, 7, 11, 21, 5] …

Selection Sort is an in-place comparison sorting algorithm. It works by repeatedly finding the minimum element from the unsorted part of the list and putting it at the beginning of the unsorted part.

The core idea is to divide the list into two parts: a sorted sublist and an unsorted sublist. Initially, the sorted sublist is empty, and the unsorted sublist is the entire list.

How Selection Sort Works (One Pass):

In each "pass" (or iteration), the algorithm performs the following steps:

1. It finds the smallest element in the unsorted sublist.
2. It swaps this smallest element with the first element of the unsorted sublist.
3. This effectively moves the smallest element to its correct position in the sorted sublist, and the boundary between the sorted and unsorted sublists shifts one position to the right.

For a list of $N$ elements, Selection Sort requires $N-1$ passes to fully sort the list. After $k$ passes, the first $k$ elements of the list will be sorted and in their final positions.

Let's trace the given list randList = [7, 11, 3, 10, 17, 23, 1, 4, 21, 5] through four complete passes.