pythonlistmultidimensional-arrayflatten

# How do I make a flat list out of a list of lists?

I have a list of lists like

``````[
[1, 2, 3],
[4, 5, 6],
[7],
[8, 9]
]
``````

How can I flatten it to get `[1, 2, 3, 4, 5, 6, 7, 8, 9]`?

If your list of lists comes from a nested list comprehension, the problem can be solved more simply/directly by fixing the comprehension; please see How can I get a flat result from a list comprehension instead of a nested list?.

The most popular solutions here generally only flatten one "level" of the nested list. See Flatten an irregular (arbitrarily nested) list of lists for solutions that completely flatten a deeply nested structure (recursively, in general).

Solution

• A list of lists named `xss` can be flattened using a list comprehension:

``````flat_list = [
x
for xs in xss
for x in xs
]
``````

The above is equivalent to:

``````flat_list = []

for xs in xss:
for x in xs:
flat_list.append(x)
``````

Here is the corresponding function:

``````def flatten(xss):
return [x for xs in xss for x in xs]
``````

This is the fastest method. As evidence, using the `timeit` module in the standard library, we see:

``````\$ python -mtimeit -s'xss=[[1,2,3],[4,5,6],[7],[8,9]]*99' '[x for xs in xss for x in xs]'
10000 loops, best of 3: 143 usec per loop

\$ python -mtimeit -s'xss=[[1,2,3],[4,5,6],[7],[8,9]]*99' 'sum(xss, [])'
1000 loops, best of 3: 969 usec per loop

\$ python -mtimeit -s'xss=[[1,2,3],[4,5,6],[7],[8,9]]*99' 'reduce(lambda xs, ys: xs + ys, xss)'
1000 loops, best of 3: 1.1 msec per loop
``````

Explanation: the methods based on `+` (including the implied use in `sum`) are, of necessity, `O(L**2)` when there are L sublists -- as the intermediate result list keeps getting longer, at each step a new intermediate result list object gets allocated, and all the items in the previous intermediate result must be copied over (as well as a few new ones added at the end). So, for simplicity and without actual loss of generality, say you have L sublists of M items each: the first M items are copied back and forth `L-1` times, the second M items `L-2` times, and so on; total number of copies is M times the sum of x for x from 1 to L excluded, i.e., `M * (L**2)/2`.

The list comprehension just generates one list, once, and copies each item over (from its original place of residence to the result list) also exactly once.