How does the bogo sort algorithm sort numbers?

The Bogo Sort algorithm sorts numbers by randomly generating permutations until it stumbles upon a sorted one.

Bogo Sort, also known as permutation sort, stupid sort, slow sort, shotgun sort or monkey sort, is a particularly ineffective sorting algorithm based on the generate and test paradigm. The algorithm successively generates permutations of its input until it finds one that is sorted. It is not useful for sorting, but it is often used as a humorous example of how not to design an algorithm.

The name 'Bogo Sort' is derived from the word 'bogus'. The algorithm works by first checking if the list is sorted and if it is, the algorithm stops. If it isn't, it randomly permutes the list's elements and then checks again. This process is repeated until a sorted list is derived.

The basic steps of the Bogo Sort algorithm are as follows:

1. Check if the list is in order. If the list is in order, stop. If not, go to step 2.
2. Randomly permute the elements of the list.
3. Go to step 1.

The main problem with Bogo Sort is its performance. The average case run-time complexity of this algorithm is O((n+1)!), making it one of the least efficient sorting algorithms. It's important to note that the time complexity is unbounded because there's no upper limit on the number of times we might have to permute the list before we stumble upon a sorted permutation.

In terms of space complexity, Bogo Sort is quite efficient. It only requires O(1) auxiliary space to produce a sorted list. However, this small advantage is vastly outweighed by its poor time complexity.

In conclusion, while Bogo Sort is an interesting algorithm to study for its simplicity and the generate-and-test paradigm it represents, it's not a practical choice for sorting large lists due to its poor performance. It's more of a theoretical curiosity than a practical algorithm.