Collections and Itertools Modules¶

The collections and itertools modules provide high-performance specialized container datatypes and memory-efficient looping constructs.

1. The `collections` Module¶

Overview of Container Types¶

Type	Purpose
`Counter`	Dictionary subclass for counting hashable objects
`defaultdict`	Dictionary subclass that calls a factory function to supply missing values
`deque`	Double-ended queue with $O(1)$ appends and pops from either end
`ChainMap`	Dictionary-like class for creating a single view of multiple mappings
`OrderedDict`	Dictionary subclass that remembers insertion order (with re-ordering methods)

Example: Frequency Counting with Counter

from collections import Counter

votes = ["Alice", "Bob", "Alice", "Charlie", "Alice", "Bob"]
tally = Counter(votes)

print("Total Tally:", tally)
print("Winner:", tally.most_common(1)[0][0])

Output

Total Tally: Counter({'Alice': 3, 'Bob': 2, 'Charlie': 1}) Winner: Alice

2. The `itertools` Module¶

The itertools module provides fast, memory-efficient building blocks for iterator manipulation.

Infinite Iterators¶

itertools.count(start=0, step=1): Infinite sequence of numbers $0, 1, 2, ...$
itertools.cycle(iterable): Cycles through an iterable indefinitely.
itertools.repeat(elem, n): Repeats an element $n$ times.

Combinatoric Iterators¶

Function	Description	Example
`itertools.product(*iterables)`	Cartesian product	`product('AB', '12') -> A1, A2, B1, B2`
`itertools.permutations(p, r)`	Permutations (order matters)	`permutations('ABC', 2) -> AB, AC, BA, BC, CA, CB`
`itertools.combinations(p, r)`	Combinations (order does not matter)	`combinations('ABC', 2) -> AB, AC, BC`

Example: Batching and Pairwise Operations

import itertools

# 1. itertools.pairwise (Python 3.10+): Successive overlapping pairs
sequence = [10, 20, 35, 55]
differences = [b - a for a, b in itertools.pairwise(sequence)]
print("Step Differences:", differences)

# 2. itertools.batched (Python 3.12+): Split sequence into chunks of n
data = range(1, 10)
batches = list(itertools.batched(data, n=3))
print("Batches:", batches)