Pseudo code of recursive method of printing all permutations of $n$ given integers
Your procedure produces all permutations of the input, returning it to its original state at the end.

When the input has length 1, there is nothing to do.

Otherwise, suppose that the input is $a_1,\ldots,a_n$. Let us represent all permutations of $a_1,\ldots,a_n$ as $[a_1,\ldots,a_n]$.

Here is what the procedure does:


Output $a_1,[a_2,a_3,\ldots,a_{n-1},a_n]$.
Output $a_2,[a_1,a_3,\ldots,a_{n-1},a_n]$.
Output $a_3,[a_2,a_1,\ldots,a_{n-1},a_n]$.
...
Output $a_n,[a_2,a_3,\ldots,a_{n-1},a_1]$.


In the first step, the procedure just goes over all permutations of the tail of the list, consisting of all but the first element.

In the second step, it switches $a_1$ and $a_2$, goes over all permutations of the tail, and then switches $a_1$ and $a_2$ back.

In the third step, it switches $a_1$ and $a_3$, goes over all permutations of the tail, and then switches $a_1$ and $a_3$ back.

And so on, until in the $n$th step, it switches $a_1$ and $a_n$, goes over all permutations of the tail, and then switches $a_1$ and $a_n$ back.