In Python, how can I naturally sort a list of alphanumeric strings such that alpha characters sort ahead of numeric characters?

Question

This is a fun little challenge that confronted me recently. I'll provide my answer below, but I'm curious to see whether there are more elegant or efficient solutions.

A delineation of the requirements as they were presented to me:

1. Strings are alphanumeric (see test dataset below)
2. Strings should be sorted naturally (see this question for explanation)
3. Alpha characters should be sorted ahead of numeric characters (i.e. 'abc' before '100')
4. Uppercase instances of alpha chars should be sorted ahead of lowercase instances (i.e. 'ABc', 'Abc', 'abc')

Here's a test dataset:

test_cases = [
    # (unsorted list, sorted list)
    (list('bca'), ['a', 'b', 'c']),
    (list('CbA'), ['A', 'b', 'C']),
    (list('r0B9a'), ['a', 'B', 'r', '0', '9']),
    (['a2', '1a', '10a', 'a1', 'a100'], ['a1', 'a2', 'a100', '1a', '10a']),
    (['GAM', 'alp2', 'ALP11', '1', 'alp100', 'alp10', '100', 'alp1', '2'],
        ['alp1', 'alp2', 'alp10', 'ALP11', 'alp100', 'GAM', '1', '2', '100']),
    (list('ra0b9A'), ['A', 'a', 'b', 'r', '0', '9']),
    (['Abc', 'abc', 'ABc'], ['ABc', 'Abc', 'abc']),
]

---

Bonus Test Case

This is inspired by Janne Karila's comment below that the selected answer currently fails (but wouldn't really be a practical concern in my case):

(['0A', '00a', 'a', 'A', 'A0', '00A', '0', 'a0', '00', '0a'],
        ['A', 'a', 'A0', 'a0', '0', '00', '0A', '00A', '0a', '00a'])

Answer 1

re_natural = re.compile('[0-9]+|[^0-9]+')

def natural_key(s):
    return [(1, int(c)) if c.isdigit() else (0, c.lower()) for c in re_natural.findall(s)] + [s]

for case in test_cases:
    print case[1]
    print sorted(case[0], key=natural_key)

['a', 'b', 'c']
['a', 'b', 'c']
['A', 'b', 'C']
['A', 'b', 'C']
['a', 'B', 'r', '0', '9']
['a', 'B', 'r', '0', '9']
['a1', 'a2', 'a100', '1a', '10a']
['a1', 'a2', 'a100', '1a', '10a']
['alp1', 'alp2', 'alp10', 'ALP11', 'alp100', 'GAM', '1', '2', '100']
['alp1', 'alp2', 'alp10', 'ALP11', 'alp100', 'GAM', '1', '2', '100']
['A', 'a', 'b', 'r', '0', '9']
['A', 'a', 'b', 'r', '0', '9']
['ABc', 'Abc', 'abc']
['ABc', 'Abc', 'abc']

Edit: I decided to revisit this question and see if it would be possible to handle the bonus case. It requires being more sophisticated in the tie-breaker portion of the key. To match the desired results, the alpha parts of the key must be considered before the numeric parts. I also added a marker between the natural section of the key and the tie-breaker so that short keys always come before long ones.

def natural_key2(s):
    parts = re_natural.findall(s)
    natural = [(1, int(c)) if c.isdigit() else (0, c.lower()) for c in parts]
    ties_alpha = [c for c in parts if not c.isdigit()]
    ties_numeric = [c for c in parts if c.isdigit()]
    return natural + [(-1,)] + ties_alpha + ties_numeric

This generates identical results for the test cases above, plus the desired output for the bonus case:

['A', 'a', 'A0', 'a0', '0', '00', '0A', '00A', '0a', '00a']

Answer 2

Here's one that works for the bonus test too:

def mykey(s):
    lst = re.findall(r'(\d+)|(\D+)', s)
    return [(0,a.lower()) if a else (1,int(n)) for n, a in lst]\
        + [a for n, a in lst if a]\
        + [len(n) for n, a in lst if n]

def mysort(lst):
    return sorted(lst, key=mykey)

With this type of pattern, re.findall breaks the string to a list of tuples, e.g.

>>> re.findall(r'(\d+)|(\D+)', 'ab12cd')
[('', 'ab'), ('12', ''), ('', 'cd')]

Answer 3

This function makes no claims as to performance at this time:

def alpha_before_numeric_natural_sensitive(unsorted_list):
    """presorting the list should work because python stable sorts; see:
    http://wiki.python.org/moin/HowTo/Sorting/#Sort_Stability_and_Complex_Sorts"""
    presorted_list = sorted(unsorted_list)
    return alpha_before_numeric_natural(presorted_list)

def alpha_before_numeric_natural(unsorted_list):
    """splice each string into tuple like so:
    'abc100def' -> ('a', 'b', 'c', 100, 'd', 'e', 'f') ->
    (ord('a'), ord('b'), ord('c'), ord('z') + 1 + 100, ...) then compare
    each tuple"""
    re_p = "([0-9]+|[A-za-z])"
    ordify = lambda s: ord('z') + 1 + int(s) if s.isdigit() else ord(s.lower())
    str_to_ord_tuple = lambda key: [ordify(c) for c in re.split(re_p, key) if c]
    return sorted(unsorted_list, key=str_to_ord_tuple)

It's based off the insight provided by this natural sort solution and this function that I wrote:

def alpha_before_numeric(unsorted_list):
    ord_shift = lambda c: c.isdigit() and chr(ord('z') + int(c.lower()) + 1) or c.lower()
    adjust_word = lambda word: "".join([ord_shift(c) for c in list(word)])

    def cmp_(a, b):
        return cmp(adjust_word(a), adjust_word(b))

    return sorted(unsorted_list, cmp_)

For full test script here that compares different functions, see http://klenwell.com/is/Pastebin20120829