Data structures

First PublishedFeb 10, 2026ByAtif Alam

Data structures

Built-in

xs = [1, 2, 3]           # list — ordered, mutable (dynamic array)
t = (1, 2)               # tuple — ordered, immutable
d = {"a": 1, "b": 2}     # dict — key–value; insertion order preserved (3.7+)
s = {1, 2, 3}            # set — unordered, unique, hashable elements only
f = frozenset({1, 2})    # frozenset — immutable set
name = "hello"           # str — immutable character sequence
b = b"bytes"             # bytes — immutable; bytearray — mutable

Empty: [] list, {} dict, set() set (not {} — that’s a dict).

Mutability and hashability

Mutable = can change in place (list, dict, set). Immutable = can’t (tuple, str, frozenset, int).
Only hashable types can be dict keys or set elements. Immutable built-ins (tuple, str, frozenset, int, float) are hashable; list, dict, and set are not. That’s why you can’t put a list in a set or use it as a dict key — use a tuple instead.

Standard library and third-party

collections: deque (double-ended queue), defaultdict, Counter, OrderedDict, namedtuple
heapq: min-heap on a list
queue: Queue, LifoQueue, PriorityQueue (thread-safe)
array: typed arrays

Third-party: NumPy, Pandas, and graph/tree libs for specialized needs.

When to use what

Use case	Structure
Ordered sequence you need to change	list (append, insert, remove) — default for “a sequence of things”
Ordered sequence that shouldn’t change	tuple (return values, dict keys, coordinates)
Look up by key	dict (names → values, id → record)
Unique items or fast “is x in here?”	set (order doesn’t matter, no duplicates)
Queue or stack from both ends	deque (use instead of list when you pop from the front often, e.g. BFS)
Smallest item, priority queue, “top K”	heapq (min-heap)

Why this matters for algorithms

These structures are the base you’ll use when learning algorithms:

list — dynamic array (indexing, sorting, DP)
dict — O(1) lookup and graph adjacency
set — visited sets and uniqueness
tuple — immutable pairs (edges, coords)
deque — BFS and queues
heapq — Dijkstra and heaps

See the Algorithms section for more.