# How to split a sequence according to a predicate?

## Question:

I very often run into the need to split a sequence into the two subsequences of elements that satisfy and don’t satisfy a given predicate (preserving the original relative ordering).

This hypothetical “splitter” function would look something like this in action:

```
>>> data = map(str, range(14))
>>> pred = lambda i: int(i) % 3 == 2
>>> splitter(data, pred)
[('2', '5', '8', '11'), ('0', '1', '3', '4', '6', '7', '9', '10', '12', '13')]
```

My question is:

does Python already have a standard/built-in way to do this?

This functionality is certainly not difficult to code (see Addendum below), but for a number of reasons, I’d prefer to use a standard/built-in method than a self-rolled one.

Thanks!

Addendum:

The best standard function I’ve found so far for handling this task in Python is `itertools.groupby`

. To use it for this particular task however, it is necessary to call the predicate function twice for each list member, which I find annoyingly silly:

```
>>> import itertools as it
>>> [tuple(v[1]) for v in it.groupby(sorted(data, key=pred), key=pred)]
[('0', '1', '3', '4', '6', '7', '9', '10', '12', '13'), ('2', '5', '8', '11')]
```

(The last output above differs from the desired one shown earlier in that the subsequence of elements that satisfy the predicate comes last rather than first, but this is very minor, and very easy to fix if needed.)

One can avoid the redundant calls to the predicate (by doing, basically, an “inline memoization”), but my best stab at this gets pretty elaborate, a far cry from the simplicity of `splitter(data, pred)`

:

```
>>> first = lambda t: t[0]
>>> [zip(*i[1])[1] for i in it.groupby(sorted(((pred(x), x) for x in data),
... key=first), key=first)]
[('0', '1', '3', '4', '6', '7', '9', '10', '12', '13'), ('2', '5', '8', '11')]
```

BTW, if you don’t care about preserving the original ordering, `sorted`

‘s default sort order gets the job done (so the `key`

parameter may be omitted from the `sorted`

call):

```
>>> [zip(*i[1])[1] for i in it.groupby(sorted(((pred(x), x) for x in data)),
... key=first)]
[('0', '1', '3', '4', '6', '7', '9', '10', '12', '13'), ('2', '5', '8', '11')]
```

## Answers:

Partitioning is one of those itertools recipes that does just that. It uses `tee()`

to make sure it’s iterating the collection in one pass despite the multiple iterators, the builtin `filter()`

function to grab items that satisfies the predicate as well as `filterfalse()`

to get the opposite effect of the filter. This is as close as you’re going to get at a standard/builtin method.

```
def partition(pred, iterable):
'Use a predicate to partition entries into false entries and true entries'
# partition(is_odd, range(10)) --> 0 2 4 6 8 and 1 3 5 7 9
t1, t2 = tee(iterable)
return filterfalse(pred, t1), filter(pred, t2)
```

I know you said you didn’t want to write your own function, but I can’t imagine why. Your solutions involve writing your own code, you just aren’t modularizing them into functions.

This does exactly what you want, is understandable, and only evaluates the predicate once per element:

```
def splitter(data, pred):
yes, no = [], []
for d in data:
if pred(d):
yes.append(d)
else:
no.append(d)
return [yes, no]
```

If you want it to be more compact (for some reason):

```
def splitter(data, pred):
yes, no = [], []
for d in data:
(yes if pred(d) else no).append(d)
return [yes, no]
```

If you don’t care about efficiency, I think `groupby`

(or any “putting data into `n`

bins” functions) has some nice correspondence,

```
by_bins_iter = itertools.groupby(sorted(data, key=pred), key=pred)
by_bins = dict((k, tuple(v)) for k, v in by_bins_iter)
```

You can then get to your solution by,

```
return by_bins.get(True, ()), by_bins.get(False, ())
```

A slight variation of one of the OP’s implementations and another commenter’s implementation above using `groupby`

:

```
groups = defaultdict(list, { k : list(ks) for k, ks in groupby(items, f) })
groups[True] == the matching items, or [] if none returned True
groups[False] == the non-matching items, or [] if none returned False
```

Sadly, as you point out, `groupby`

requires that the items be sorted by the predicate first, so if that’s not guaranteed, you need this:

```
groups = defaultdict(list, { k : list(ks) for k, ks in groupby(sorted(items, key=f), f) })
```

Quite a mouthful, but it is a single expression that partitions a list by a predicate using only built-in functions.

I don’t think you can just use `sorted`

without the `key`

parameter, because `groupby`

creates a new group when it hits a new value from the key function. So `sorted`

will only work if the items sort naturally by the predicate provided.

As a slightly more general solution to partitioning, consider grouping. Consider the following function, inspired by clojure’s group-by function.

You give it a collection of items to group, and a function that will be used to group them. Here’s the code:

```
def group_by(seq, f):
groupings = {}
for item in seq:
res = f(item)
if res in groupings:
groupings[res].append(item)
else:
groupings[res] = [item]
return groupings
```

For the OP’s original case:

```
y = group_by(range(14), lambda i: int(i) % 3 == 2)
{False: [0, 1, 3, 4, 6, 7, 9, 10, 12, 13], True: [2, 5, 8, 11]}
```

A more general case of grouping elements in a sequence by string length:

```
x = group_by(["x","xx","yy","zzz","z","7654321"], len)
{1: ['x', 'z'], 2: ['xx', 'yy'], 3: ['zzz'], 7: ['7654321']}
```

This can be extended to many cases, and is a core functionality of functional languages. It works great with the dynamically typed python, as the keys in the resulting map can be any type. Enjoy!

In built-in module `more_itertools`

there is a function called `partition`

, which does exactly what topicstarter asked for.

```
from more_itertools import partition
numbers = [1, 2, 3, 4, 5, 6, 7]
predicate = lambda x: x % 2 == 0
predicate_false, predicate_true = partition(predicate, numbers)
print(list(predicate_false), list(predicate_true))
```

The result is `[1, 3, 5, 7] [2, 4, 6]`

.