Algorithm to generate all possible permutations of a list?

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Basically, for each item from left to right, all the permutations of the remaining items are generated (and each one is added with the current elements). This can be done recursively (or iteratively if you like pain) until the last item is reached at which point there is only one possible order.

So with the list [1,2,3,4] all the permutations that start with 1 are generated, then all the permutations that start with 2, then 3 then 4.

This effectively reduces the problem from one of finding permutations of a list of four items to a list of three items. After reducing to 2 and then 1 item lists, all of them will be found.
Example showing process permutations using 3 coloured balls:
Red, green and blue coloured balls ordered permutations image (from https://en.wikipedia.org/wiki/Permutation#/media/File:Permutations_RGB.svg – https://commons.wikimedia.org/wiki/File:Permutations_RGB.svg)

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