All possible permutations of N lists in Python

When we have multiple lists and need to combine each element from one list with each element from another list, we're creating what's called a Cartesian product (not permutations). Python provides several approaches to achieve this combination.

Using List Comprehension

This straightforward approach uses nested list comprehension to create all possible combinations. The outer loop iterates through the first list, while the inner loop iterates through the second list ?

Example

A = [5, 8]
B = [10, 15, 20]

print("The given lists:", A, B)
combinations = [[m, n] for m in A for n in B]
print("Combinations of the given values are:", combinations)

Output

The given lists: [5, 8] [10, 15, 20]
Combinations of the given values are: [[5, 10], [5, 15], [5, 20], [8, 10], [8, 15], [8, 20]]

Using itertools.product()

The itertools.product() function provides a more elegant solution for creating Cartesian products. It internally creates nested loops to generate all possible combinations ?

Example

import itertools

A = [5, 8]
B = [10, 15, 20]

print("The given lists:", A, B)
result = list(itertools.product(A, B))
print("Combinations of the given lists are:", result)

Output

The given lists: [5, 8] [10, 15, 20]
Combinations of the given lists are: [(5, 10), (5, 15), (5, 20), (8, 10), (8, 15), (8, 20)]

Working with Multiple Lists

Both approaches can handle more than two lists. Here's an example with three lists ?

import itertools

A = [1, 2]
B = ['x', 'y']
C = [10, 20]

# Using itertools.product()
result = list(itertools.product(A, B, C))
print("Three-list combinations:", result)

Three-list combinations: [(1, 'x', 10), (1, 'x', 20), (1, 'y', 10), (1, 'y', 20), (2, 'x', 10), (2, 'x', 20), (2, 'y', 10), (2, 'y', 20)]

Comparison

Conclusion

Use itertools.product() for creating Cartesian products of multiple lists as it's more efficient and handles any number of lists. List comprehension works well for simple two-list combinations when you need the result as lists.