🐍 Complete Guide to Python itertools — Permutations, Combinations and Subsets Explained
The itertools module in Python is one of the most powerful tools for working with
permutations, combinations, subsets (power sets), Cartesian products and more.
In this guide, we’ll understand:
- ✔️ What are permutations?
- ✔️ What are combinations?
- ✔️ What are subsets?
- ✔️ How itertools functions work internally
- ✔️ Differences between each
This post is perfect for students, programmers, competitive coders, and data scientists.
📘 What Are Permutations?
Permutation = Arrangement where order matters.
Example: For digits [1, 2, 3], permutations of length 2:
# Order matters
(1, 2) ≠ (2, 1)
Formula: nPr = n! / (n-r)!
🧪 Code: Generating Permutations
from itertools import permutations
nums = [1, 2, 3]
perms = list(permutations(nums, 2))
print("All permutations of length 2:")
for p in perms:
print(p)
# Output:
# (1, 2)
# (1, 3)
# (2, 1)
# (2, 3)
# (3, 1)
# (3, 2)
⚙️ How permutations() works internally
The function returns an iterator that produces all possible ordered arrangements of the chosen elements.
It does NOT reuse elements unless you tell it (use product for repetition).
📗 What Are Combinations?
Combination = Selection where order does NOT matter.
# Order does NOT matter
(1, 2) == (2, 1)
Formula: nCr = n! / r! (n-r)!
🧪 Code: Combinations Example
from itertools import combinations
nums = [1, 2, 3]
combs = list(combinations(nums, 2))
print("Combinations of length 2:")
for c in combs:
print(c)
# Output:
# (1, 2)
# (1, 3)
# (2, 3)
✨ combinations_with_replacement()
Allows picking the same element more than once.
from itertools import combinations_with_replacement
nums = [1, 2, 3]
crep = list(combinations_with_replacement(nums, 2))
print("Combinations with repetition:")
for c in crep:
print(c)
# Output:
# (1, 1)
# (1, 2)
# (1, 3)
# (2, 2)
# (2, 3)
# (3, 3)
⚙️ How combinations() works internally
The function picks r items at a time, but does NOT change their order.
It treats (1,2) and (2,1) as the same combination, so it only returns one.
📙 What Are Subsets (Power Sets)?
A subset / power set contains all possible selections of items:
[1,2,3] subsets =
()
(1)
(2)
(3)
(1,2)
(1,3)
(2,3)
(1,2,3)
We generate subsets using combinations in a loop.
🧪 Code: Power Set Function
from itertools import combinations
def powerset(iterable):
items = list(iterable)
result = []
for r in range(len(items)+1):
for combo in combinations(items, r):
result.append(combo)
return result
print("Power set of [1,2,3]:")
for s in powerset([1,2,3]):
print(s)
🔍 Differences at a Glance (Comparison Table)
| Operation | Function | Order Matters? | Repetition Allowed? | Example |
|---|---|---|---|---|
| Permutations | permutations() |
Yes | No | (1,2) ≠ (2,1) |
| Combinations | combinations() |
No | No | (1,2) == (2,1) |
| CWR (repetition) | combinations_with_replacement() |
No | Yes | (1,1), (1,2)… |
| Power Set | loop of combinations() |
No | No | All subsets |
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