How#

Two important data structures have already been seen in previous chapters:

We covered functions in a previous chapter as well: Probability: How to define a function.

How to write a docstring#

A docstring is an attribute of a function that describes what it is. This can describe what it does, how it does it and/or why it does it. Here is how to write a docstring for a function that takes variables and returns a value.

Tip

def name(parameter1, parameter2, ...):
    """
    <A description of what the function is.>

    Parameters
    ----------
    parameter1 : <type of parameter1>
        <description of parameter1>
    parameter2 : <type of parameter2>
        <description of parameter2>
    ...

    Returns
    -------
    <type of what the function returns>
        <description of what the function returns>

    """
    INDENTED BLOCK OF CODE
    return output

For example, here is how to write a function that returns \(x ^ 3\) for a given \(x\):

def x_cubed(x):
    """
    Calculates and returns the cube of x. Does this by using Python
    exponentiation.

    Parameters
    ----------
    x : float
        The value of x to be raised to the power 3

    Returns
    -------
    float
        The cube.
    """
    return x ** 3

Create a set#

A set is a collection of distinct objects. This can be created in Python using the set command on any iterable. If there are non distinct objects in the iterable then this is an efficient way to remove duplicates.

Tip

set(iterable)

Here is an example of creating a set:

iterable = (1, 1, 3, 4, 4, 3, 2, 1, 10)
unique_values = set(iterable)
unique_values

{1, 2, 3, 4, 10}

Do set operations#

Set operations between two sets can be done using Python:

  • \(S_1 \cup S_2\): set_1 | set_2

  • \(S_1 \cap S_2\): set_1 & set_2

  • \(S_1 \setminus S_2\): set_1 - set_2

  • \(S_1 \subseteq S_2\) (checking if \(S_1\) is a subset of \(S_2\)): set_1 <= set_2

Here are some examples of carrying out the above:

set_1 = set((1, 2, 3, 4, 5))
set_2 = set((4, 5, 6, 7, 8, 9))

set_1 | set_2

{1, 2, 3, 4, 5, 6, 7, 8, 9}

set_1 & set_2

{4, 5}

set_1 - set_2

{1, 2, 3}

set_1 <= set_2

False

Using hash tables#

Lists and tuples allow us to immediately recover a value given its position. Hash tables allow us to create arbitrary key value pairs so that given any key we can immediately recover the value. This is called a dictionary in Python and is created using {} which takes a collection of key: value pairs.

Tip

{key_1: value, key_2: value, …}

For example the following dictionary maps pet names to their ages:

ages = {"Riggins": 4, "Chick": 7, "Duck": 7}
ages

{'Riggins': 4, 'Chick': 7, 'Duck': 7}

To recover a value we pass the key to the dictionary using [].

For example:

ages["Riggins"]

4

Attention

If a key is used to recover the value but the key is not in the dictionary then an error will be raised.