# Divide a set of strings into those which contain "a" and those which don't

I am beginning to learn Python on my own through edX and I was given this basic problem: "Given a list of cities, separate the list into two lists, namely one with cities containing the letter 'a' in their name and one with cities not containing the letter 'a'."

This is my approach. It works, but I can't help but feel like there is a much more concise way to get this result. If anybody could offer some other methods I would be interested:

cities = ["New York", "Shanghai", "Munich", "Tokyo", "Dubai", "Mexico City", "São Paulo", "Hyderabad"]

a_city, no_a_city = [],[]
for city in cities:
for x in range(0, len(city)):
if city[x] == "a":
a_city.append(city)
break
else:
if x == len(city) - 1:
no_a_city.append(city)

print("a_city:", a_city)
print("no_a_city:", no_a_city)


I am also interested in learning more about the interaction between nested loops/conditionals and complexity if anybody has some resources.

This usecase is actually covered by one of the itertools recipes. itertools is a package in the Python standard library that supplies fast and efficient tools for iterating over things or creating certain iterable things (like the combination of all pairs and such). It is an often used library and well worth it to get acquainted with.

The recipe is as follows:

from itertools import filterfalse, tee

def partition(pred, iterable):
'Use a predicate to partition entries into false entries and true entries'
# partition(is_odd, range(10)) --> 0 2 4 6 8   and  1 3 5 7 9
t1, t2 = tee(iterable)
return filterfalse(pred, t1), filter(pred, t2)


In your specific case you would use it like this:

if __name__ == "__main__":
cities = ["New York", "Shanghai", "Munich", "Tokyo", "Dubai", "Mexico City", "São Paulo", "Hyderabad"]
no_a_city, a_city = map(list, partition(lambda city: "a" in city, cities))
print("a_city:", a_city)
print("no_a_city:", no_a_city)


The map(list, ...) part is needed because what the partition function returns are generators that generate values on the fly. They can be consumed into a list.

The predicate used is a lambda function, an anonymous function which in this case returns truthy or falsy values. It is used to test each element of the iterable.

Instead of manually iterating over each name (even worse, over each index of each name, have a look at Loop Like A Native), I used the fact that strings support the in operator.

I also added a if __name__ == "__main__": guard to allow importing from this script from another script.

One thing you could have used in your code is the fact that for loops have an optional else clause which is run if no break statement interrupted the loop:

a_city, no_a_city = [],[]
for city in cities:
for char in city:
if char == "a":
a_city.append(city)
break
else:
no_a_city.append(city)


As for complexity, this has the same complexity as your code. You have two nested for loops, making this on average $$\\mathcal{O}(nk)\$$ with $$\n\$$ being the number of cities and $$\k\$$ being the average length of the city names.

The in operator for strings is $$\\mathcal{O}(k)\$$ (it is just the same loop you wrote, but probably written in C) and it is used once per city. However, due to the tee my code iterates twice over the cities, so would be $$\\mathcal{O}(2nk)\$$, which in terms of algorithmic complexity is also $$\\mathcal{O}(nk)\$$.

• Thank you Graipher, That is a lot to take in for a beginner, but I will work on dissecting some of it to improve my coding. I briefly checked out that link that you provided and already see some issues with what I am doing (as you pointed out, iterating over each name AND each index of each name) so thanks for that. You've given me a lot to look into. On complexity: using the link that you provided, I can see a way to write this same code using only one for loop. Does this imply that it is less complex than your code? Nov 21 '18 at 13:07
• @JacobCheverie: Yes, there is still some road left ahead of you, but don't despair. And no, just because there is only one visible for loop does not make it linear in time (my solution has no visible for loop and yet it is not). I cannot think of a way that does not have to look at each character of each city name, but maybe you are more clever than I. Nov 21 '18 at 13:24
• I'm not convinced that this approach makes sense; the main benefit of working with generators is a small memory footprint which is completely comprised by the use of tee. Nov 22 '18 at 18:51

The task here is to collate the list of cities according to a key. In this case the key can be 'a' in city, which is True if the city contains 'a' and False otherwise.

It's common to encounter processing tasks which require collation, for example to find words that are anagrams of each other we could collate the words in a dictionary according to their sorted letters.

There is a standard pattern for collation in Python, which is to use collections.defaultdict and a loop. In the cities case, it goes like this:

from collections import defaultdict
with_a = defaultdict(list)
for city in cities:
with_a['a' in city].append(city)


After running this loop, with_a[True] is the list of cities with 'a' and with_a[False] is the list of cities without.

I prefer this approach to itertools.partition because it iterates over the input just once (whereas partition iterates over the input twice), and it's clear how to generalize it to other kinds of key.

• This is seemingly high-powered. I will look into defaultdict some more to gain a better understanding of the code. When you mention your preference of this over partition, does that imply that this would be a more efficient/less complex approach? Nov 21 '18 at 18:15
• +1 Imo, this approach is easier to digest, and has better space and time complexity than the itertools.partition approach. Nov 22 '18 at 18:47

This is not a complete review, but rather two simpler alternatives that illustrate how you can cut the some of the inner control flow using the in keyword. This keyword tests for membership of an object in an iterable. In this case, you want to test for membership of 'a' in the name of each element of cities.

The first takes the same approach as your code

cities = ["New York", "Shanghai", "Munich", "Tokyo", "Dubai", "Mexico City", "São Paulo", "Hyderabad"]

a_city, no_a_city = [],[]
for city in cities:
if 'a' in city:
a_city.append(city)
else:
no_a_city.append(city)

print("a_city:", a_city)
print("no_a_city:", no_a_city)


The membership test using in is a drop-in replacement for the harder-to-read and more error-prone explicit loop over the characters.

An even cleaner solution makes use of the built-in set data type. In simplistic terms, a set is like a list, except that it is not ordered and does not contain duplicates.

# a set is constructed with {}, unlike the the [] used for lists
cities = {"New York", "Shanghai", "Munich", "Tokyo", "Dubai", "Mexico City", "São Paulo", "Hyderabad"}

# we can also construct one using the set builtin function (analogous to list)
a_city = set(city for city in cities if 'a' in city)

# subtracting one set from another is well-defined and does the obvious thing
no_a_city = cities - a_city

print("a_city:", a_city)
print("no_a_city:", no_a_city)


Check out the docs for a flavor of the kinds of rich membership and comparison that sets allow. These operations can typically be expected to be more efficient than equivalent algorithms on lists, mainly due to the fact that sets are guaranteed not to have duplicate elements.

• Thanks @Endulum, I like the set approach. I can see where I would have to be careful using this, however. If I was not guaranteed to have distinct members then I assume that the set approach would discard some information and thus not be appropriate. When you define a_city, do I read this as I would read a mathematical set (set of all 'city' such that for 'city' in 'cities' if 'a' in 'city')? Without reading as so, it appears to me as a typo. Nov 21 '18 at 18:09
• Regarding the appropriateness of sets versus dictionaries: yes, if is desirable that you retain duplicates, then a set is likely not the right collection to choose. Nov 21 '18 at 18:19
• Regarding the relationship to mathematical set notation, it should be read like (the set of all 'city' in 'cities' such that 'a' in 'city'). It is an alternative syntax for consisely building lists, sets, or other collections without an explicit loop. It is called a "comprehension", in this case a "set comprehension". If you have not learned about these yet, I expect you will before long. They are very popular among Python programmers. Nov 21 '18 at 18:26
• I had touched on list comprehensions briefly last night while reading but I didn't recognize the form. I only asked about the relationship to mathematics because city is written twice at the start of the set definition which seems a bit hard to remember, but I think that this is just Python syntax I must get used to. Thanks again! Nov 21 '18 at 19:06

List comprehensions are very well-suited for this task. The basic syntax is the following:

new_list = [ expression(x) for x in old_list if condition(x) ]


In this case we don't want to change the list elements, simply select them according to a condition. What should be this condition? Well, Python also provides a simple syntax to check if a string (or a list) contains an element, with the keyword in,or not in for the negation (this is the same keyword used for iterationg through a list, so be careful to not get confused).

With these tools, your code can fit on two lines, with no import required:

a_city = [ city for city in cities if "a" in city ]
no_a_city = [ city for city in cities if "a" not in city ]