# Comprehensions

Imagine we wanted a list comprising even squares such as [0, 4, 16, 36, 64]. One natural way to tackle this problem is the following:

even_squares = []
for n in range(10):
if n % 2 == 0:
even_squares.append(n**2)


But here again, Python offers a convenient and concise feature to create lists whose syntax resembles the mathematical definition of sets:

even_squares = [n**2 for n in range(10) if n % 2 == 0]


Multiple levels of nesting are also possible:

>>> [(x, y) for x in range(3) for y in range(3) if x != y]
[(0, 1), (0, 2), (1, 0), (1, 2), (2, 0), (2, 1)]


We can define sets by comprehension as well. For instance, given a list we might want to generate a set of its duplicate elements.

>>> input_list = ['a', 'b', 'c', 'a', 'd', 'd', 'g']
>>> duplicates = {c for c in input_list if input_list.count(c) > 1}
>>> duplicates
{'a', 'd'}


Another illustrative example is the generation of the set of prime numbers up to 100.

>>> {x for x in range(2, 101) if all(x%y for y in range(2, min(x, 11)))}
{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}


We are taking advantage of the all() function which returns True if all the elements in an iterable are true. In this case, if all the modulos of x%y are different from 0.

Finally, in dictionaries:

>>> {x: 2*x for x in range(10)}
{0: 0, 1: 2, 2: 4, 3: 6, 4: 8, 5: 10, 6: 12, 7: 14, 8: 16, 9: 18}


All in all, comprehensions are the quintessential example of Python principles.

The Zen of Python, by Tim Peters

Explicit is better than implicit.

Flat is better than nested.