# List comprehensions¶

## Basic comprehensions¶

List comprehensions are a tool that in many cases makes it easier to create a list of elements. For example, if we want to create a list of squares of the first few positive integers, we can do it using the for loop as follows:

squares = []              # start with an empty list
for n in range(10):
squares.append(n**2)  # append n**2

print(squares)


[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]

The same task can be accomplished with less code using list comprehensions:

squares = [n**2 for n in range(10)]   # list comprehension generating a list of squares

print(squares)


[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]

The syntax of list comprehensions is as follows:

mylist = [<expression> for <item> in <iterable_object>]


Such code will take one by one items from the iterable object, compute the value of the expression for each item, and create a list consisting of all these values. The iterable object can be a list, tuple, string etc. In the next example we use list comprehensions to create a list from characters of a string:

mylist  = [letter + '!' for letter in 'Buffalo']

print(mylist)


[‘B!’, ‘u!’, ‘f!’, ‘f!’, ‘a!’, ‘l!’, ‘o!’]

## Generalized comprehensions¶

In a more general form list comprehensions can include an if statement. For example, in order to create a list of squares of odd integers we can use the following code:

odd_squares = []                  # start with an empty list
for n in range(10):
if n%2 == 1:                  # check if n is odd
odd_squares.append(n**2)  # if n is odd append n**2 to the list

print(odd_squares)


[1, 9, 25, 49, 81]

Using generalized list comprehensions we can get the same list as follows:

odd_squares = [n**2 for n in range(10) if n%2 == 1]

print(odd_squares)


[1, 9, 25, 49, 81]

The syntax of generalized comprehensions is as follows:

mylist = [<expression> for <variable> in <iterable_object> if <condition>]


This code will take items from the iterable object, and check for each item if the condition holds. If it does it will compute the value of the expression, and produce a list consisting of all these values.

As one more application of this generalized syntax we create a list consisting of all vowels in a string:

vowels = [letter for letter in 'euforia' if letter in 'aeiou']

print(vowels)


[‘e’, ‘u’, ‘o’, ‘i’, ‘a’]

## Nested comprehensions¶

List comprehensions can be nested to involve more than one variable. For example, the following code takes values from two different lists of strings and produces a list of combined strings:

greeting_list = ['Hello', 'Hi']
name_list = ['Alice', 'Bob', 'Caroline']

mylist = [greeting + ' ' + name + '!' for greeting in greeting_list for name in name_list]

print(mylist)


[‘Hello Alice!’, ‘Hello Bob!’, ‘Hello Caroline!’, ‘Hi Alice!’, ‘Hi Bob!’, ‘Hi Caroline!’]

The above code produces the same output as a nested for loop:

greeting_list = ['Hello', 'Hi']
name_list = ['Alice', 'Bob', 'Caroline']

mylist = []
for greeting in greeting_list:
for name in name_list:
mylist.append(greeting + ' ' + name + '!')

print(mylist)


[‘Hello Alice!’, ‘Hello Bob!’, ‘Hello Caroline!’, ‘Hi Alice!’, ‘Hi Bob!’, ‘Hi Caroline!’]

Nested comprehensions can be used with the if statement. In the next example we create a list of tuples $$(a, b)$$ such that $$b$$ divides $$a$$:

divisors = [(a, b) for a in range(1,6) for b in range(1,6) if a%b == 0]

print(divisors)


[(1, 1), (2, 1), (2, 2), (3, 1), (3, 3), (4, 1), (4, 2), (4, 4), (5, 1), (5, 5)]

Equivalent code using nested for loops looks as follows:

divisors = []

for a in range(1,6):
for b in range(1,6):
if a%b == 0:
divisors.append((a,b))

print(divisors)


[(1, 1), (2, 1), (2, 2), (3, 1), (3, 3), (4, 1), (4, 2), (4, 4), (5, 1), (5, 5)]