As you know from Discrete Math, a permutation is any possible ordering of the distinct items of a set S$.$ If $|$S$|=$ n$,$ there are n$!$ permutations. This means that for large sets, it is computationally infeasible to generate all possible permutations. One well$-$known algorithm for generating set permutations $($at least for small sets$)$ is presented below:ALGORITHM Johnson$-$Trotter$($n$)//$ Input: a positive integer n$//$ Output: A list of all permutations of $\{1,2,,$ n$\}$initialize the first permutation as $12$ n with directions pointing leftwhile the last permutation has a mobile elementfind its largest mobile element kswap k and the element to which k is directedreverse the direction of all elements that are larger than kadd the new permutation to the listNote: an element is mobile if its direction points to a smaller adjacent element