Python Disjoint Set Operations

Introduction

Disjoint sets, also known as mutually exclusive sets, are sets that have no element in common. In Python, you can check whether sets are disjoint using the isdisjoint() instance or class method.

Testing for disjoint sets is valuable in scenarios where you need to ensure that two sets don’t share any elements. For example, in a scheduling application, you might want to make sure that the time slots of two events are disjoint, indicating they don’t overlap. Another example is ensuring that the ingredients of a food item don’t include ingredients a person is allergic to.

Using the isdisjoint() Instance Method

The isdisjoint() instance method of Python set objects checks whether the calling set and another iterable have no elements in common. It returns True if they don’t, i.e. they are disjoint, and False otherwise.

Example:

set_a = {1, 2, 3}
set_b = {4, 5, 6}

result = set_a.isdisjoint(set_b)
print(result)

Output:

True

In the example above, set_a and set_b are disjoint since they have no common elements, resulting in True.

Example:

set_a = {1, 2, 3}
set_b = {3, 4, 5}

result = set_a.isdisjoint(set_b)
print(result)

Output:

False

Here, set_a and set_b are not disjoint because they share the element 3, leading to False.

The following example demonstrates that isdisjoint() works with other iterable types, e.g. a list.

Example:

set_a = {1, 2, 3}
lst = [4, 5, 6]

result = set_a.isdisjoint(lst)
print(result)

Output:

True

The above example tests whether the set set_a and the list lst are disjoint. Except for issubset()‘s argument being a list and not a set, it is identical to the first example.

Using the isdisjoint() Class Method

Similar to the instance method, the isdisjoint() class method allows you to check whether a set, given as the first argument, has no elements in common with an iterable, given as the second.

The difference between the class method and instance method version of isdisjoint() is that the instance method is called on a specific set object, whereas the class method includes the set object as its first parameter. Following the first argument, which must be a set, the second argument can be objects of any iterable type.

Since this version of isdisjoint() is a class method of the set class, you call it with a set. prefix.

Example:

set_a = {1, 2, 3}
lst = [4, 5, 6]

result = set.isdisjoint(set_a, lst)
print(result)

Output:

True

This achieves the same result as the previous example but using the class method.

Summary & Reference for Python Disjoint Set Operations

Python disjoint set operations allow you to determine whether two sets contain no elements in common.

The isdisjoint() instance method checks whether the calling set and another iterable object have no common elements. It returns True if they don’t, and False otherwise.

set_a = {1, 2, 3}
lst = [4, 5, 6]
result = set_a.isdisjoint(lst)  # result --> True

The isdisjoint() class method, an alternative to the instance method, is called directly on the set class. Its first argument must be a set, and the second can be an object of any iterable type.

set_a = {1, 2, 3}
lst = [4, 5, 6]
result = set.isdisjoint(set_a, lst)  # result --> True