Using Python’s itertools for Combinatorics (with Examples)

 

Using Python’s itertools for Combinatorics

Introduction

When solving coding problems, especially involving permutations, combinations, or Cartesian products, writing loops can get messy and time-consuming.

That’s where Python’s itertools module comes in — a built-in library that provides efficient tools for iteration, combinatorics, and data processing.

In this post, we’ll explore the most useful itertools functions with clear examples.

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What is itertools?

itertools is a standard Python module that provides fast, memory-efficient tools to handle iterators — especially when working with large data sets.

You can import it easily:

import itertools

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1. itertools.product() – Cartesian Product

Use Case:
Generate all possible pairs (like nested loops).

Example:

import itertools

colors = ['red', 'green']
shapes = ['circle', 'square']

result = list(itertools.product(colors, shapes))
print(result)

Output:

[('red', 'circle'), ('red', 'square'), ('green', 'circle'), ('green', 'square')]

Great for generating test cases or combinations of options.

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2. itertools.permutations() – All Possible Arrangements

Use Case:
Generate all possible orderings of elements.

Example:

import itertools

nums = [1, 2, 3]
result = list(itertools.permutations(nums))
print(result)

Output:

[(1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), (3, 2, 1)]

Useful for problems like string rearrangements or route planning.

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3. itertools.combinations() – Choose Elements Without Repetition

Use Case:
Generate all possible combinations (unordered, no repetition).

Example:

import itertools

letters = ['A', 'B', 'C']
result = list(itertools.combinations(letters, 2))
print(result)

Output:

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

Perfect for pairing problems or subset generation.

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4. itertools.combinations_with_replacement()

Use Case:
Combinations with repetition allowed.

Example:

import itertools

letters = ['A', 'B']
result = list(itertools.combinations_with_replacement(letters, 2))
print(result)

Output:

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

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5. itertools.cycle() – Infinite Loop Through Sequence

Use Case:
Repeat elements of a list endlessly.

Example:

import itertools

count = 0
for color in itertools.cycle(['Red', 'Green', 'Blue']):
    print(color)
    count += 1
    if count == 6:
        break

Output:

Red
Green
Blue
Red
Green
Blue

Great for repeating patterns or animations.

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6. itertools.chain() – Combine Multiple Iterables

Use Case:
Link multiple iterables into a single sequence.

Example:

import itertools

result = list(itertools.chain([1, 2], ['A', 'B']))
print(result)

Output:

[1, 2, 'A', 'B']

 Simplifies merging lists or tuples.

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7. itertools.groupby() – Group Data by Key

Use Case:
Group consecutive elements that share the same key.

Example:

import itertools

data = [('A', 1), ('A', 2), ('B', 3), ('B', 4)]
for key, group in itertools.groupby(data, lambda x: x[0]):
    print(key, list(group))

Output:

A [('A', 1), ('A', 2)]
B [('B', 3), ('B', 4)]

Common in data aggregation and sorting tasks.

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Summary

The itertools module is one of the most powerful yet underused tools in Python.
It helps you:
- Reduce nested loops
- Write cleaner code
- Handle combinations efficiently

Next time you face a combinatorics or iteration problem — reach for itertools first!