How to Intersect Multiple Sets in Python?

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To intersect multiple sets, stored in a list l, use the Python one-liner l.pop().intersection(*l) that takes the first set from the list, calls the intersection() method on it, and passes the remaining sets as arguments by unpacking them from the list.

A set is a unique collection of unordered elements. The intersection operation creates a new set that consists of the elements that exist in all sets.

So, let’s dive into the formal problem formulation, shall we?

Problem: Given a list or a collection of sets. How to join those sets using the intersection operation?

Example: You’ve got a list of sets [{1, 2, 3}, {1, 4}, {2, 3, 5}] and you want to calculate the intersection {1}.

Solution: To intersect a list of sets, use the following strategy:

  • Get the first element from the list as a starting point. This assumes the list has at least one element.
  • Call the intersection() method on the first set object.
  • Pass all sets as arguments into the intersection() method by unpacking the list with the asterisk operator *list.
  • The result of the intersection() method is a new set containing all elements that are in all of the sets.

Code: Here’s the one-liner code that intersects a collection of sets.

# Create the list of sets
lst = [{1, 2, 3}, {1, 4}, {1, 2, 3}]

# One-Liner to intersect a list of sets
print(lst[0].intersection(*lst))

The output of this code is the intersection of the three sets {1, 2, 3}, {1, 4}, and {2, 3, 5}. Only one element appears in all three sets:

{1}

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Try it yourself: Here’s the code in an interactive code shell that runs it in your browser:

Exercise: Change the code to calculate the union of the sets in the list!

Related video: A similar problem is to perform the union operation on a list of sets. In the following video, you can watch me explain how to union multiple sets in Python:

How to Union Multiple Sets in Python?

Where to Go From Here?

Enough theory. Let’s get some practice!

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Nerd Humor

Oh yeah, I didn’t even know they renamed it the Willis Tower in 2009, because I know a normal amount about skyscrapers. — xkcd (source)