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 1 2 ... n with directions pointing left while the last permutation has a mobile element find its largest mobile element k swap k and the element to which k is directed reverse the direction of all elements that are larger than k add the new permutation to the list Note: an element is mobile if its direction points to a smaller adjacent element. Example: 1 2 3 13 2 3 1 2 3 2 1 2 3 1 2 1 3 REQUIREMENTS: Design and implement a program to generate all permutations of the set of least n positive integers. INPUT: an integer n with 1 < n < 25. OUTPUT: The tag "There are x permutations of the set {1, 2, ..., n}:", where x = n! a list of all permutations of the set {1, 2, n}, one per line. .... EXAMPLE OUTPUT:

Here are some of the main differences between Scilab and C++:

Explain the use of pointer and address-of operators in C/C++ programming. Provide examples demonstrating their significance.

Are there different types of modules in c++?