How can I get 2.x-like sorting behaviour in Python 3.x?

I'm trying to replicate (and if possible improve on) Python 2.x's sorting behaviour in 3.x, so that mutually orderable types like int, float etc. are sorted as expected, and mutually unorderable types are grouped within the output.

Here's an example of what I'm talking about:

>>> sorted([0, 'one', 2.3, 'four', -5])  # Python 2.x
[-5, 0, 2.3, 'four', 'one']

>>> sorted([0, 'one', 2.3, 'four', -5])  # Python 3.x
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: unorderable types: str() < int()

My previous attempt at this, using a class for the key parameter to sorted() (see Why does this key class for sorting heterogeneous sequences behave oddly?) is fundamentally broken, because its approach of

1. Trying to compare values, and
2. If that fails, falling back to comparing the string representation of their types

can lead to intransitive ordering, as explained by BrenBarn's excellent answer.

A naïve approach, which I initially rejected without even trying to code it, would be to use a key function that returns a (type, value) tuple:

def motley(value):
    return repr(type(value)), value

However, this doesn't do what I want. In the first place, it breaks the natural ordering of mutually orderable types:

>>> sorted([0, 123.4, 5, -6, 7.89])
[-6, 0, 5, 7.89, 123.4]
>>> sorted([0, 123.4, 5, -6, 7.89], key=motley)
[7.89, 123.4, -6, 0, 5]

Secondly, it raises an exception when the input contains two objects of the same intrinsically unorderable type:

>>> sorted([{1:2}, {3:4}], key=motley)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: unorderable types: dict() < dict()

... which admittedly is the standard behaviour in both Python 2.x and 3.x – but ideally I'd like such types to be grouped together (I don't especially care about their ordering, but it would seem in keeping with Python's guarantee of stable sorting that they retain their original order).

I can work around the first of these problems for numeric types by special-casing them:

from numbers import Real
from decimal import Decimal

def motley(value):
    numeric = Real, Decimal
    if isinstance(value, numeric):
        typeinfo = numeric
    else:
        typeinfo = type(value)
    return repr(typeinfo), value

... which works as far as it goes:

>>> sorted([0, 'one', 2.3, 'four', -5], key=motley)
[-5, 0, 2.3, 'four', 'one']

... but doesn't account for the fact that there may be other distinct (possibly user-defined) types which are mutually orderable, and of course still fails with intrinsically unorderable types:

>>> sorted([{1:2}, {3:4}], key=motley)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: unorderable types: dict() < dict()

Is there another approach which solves both the problem of arbitrary, distinct-but-mutually-orderable types and that of intrinsically unorderable types?

Stupid idea: make a first pass to divide all the different items in groups that can be compared between each other, sort the individual groups and finally concatenate them. I assume that an item is comparable to all members of a group, if it is comparable with the first member of a group. Something like this (Python3):

import itertools

def python2sort(x):
    it = iter(x)
    groups = [[next(it)]]
    for item in it:
        for group in groups:
            try:
                item < group[0]  # exception if not comparable
                group.append(item)
                break
            except TypeError:
                continue
        else:  # did not break, make new group
            groups.append([item])
    print(groups)  # for debugging
    return itertools.chain.from_iterable(sorted(group) for group in groups)

This will have quadratic running time in the pathetic case that none of the items are comparable, but I guess the only way to know that for sure is to check all possible combinations. See the quadratic behavior as a deserved punishment for anyone trying to sort a long list of unsortable items, like complex numbers. In a more common case of a mix of some strings and some integers, the speed should be similar to the speed of a normal sort. Quick test:

In [19]: x = [0, 'one', 2.3, 'four', -5, 1j, 2j,  -5.5, 13 , 15.3, 'aa', 'zz']

In [20]: list(python2sort(x))
[[0, 2.3, -5, -5.5, 13, 15.3], ['one', 'four', 'aa', 'zz'], [1j], [2j]]
Out[20]: [-5.5, -5, 0, 2.3, 13, 15.3, 'aa', 'four', 'one', 'zz', 1j, 2j]

It seems to be a 'stable sort' as well, since the groups are formed in the order the incomparable items are encountered.

This answer aims to faithfully re-create the Python 2 sort order, in Python 3, in every detail.

The actual Python 2 implementation is quite involved, but object.c's default_3way_compare does the final fallback after instances have been given a chance to implement normal comparison rules. This is after individual types have been given a chance to compare (via the __cmp__ or __lt__ hooks).

Implementing that function as pure Python in a wrapper, plus emulating the exceptions to the rules (dict and complex numbers specifically) gives us the same Python 2 sorting semantics in Python 3:

from numbers import Number


# decorator for type to function mapping special cases
def per_type_cmp(type_):
    try:
        mapping = per_type_cmp.mapping
    except AttributeError:
        mapping = per_type_cmp.mapping = {}
    def decorator(cmpfunc):
        mapping[type_] = cmpfunc
        return cmpfunc
    return decorator


class python2_sort_key(object):
    _unhandled_types = {complex}

    def __init__(self, ob):
       self._ob = ob

    def __lt__(self, other):
        _unhandled_types = self._unhandled_types
        self, other = self._ob, other._ob  # we don't care about the wrapper

        # default_3way_compare is used only if direct comparison failed
        try:
            return self < other
        except TypeError:
            pass

        # hooks to implement special casing for types, dict in Py2 has
        # a dedicated __cmp__ method that is gone in Py3 for example.
        for type_, special_cmp in per_type_cmp.mapping.items():
            if isinstance(self, type_) and isinstance(other, type_):
                return special_cmp(self, other)

        # explicitly raise again for types that won't sort in Python 2 either
        if type(self) in _unhandled_types:
            raise TypeError('no ordering relation is defined for {}'.format(
                type(self).__name__))
        if type(other) in _unhandled_types:
            raise TypeError('no ordering relation is defined for {}'.format(
                type(other).__name__))

        # default_3way_compare from Python 2 as Python code
        # same type but no ordering defined, go by id
        if type(self) is type(other):
            return id(self) < id(other)

        # None always comes first
        if self is None:
            return True
        if other is None:
            return False

        # Sort by typename, but numbers are sorted before other types
        self_tname = '' if isinstance(self, Number) else type(self).__name__
        other_tname = '' if isinstance(other, Number) else type(other).__name__

        if self_tname != other_tname:
            return self_tname < other_tname

        # same typename, or both numbers, but different type objects, order
        # by the id of the type object
        return id(type(self)) < id(type(other))


@per_type_cmp(dict)
def dict_cmp(a, b, _s=object()):
    if len(a) != len(b):
        return len(a) < len(b)
    adiff = min((k for k in a if a[k] != b.get(k, _s)), key=python2_sort_key, default=_s)
    if adiff is _s:
        # All keys in a have a matching value in b, so the dicts are equal
        return False
    bdiff = min((k for k in b if b[k] != a.get(k, _s)), key=python2_sort_key)
    if adiff != bdiff:
        return python2_sort_key(adiff) < python2_sort_key(bdiff)
    return python2_sort_key(a[adiff]) < python2_sort_key(b[bdiff])

I incorporated handling dictionary sorting as implemented in Python 2, since that'd be supported by the type itself via a __cmp__ hook. I've stuck to the Python 2 ordering for the keys and values as well, naturally.

I've also added special casing for complex numbers, as Python 2 raises an exception when you try sort to these:

>>> sorted([0.0, 1, (1+0j), False, (2+3j)])
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: no ordering relation is defined for complex numbers

You may have to add more special cases if you want to emulate Python 2 behaviour exactly.

If you wanted to sort complex numbers anyway you'll need to consistently put them with the non-numbers group; e.g.:

# Sort by typename, but numbers are sorted before other types
if isinstance(self, Number) and not isinstance(self, complex):
    self_tname = ''
else:
    self_tname = type(self).__name__
if isinstance(other, Number) and not isinstance(other, complex):
    other_tname = ''
else:
    other_tname = type(other).__name__

Some test cases:

>>> sorted([0, 'one', 2.3, 'four', -5], key=python2_sort_key)
[-5, 0, 2.3, 'four', 'one']
>>> sorted([0, 123.4, 5, -6, 7.89], key=python2_sort_key)
[-6, 0, 5, 7.89, 123.4]
>>> sorted([{1:2}, {3:4}], key=python2_sort_key)
[{1: 2}, {3: 4}]
>>> sorted([{1:2}, None, {3:4}], key=python2_sort_key)
[None, {1: 2}, {3: 4}]

Not running Python 3 here, but maybe something like this would work. Test to see if doing a "less than" compare on "value" creates an exception and then do "something" to handle that case, like convert it to a string.

Of course you'd still need more special handling if there are other types in your list that are not the same type but are mutually orderable.

from numbers import Real
from decimal import Decimal

def motley(value):
    numeric = Real, Decimal
    if isinstance(value, numeric):
        typeinfo = numeric
    else:
        typeinfo = type(value)

    try:
        x = value < value
    except TypeError:
        value = repr(value)

    return repr(typeinfo), value

>>> print sorted([0, 'one', 2.3, 'four', -5, (2+3j), (1-3j)], key=motley)
[-5, 0, 2.3, (1-3j), (2+3j), 'four', 'one']

One way for Python 3.2+ is to use functools.cmp_to_key(). With this you can quickly implement a solution that tries to compare the values and then falls back on comparing the string representation of the types. You can also avoid an error being raised when comparing unordered types and leave the order as in the original case:

from functools import cmp_to_key

def cmp(a,b):
    try:
        return (a > b) - (a < b)
    except TypeError:
        s1, s2 = type(a).__name__, type(b).__name__
        return (s1 > s2) - (s1 < s2)

Examples (input lists taken from Martijn Pieters's answer):

sorted([0, 'one', 2.3, 'four', -5], key=cmp_to_key(cmp))
# [-5, 0, 2.3, 'four', 'one']
sorted([0, 123.4, 5, -6, 7.89], key=cmp_to_key(cmp))
# [-6, 0, 5, 7.89, 123.4]
sorted([{1:2}, {3:4}], key=cmp_to_key(cmp))
# [{1: 2}, {3: 4}]
sorted([{1:2}, None, {3:4}], key=cmp_to_key(cmp))
# [None, {1: 2}, {3: 4}]

This has the disadvantage that the three-way compare is always conducted, increasing the time complexity. However, the solution is low overhead, short, clean and I think cmp_to_key() was developed for this kind of Python 2 emulation use case.