Question

Explain the concept of selection sort and provide a step-by-step algorithm for sorting an array using selection sort.

Answer

Selection sort is a simple sorting algorithm that works by repeatedly finding the minimum element from the unsorted part of the array and swapping it with the element at the beginning of the unsorted part. This process is repeated until the entire array is sorted.

Here is the step-by-step algorithm for selection sort:

1. Start with the first element of the array.
2. Find the minimum element in the rest of the array (starting from the current position).
3. Swap the minimum element with the current element.
4. Move the starting position one step forward.
5. Repeat steps 2-4 until the entire array is sorted.

Let's illustrate the selection sort algorithm with an example. Consider the following array:

[6, 3, 8, 1, 9, 2]

Step 1:

The first element of the array is 6. We compare it with the rest of the array to find the minimum element, which is 1. We swap 6 with 1, resulting in the partially sorted array:

[1, 3, 8, 6, 9, 2]

Step 2:

We move the starting position one step forward and consider the second element, which is 3. The rest of the array is [8, 6, 9, 2]. The minimum element is 2. We swap 3 with 2, resulting in the partially sorted array:

[1, 2, 8, 6, 9, 3]

Step 3:

We move the starting position one step forward and consider the third element, which is 8. The rest of the array is [6, 9, 3]. The minimum element is 3. We swap 8 with 3, resulting in the partially sorted array:

[1, 2, 3, 6, 9, 8]

Step 4:

We move the starting position one step forward and consider the fourth element, which is 6. The rest of the array is [9, 8]. The minimum element is 6. We swap 6 with 6 (no change), resulting in the partially sorted array:

[1, 2, 3, 6, 9, 8]

Step 5:

We move the starting position one step forward and consider the fifth element, which is 9. The rest of the array is [8]. The minimum element is 8. We swap 9 with 8, resulting in the partially sorted array:

[1, 2, 3, 6, 8, 9]

Step 6:

We move the starting position one step forward and consider the sixth element, which is 8. The rest of the array is empty. No need for further swaps, as the array is already sorted. The final sorted array is:

[1, 2, 3, 6, 8, 9]

The time complexity of the selection sort algorithm is O(n^2) in all cases, where n is the number of elements in the array.