Permutations Basics in Python   

When working with lists in Python, you might need to match all possible permutations of a longer list against a shorter list. This is useful in scenarios like:

• Generating possible sequences of a fixed length from a larger pool of items
• Finding all ordered combinations of a subset from a larger list
• Testing different arrangements in optimization or search problems

Example 1: Using itertools.permutations

The easiest way is to use itertools.permutations, which generates all possible ordered arrangements of a given length.

from itertools import permutations

long_list = ['A', 'B', 'C', 'D']
short_length = 2  # We want permutations of length 2

# Generate all possible permutations of length 2
perms = permutations(long_list, short_length)

for perm in perms:
    print(perm)

Output:

('A', 'B')  
('A', 'C')  
('A', 'D')  
('B', 'A')  
('B', 'C')  
... (and so on)  

Example 2: Matching Permutations Against a Target List

If you want to check which permutations match a specific short list:

from itertools import permutations

long_list = ['A', 'B', 'C', 'D']
target = ['B', 'A']  # We want to find if this permutation exists

perms = permutations(long_list, len(target))

if tuple(target) in perms:
    print("Match found!")
else:
    print("No match.")

Output: Match found!

Example 3: Storing Permutations in a List

If you need all permutations stored in a list for further processing:

from itertools import permutations

long_list = ['A', 'B', 'C']
short_length = 2

all_perms = list(permutations(long_list, short_length))
print(all_perms)

Output:

[('A', 'B'), ('A', 'C'), ('B', 'A'), ('B', 'C'), ('C', 'A'), ('C', 'B')]

Example 4: Permutations with Repeated Elements (Using product)

If you want to allow repeated elements (like ('A', 'A')), use itertools.product instead:

from itertools import product

long_list = ['A', 'B', 'C']
short_length = 2

perms_with_repeats = list(product(long_list, repeat=short_length))
print(perms_with_repeats)

Output:

[('A', 'A'), ('A', 'B'), ('A', 'C'), ('B', 'A'), ('B', 'B'), ('B', 'C'), ('C', 'A'), ('C', 'B'), ('C', 'C')]

Key Takeaways

• permutations() → Ordered, non-repeating sequences.
• product() → Ordered, allows repeating elements.
• Convert permutations to a list if you need to reuse them.
• Use tuple(target) to check if a specific permutation exists.

This approach is efficient and leverages Python’s built-in libraries for clean and fast results.