Sets¶

Python comes equipped with different objects to help organize your data. These data structures include lists, tuples, sets and dictionaries. But right now, we’ll focus on sets.

Sets are useful when you are working with data and the order or frequency of the values does not matter. Get ready to become an element of the set of people who understand sets.

Create¶

We will begin by creating an empty set.

example = set()

Now we want to add things to our set, and the add() function does exactly what we expect. Duplicates are not stored: if you try to add the same item twice, the set will store it the first time and ignore it the second time. We will use this method to add several objects to this set.

example.add(42)
example.add(False)
example.add(3.141592653589793)
example.add("Thorium")

Notice that you can add data of different types to the same set. If you print the example set we just prepared, Python will show you the items inside the set. Each item inside a set is called an “element”.

print(example)
# Output
{False, 42, 3.141592653589793, 'Thorium'}

When you try this, the elements may appear in a different order for you than what is displayed here. Do not panic. For sets, the order does not matter. This is different for lists and tuples where the order does matter.

Now look what happens when you try to add the number 42 to the set a second time.

example.add(42)
print(example)
# Output
{False, 42, 3.141592653589793, 'Thorium'}

The set still contains just one copy of the number 42. Sets do not contain duplicate elements. To see the number of elements in a set, use the length function, which is shortened to : len(example).

There is a second way to create a set, which can be faster in some instances. When creating the set you can pre-populate the set with a collection of elements.

example2 = set([False, 42, 3.141592653589793, 'Thorium'])
print(example2)
# Output
{False, 42, 3.141592653589793, 'Thorium'}

Remove¶

To remove an element from this set, use the remove method. Beware, if you attempt to remove an element that is not in the set you will get an error. To test this method, let’s remove the number 42.

example.remove(42)
print(len(example))
print(example)
# Output
3
{False, 3.141592653589793, 'Thorium'}

We can check that it worked either by looking at the number of elements or displaying all the elements inside the set. Look what happens if we try to remove the number 50 which is not in the set:

example.remove(50)
# Output
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
KeyError: 50

To avoid the possibility of an error, there is a second way to remove an element: the discard method. With the discard method, if you try to remove an element which is not in the set, the method does nothing – it quietly returns without making a change. Watch what happens when we discard the integer 50, which is not in the set.

>>> example.discard(50)
>>>

Nothing… Peace and quiet. The choice is yours; if you want to be alerted when your code tries to remove an element not in the set, use remove(). Otherwise, discard provides a convenient alternative.

There is also a faster way to remove elements. To empty out the set and remove all elements, use the clear() method.

>>> print(example)
{False, 3.141592653589793, 'Thorium'}
>>> example.clear()
>>> len(example)
0

This set now contains no elements – it has become the empty set. We can move along; there is nothing to see here.

Union and intersection¶

Now that we know how to create and modity a set, let’s learn how to evaluate the union and intersection of two sets. If you have two sets A and B, then the union is the combination of all elements from the two sets and in math is denoted as \(A \bigcup B\). The intersection is the set of elements inside both A and B, and is denoted as \(A \bigcap B\).

To see these in action, let’s look at the integers from 1 through 10.

odds = set([1, 3, 5, 7, 9])
evens = set([2, 4, 6, 8, 10])
primes = set([2, 3, 5, 7])
composites = set([4, 6, 8, 9, 10])

The union of the odd and even integers are all numbers from 1 to 10. You get the same answer if you reverse everything.

>>> odds.union(evens)
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
>>> evens.union(odds)
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

>>> odds
{1, 3, 5, 7, 9}
>>> evens
{2, 4, 6, 8, 10}

Notice how the set of odds and the set of evens are unchanged. We can find the set of odd prime numbers by computing the intersection of the sets of odds and primes.

>>> odds.intersection(primes)
{3, 5, 7}
>>> primes.intersection(evens)
{2}

And there is only one even prime number: 2.

Which integers are both even and odd ?

>>> evens.intersection(odds)
set()

There are none. The intersection of these two sets is the empty set.

>>> primes.union(composites)
{2, 3, 4, 5, 6, 7, 8, 9, 10}

The union of the prime numbers and composite numbers are the integers from 2 through 10. Notice 1 is missing – this is becausse 1 is neither prime nor composite.

Membership¶

Another common opreation is testing to see if one element is inside a set. To do this in Python use the in operator. Is 2 in the set of prime numbers ?

>>> 2 in primes
True

Yes. This is a true statement.

Is 6 an odd integer?

>>> 6 in odds
False

No. This is a false statement. You can also test to see if an element is NOT in a set.

>>> 9 not in evens
True

9 is not an even integer, so this is a true statement.

There are many more methods and operations you can perform with sets. Take a moment to explore these methods. You will not regret it.

Sets are a built-in data type in Python. They come equipped with all the luxury features: unions, intersections, adding elements, removing elements, and much more. Everything you will ever need for your data hungry code… Provided your sets are finite.

Exercises¶

Add a list of elements to a given set.

given = {"Yellow", "Orange", "Black"}
some_items = ["Blue", "Green", "Red"]
expected = {"Green", "Yellow", "Black", "Orange", "Red", "Blue"}

Create a new set with all items from both sets by removing duplicates

given_a = {10, 20, 30, 40, 50}
given_b = {30, 40, 50, 60, 70}
expected = {70, 40, 10, 50, 20, 60, 30}

Remove 10, 20, 30 elements from the following set

given_a = {10, 20, 30, 40, 50}
expected = {40, 50}

Determine wether or not the following two sets have any elements in common

given_a = {10, 20, 30, 40, 50}
given_b = {60, 70, 80, 90, 10}
# Expected output:
The two sets have items in common.
{10}

Count the number of vowels in a given string

given = "Understanding sets is easy."
# Expected output
The given string has 7 vowels.