Sequences

Sometimes we care about some sets of items, but the order matters.

• Bytes in a file
• Ranked sports team in a league

We use sequences for this job. These are often implemented as lists or arrays.

A sequence of length $n$ is a function $x : \{1 \dots n\} \implies S$ for some set $S$.

info

1. Sequences are often notated like $x_j$ rather than $x(j)$
2. Another notation could be [1,5,7,1]

Sequences in Python: lists

my_list = [1,5,6]
my_list[2] = 12
print(my_list[2])

my_list.append(8)
my_list.pop()
len(my_list)
17 in my_list

Sequences in Python: tuples

see tuples.

Mutability

In Python, some objects can be changed, others are static.

• mutable types can change overtime: lists, dict and, set.
• immutable types don't change: tuple, frozenset, number, and string

Hashability

Hashable types can be identified by a hash value, used internally by some containers

• mutable types are not hashable
• immutable types are generally hashable
• immutable containers are hashable only if they contain only hashable elements.

info

Set elements and dictionary keys must be hashable.

Set

S = {[1]}
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
TypeError: unhashable type: 'list'

Dictionary

D = {["my_key"]:7}
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
TypeError: unhashable type: 'list'

References

• QUT Materials