permutations of the set {1, 2, ..., n} is given by the following pseudocode: In the above pseudocode, the statement "yield P" means to output or record the set of permuted indices P. If the algorithm is implemented correctly, P will be yielded exactly n!
This algorithm is not the most efficient one among all existing permutation generation methods.
[2] Not only does it have to keep track of an auxiliary counting array (c), redundant permutations are also produced and ignored (because P is not yielded after left-rotation if c[i] ≥ i) in the course of generation.
For instance, when n = 4, the algorithm will first yield P = [1,2,3,4] and then generate the other 23 permutations in 40 iterations (i.e. in 17 iterations, there are redundant permutations and P is not yielded).
The following lists, in the order of generation, all 41 values of P, where the parenthesized ones are redundant: