Help understanding code

[Willi]

Hi,
I have started learning Python a week ago (I have previous experience with C++ and Java) and stumbled over piece of code I have trouble to understand. 

def power_set(l):
   if not l: 
      return [[]]
   return power_set(l[1:]) + [[l[0]] + x for x in power_set(l[1:])]

The code calculates the power set. For power_set({1,2,3,4}) the output is {{}, {1}, {2}, {1,2}, {3}, {1,3}, {2,3}, {1,2,3}, {4}, {1,4}, {2,4}, {1,2,4}, {3,4}, {1,3,4}, {2,3,4}, {1,2,3,4}}. While the if statement is clear, the last is not .

I would be thankful if someone could explain me the last line.

[Mekire]

So, nasty recursive code with part of it wrapped in a list comp... wonderful.

Let's try breaking that line up:

power_set(l[1:]) + [[l[0]] + x for x in power_set(l[1:])]

We have:

power_set(l[1:])

and

[[l[0]] + x for x in power_set(l[1:])]

The first part is easy.  power_set(l[1:]) is the powerset of the current sequence without the first entry.
So if you ask for the power set of [1,2,3,4] it gives the power set of [2,3,4].

The second part is the first character in the sequence + the previous expression.
So if you ask for the powerset of [1,2,3,4] it gives you [1] + each set in the powerset of [2,3,4].


So to try once again to put this into words:
""" The powerset of any sequence is equal to (the powerset of the sequence without the first entry) + (the first entry +  (each set in the powerset of the sequence without the first entry))."""

Not sure if that is any clearer.  I tried. =P

[Willi]

Thank you very much. I have understood it now.
 
And yeah, it's the kind of recursive methods I wouldn't write myself voluntarily because of the hardness to read it (especially month later).

[Skaperen]

sometimes, code like that can earn you elegance points from the Ph.D people ... even if the code is wrong.