# Python’s “Itertools”¶

Python has an itertools module, which provides a core set of fast, memory-efficient tools for creating iterators. We will briefly showcase a few itertools here. The majority of these functions create generators, thus we will have to iterate over them in order to explicitly demonstrate their use. It is hard to overstate the utility of this module - it is strongly recommended that you take some time to see what it has in store.

There are three built-in functions, `range`

, `enumerate`

, and
`zip`

, that belong in itertools, but they are so useful that they are
made accessible immediately and do not need to be imported. It is
essential that `range`

, `enumerate`

, and `zip`

become tools that
you are comfortable using.

**range**

Generate a sequence of integers in the specified “range”:

```
# will generate 0.. 1.. 2.. ... 8.. 9
>>> range(10)
range(0, 10)
>>> list(range(10))
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
# will generate 0.. 3.. 6.. 9
>>> range(0, 10, 3)
range(0, 10, 3)
>>> list(range(0, 10, 3))
[0, 3, 6, 9]
```

**enumerate**

Enumerates the items in an iterable: yielding a tuple containing the iteration count (starting with 0) and the corresponding item from the the iterable.

```
# will generate (0, 'apple').. (1, 'banana').. (2, 'cat').. (3, 'dog')]
>>> enumerate(["apple", "banana", "cat", "dog"])
<enumerate at 0x23e3557b3f0>
>>> list(enumerate(["apple", "banana", "cat", "dog"]))
[(0, 'apple'), (1, 'banana'), (2, 'cat'), (3, 'dog')]
```

**zip**

Zips together the corresponding elements of several iterables into tuples. This is valuable for “pairing” corresponding items across multiple iterables.

```
>>> names = ["Angie", "Brian", "Cassie", "David"]
>>> exam_1_scores = [90, 82, 79, 87]
>>> exam_2_scores = [95, 84, 72, 91]
# will generate ('Angie', 90, 95).. ('Brian', 82, 84).. ('Cassie', 79, 72).. ('David', 87, 91)]
>>> zip(names, exam_1_scores, exam_2_scores)
<zip at 0x20de1082608>
>>> list(zip(names, exam_1_scores, exam_2_scores))
[('Angie', 90, 95), ('Brian', 82, 84), ('Cassie', 79, 72), ('David', 87, 91)]
```

The following are some of the many useful tools provided by the
`itertools`

module:

**itertools.chain**

Chains together multiple iterables, end-to-end, forming a single iterable:

```
>>> from itertools import chain
>>> gen_1 = range(0, 5, 2) # 0.. 2.. 4
>>> gen_2 = (i**2 for i in range(3, 6)) # 9.. 16.. 25
>>> iter_3 = ["moo", "cow"]
>>> iter_4 = "him"
# will generate: 0.. 2.. 4.. 9.. 16.. 25.. 'moo'.. 'cow'.. 'h'.. 'i'.. 'm'
>>> chain(gen_1, gen_2, iter_3, iter_4)
<itertools.chain at 0x20de109ec18>
```

**itertools.combinations** Generate all length-n tuples storing
“combinations” of items from an iterable:

```
>>> from itertools import combinations
# will generate: (0, 1, 2).. (0, 1, 3).. (0, 2, 3).. (1, 2, 3)
>>> combinations([0, 1, 2, 3], 3) # generate all length-3 combinations from [0, 1, 2, 3]
<itertools.combinations at 0x20de10a7728>
```

**Reading Comprehension: Itertools I**

Using the `itertools.combinations`

function, find the probability that
two randomly drawn items from the list
`["apples", "bananas", "pears", "pears", "oranges"]`

would yield a
combination of “apples” and “pears”.

**Reading Comprehension: Itertools II**

Given the list `x_vals = [0.1, 0.3, 0.6, 0.9]`

, create a generator,
`y_gen`

, that will generate the y-value \(y = x^2\) for each value
of \(x\). Then, using `zip`

, create a list of the \((x, y)\)
pairs, each pair stored in a tuple.

## Reading Comprehension: Solutions¶

**Itertools I: Solution**

```
>>> from itertools import combinations
>>> ls = ["apples", "bananas", "pears", "pears", "oranges"]
>>> comb_ls = list(combinations(ls, 2))
>>> comb_ls.count(("apples", "pears")) / len(comb_ls)
0.2
```

**Itertools II: Solution**

```
>>> x_vals = [0.1, 0.3, 0.6, 0.9]
>>> y_gen = (x**2 for x in x_vals)
>>> list(zip(x_vals, y_gen))
[(0.1, 0.01), (0.3, 0.09), (0.6, 0.36), (0.9, 0.81)]
```

In this instance, the use of `zip`

is a bit contrived. We could have
foregone creating `y_gen`

by just using the following
list-comprehension:

```
>>> x_vals = [0.1, 0.3, 0.6, 0.9]
>>> [(x, x**2) for x in x_vals]
[(0.1, 0.01), (0.3, 0.09), (0.6, 0.36), (0.9, 0.81)]
```