Can someone please explain why the output of this question is the list in reverse order?

Question

def mystery(l):
    if l == []:
        return(l)
    else:
        return(mystery(l[1:])+l[:1])
mystery([22,14,19,65,82,55])

#output: [55, 82, 65, 19, 14, 22]

Please explain how this code is working. I am not able to understand the recursion part here.

You should either run the code through a [debugger](https://ericlippert.com/2014/03/05/how-to-debug-small-programs/) or throw in some `print` statements and watch what it is doing step-by-step. — 0x5453, Dec 15 '20 at 18:20
Have you tried following the code on [PythonTutor](http://pythontutor.com/visualize.html#mode=edit)? — Mr. T, Dec 15 '20 at 18:45

score 2 · Accepted Answer · answered Dec 15 '20 at 18:22

It's done by list slicing. By returning

mystery(I[1:]) + I[:1]

you just keep going recursive and adding the first element from the list leftover.

for example:

mystery([1,2,3]) -> return mystery([2,3]) + [1] -> return mystery([3]) + [2] + [1]

and so on

evenodd · Answer 2 · 2020-12-15T18:43:12.220

The recursive part is the following line:

return (mystery(l[1:]) + l[:1])

Observe that l[:1] (i.e., l[0:1]) is the list consisting of the first element of l and l[1:] (i.e., l[1:len(l)]) is the list consisting of the remaining part of l. The + concatenates lists. Thus,

mystery([1,2,3,4]) = mystery([2,3,4]) + [1]
                   = mystery([3,4]) + [2] + [1]
                   = mystery([4]) + [3] + [2] + [1]
                   = mystery([]) + [4] + [3] + [2] + [1]
                   = [] + [4] + [3] + [2] + [1]
                   = [4,3,2,1]

Therefore, mystery(l) is the reverse of l. That is,

mystery(l) = l[::-1]

score 1 · Answer 3 · answered Dec 15 '20 at 18:27

Let's follow an example, each line is equivalent to the one after it:

mystery([22,14,19,65,82,55])
mystery([22,14,19,65,82,55][1:]) + [22,14,19,65,82,55][:1]
mystery([14,19,65,82,55]) + [22]
mystery([14,19,65,82,55][1:]) + [14,19,65,82,55][:1] + [22]
mystery([19,65,82,55]) + [14] + [22]
...
mystery([19,65]) + [82] + [55] + [14] + [22]
mystery([19,65][1:]) + [19, 65][:1] + [82] + [55] + [14] + [22]
mystery([65]) + [19] + [82] + [55] + [14] + [22]
mystery([65][1:]) + [65][:1] + [19] + [82] + [55] + [14] + [22]
mystery([]) + [65] + [19] + [82] + [55] + [14] + [22]
[] + [65] + [19] + [82] + [55] + [14] + [22]
[65, 19, 82, 55, 14, 22]

If you don't understand what [:1] [1:] means please read this SO question.

Can someone please explain why the output of this question is the list in reverse order?

3 Answers3