Generating all permutations of $\{1,2,3,4\}$ will result to all of these except

a$.$ the bottom$-$up minimal$-$change algorithm.

b$.$ The correctness of the algorithm stems from the fact that it generates $2$n bit strings and all of them are distinct.

c$.$ the Johnson$-$Trotter algorithm.

d$.$ the lexicographic$-$order algorithm.