Explanation of how nested list comprehension works?

Question

I have no problem for understanding this:

a = [1,2,3,4]
b = [x for x in a]

I thought that was all, but then I found this snippet:

Answer 1

if a = [[1,2],[3,4],[5,6]], then if we unroll that list comp, we get:

      +----------------a------------------+ 
      | +--xs---+ , +--xs---+ , +--xs---+ | for xs in a
      | | x , x |   | x , x |   | x , x | | for x in xs
a  =  [ [ 1 , 2 ] , [ 3 , 4 ] , [ 5 , 6 ] ]
b  =  [ x for xs in a for x in xs ] == [1,2,3,4,5,6] #a list of just the "x"s

Answer 2

b = [x for xs in a for x in xs] is similar to following nested loop.

b = []
for xs in a:
   for x in xs:
       b.append(x)

Answer 3

This is an example of a nested comprehension. Think of a = [[1,2],[3,4],[5,6]] as a 3 by 2 matrix (matrix= [[1,2],[3,4],[5,6]]).

       ______
row 1 |1 | 2 |
       ______
row 2 |3 | 4 |
       ______
row 3 |5 | 6 |
       ______

The list comprehension you see is another way to get all the elements from this matrix into a list.

I will try to explain this using different variables which will hopefully make more sense.

b = [element for row in matrix for element in row]

The first for loop iterates over the rows inside the matrix ie [1,2],[3,4],[5,6]. The second for loop iterates over each element in the list of 2 elements.

I have written a small article on List Comprehension on my website http://programmathics.com/programming/python/python-list-comprehension-tutorial/ which actually covered a very similar scenario to this question. I also give some other examples and explanations of python list comprehension.

Disclaimer: I am the creator of that website.

Answer 4

Here is how I best remember it: (pseudocode, but has this type of pattern)

[(x,y,z) (loop 1) (loop 2) (loop 3)]

where the right most loop (loop 3) is the inner most loop.

[(x,y,z)    for x in range(3)    for y in range(3)    for z in range(3)]

has the structure as:

for x in range(3):
    for y in range(3):
        for z in range(3):
            print((x,y,z))

Edit I wanted to add another pattern:

[(result) (loop 1) (loop 2) (loop 3) (condition)]

Ex:

[(x,y,z)    for x in range(3)    for y in range(3)    for z in range(3)    if x == y == z]

Has this type of structure:

for x in range(3):
    for y in range(3):
        for z in range(3):
            if x == y == z:
                print((x,y,z))

Answer 5

Ah, the incomprehensible "nested" comprehensions. Loops unroll in the same order as in the comprehension.

[leaf for branch in tree for leaf in branch]

It helps to think of it like this.

for branch in tree:
    for leaf in branch:
        yield leaf

The PEP202 asserts this syntax with "the last index varying fastest" is "the Right One", notably without an explanation of why.

Answer 6

Yes, you can nest for loops INSIDE of a list comprehension. You can even nest if statements in there.

dice_rolls = []
for roll1 in range(1,7):
    for roll2 in range(1,7):
        for roll3 in range(1,7):
            dice_rolls.append((roll1, roll2, roll3))

# becomes

dice_rolls = [(roll1, roll2, roll3) for roll1 in range(1, 7) for roll2 in range(1, 7) 
              for roll3 in range(1, 7)]

I wrote a short article on medium explaining list comprehensions and some other cool things you can do with python, you should have a look if you're interested : )