w3resource

Python: Union of sets

Python sets: Exercise-7 with Solution

Write a Python program to create a union of sets.

From Wikipedia,
In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations through which sets can be combined and related to each other. A nullary union refers to a union of zero (0) sets and it is by definition equal to the empty set.

The union of two sets A and B is the set of elements which are in A, in B, or in both A and B. In symbols,
A ∪ B = {x : x ∈ A or x ∈ B}
For example, if A = {1, 3, 5, 7} and B = {1, 2, 4, 6, 7} then A ∪ B = {1, 2, 3, 4, 5, 6, 7}. A more elaborate example (involving two infinite sets) is:
A = {x is an even integer larger than 1}
B = {x is an odd integer larger than 1}
A ∪ B = {2,3,4,5,6,...}

NumPy Sets: Union of sets.
As another example, the number 9 is not contained in the union of the set of prime numbers {2, 3, 5, 7, 11, ...} and the set of even numbers {2, 4, 6, 8, 10, ...}, because 9 is neither prime nor even.
Sets cannot have duplicate elements, so the union of the sets {1, 2, 3} and {2, 3, 4} is {1, 2, 3, 4}. Multiple occurrences of identical elements have no effect on the cardinality of a set or its contents.

Sample Solution-1:

Using union() function

Python Code:

setc1 = set(["green", "blue"])
setc2 = set(["blue", "yellow"])
print("Original sets:")
print(setc1)
print(setc2)
setc = setc1.union(setc2)
print("\nUnion of above sets:")
print(setc)
setn1 = set([1, 1, 2, 3, 4, 5])
setn2 = set([1, 5, 6, 7, 8, 9])
print("\nOriginal sets:")
print(setn1)
print(setn2)
print("\nUnion of above sets:")
setn = setn1.union(setn2)
print(setn)

Sample Output:

Original sets:
{'blue', 'green'}
{'blue', 'yellow'}

Union of above sets:
{'blue', 'yellow', 'green'}

Original sets:
{1, 2, 3, 4, 5}
{1, 5, 6, 7, 8, 9}

Union of above sets:
{1, 2, 3, 4, 5, 6, 7, 8, 9}

Pictorial Presentation:

NumPy Sets: Union of sets.

Visualize Python code execution:

The following tool visualize what the computer is doing step-by-step as it executes the said program:


Sample Solution-2:

Using | operator

Python Code:

setc1 = set(["green", "blue"])
setc2 = set(["blue", "yellow"])
print("Original sets:")
print(setc1)
print(setc2)
setc = setc1 | setc2
print("\nUnion of above sets:")
print(setc)
setn1 = set([1, 1, 2, 3, 4, 5])
setn2 = set([1, 5, 6, 7, 8, 9])
print("\nOriginal sets:")
print(setn1)
print(setn2)
print("\nUnion of above sets:")
setn = setn1 | setn2
print(setn)

Sample Output:

Original sets:
{'green', 'blue'}
{'blue', 'yellow'}

Union of above sets:
{'green', 'yellow', 'blue'}

Original sets:
{1, 2, 3, 4, 5}
{1, 5, 6, 7, 8, 9}

Union of above sets:
{1, 2, 3, 4, 5, 6, 7, 8, 9}

Visualize Python code execution:

The following tool visualize what the computer is doing step-by-step as it executes the said program:


Sample Solution-3:

Union of more than two sets:

Python Code:

setn1 = set([1, 1, 2, 3, 4, 5])
setn2 = set([1, 5, 6, 7, 8, 9])
setn3 = set([3, 4, 5, 3, 9, 10])
setn4 = set([5, 7, 9, 10, 12, 14])

print("\nOriginal sets:")
print(setn1)
print(setn2)
print(setn3)
print(setn4)
print("\nUnion of first three sets:")
setn = setn1.union(setn2, setn3)
print(setn)
print("\nUnion of above four sets:")
setn = setn1.union(setn2, setn3, setn4)
print(setn)

Sample Output:

Original sets:
{1, 2, 3, 4, 5}
{1, 5, 6, 7, 8, 9}
{3, 4, 5, 9, 10}
{5, 7, 9, 10, 12, 14}

Union of first three sets:
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Union of above four sets:
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14}

Visualize Python code execution:

The following tool visualize what the computer is doing step-by-step as it executes the said program:


Python Code Editor:

Have another way to solve this solution? Contribute your code (and comments) through Disqus.

Previous: Write a Python program to create an intersection of sets.
Next: Write a Python program to create set difference.

What is the difficulty level of this exercise?

Test your Programming skills with w3resource's quiz.



Python: Tips of the Day

Find the index of an item in a list?

Given a list ["foo", "bar", "baz"] and an item in the list "bar", how do I get its index (1) in Python?

>>> ["foo", "bar", "baz"].index("bar")
1

Caveats follow

Note that while this is perhaps the cleanest way to answer the question as asked, index is a rather weak component of the list API, and I can't remember the last time I used it in anger. It's been pointed out to me in the comments that because this answer is heavily referenced, it should be made more complete. Some caveats about list.index follow. It is probably worth initially taking a look at the documentation for it:

list.index(x[, start[, end]])

Linear time-complexity in list length

An index call checks every element of the list in order, until it finds a match. If your list is long, and you don't know roughly where in the list it occurs, this search could become a bottleneck. In that case, you should consider a different data structure. Note that if you know roughly where to find the match, you can give index a hint. For instance, in this snippet, l.index(999_999, 999_990, 1_000_000) is roughly five orders of magnitude faster than straight l.index(999_999), because the former only has to search 10 entries, while the latter searches a million:

>>> import timeit
>>> timeit.timeit('l.index(999_999)', setup='l = list(range(0, 1_000_000))', number=1000)
9.356267921015387
>>> timeit.timeit('l.index(999_999, 999_990, 1_000_000)', setup='l = list(range(0, 1_000_000))', number=1000)
0.0004404920036904514

Only returns the index of the first match to its argument

A call to index searches through the list in order until it finds a match, and stops there. If you expect to need indices of more matches, you should use a list comprehension, or generator expression.

>>> [1, 1].index(1)
0
>>> [i for i, e in enumerate([1, 2, 1]) if e == 1]
[0, 2]
>>> g = (i for i, e in enumerate([1, 2, 1]) if e == 1)
>>> next(g)
0
>>> next(g)
2

Most places where I once would have used index, I now use a list comprehension or generator expression because they're more generalizable. So if you're considering reaching for index, take a look at these excellent Python features.

Throws if element not present in list

A call to index results in a ValueError if the item's not present.

>>> [1, 1].index(2)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: 2 is not in list

If the item might not be present in the list, you should either

  • Check for it first with item in my_list (clean, readable approach), or
  • Wrap the index call in a try/except block which catches ValueError (probably faster, at least when the list to search is long, and the item is usually present.)

Ref: https://bit.ly/2ALwXwe