How does the bogo sort algorithm work?

The Bogo Sort algorithm works by repeatedly generating permutations of its input until it finds one that is sorted.

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 may be used for educational purposes, to contrast it with more efficient algorithms.

The name 'bogo' comes from 'bogus', which means 'not genuine' or 'counterfeit'. This is a fitting name, as the algorithm is not a genuine sorting algorithm in the sense that it does not take advantage of any particular properties of the data it's sorting. Instead, it relies purely on chance to sort the data.

The basic operation of Bogo Sort is very simple. It works by first checking if the list is in order. If it is, the algorithm stops. If it isn't, the algorithm randomly permutes the list's elements and then checks again. This process is repeated until the list is sorted.

The time complexity of Bogo Sort is O((n+1)!), making it one of the least efficient sorting algorithms. This is because the average number of times it needs to permute the list before stumbling upon a sorted permutation is (n+1)!. For a list of 3 elements, this is 24 permutations on average. For a list of 10 elements, this is over 3.6 million permutations on average. As such, Bogo Sort is impractical for lists of more than a very few elements.

In summary, Bogo Sort is a simple and highly inefficient sorting algorithm that works by repeatedly generating random permutations of its input until it finds a sorted one. It serves as a good example of how not to design a sorting algorithm, and is useful for teaching the importance of algorithm efficiency.