Python sort lib different behavior with different comparing functions, some comparing function will not work

I want get a max alphabetically order by sub string, so I need to have a comparing method. For the comparing function function

from functools import cmp_to_key
def compare(a,b):
    print(a,b, a+b,b+a,a+b>b+a) 
    return (a+b)>(b+a) # first comparing function

def sortArr(ls):
    ls = sorted(ls,key =cmp_to_key(compare),reverse=True)
    return "".join(ls)

ls = ["8","81","82","829"]
print(sortArr(ls))

Which will output as:

82 829 82829 82982 False
81 82 8182 8281 False
8 81 881 818 True
88182829

But using comparing function as:

from functools import cmp_to_key
def compare(a,b):
    print(a,b, a+b,b+a,a+b>b+a)
    return int(a+b) -int(b+a) # second comparing function

def sortArr(ls):
    ls = sorted(ls,key =cmp_to_key(compare),reverse=True)
    return "".join(ls)

ls = ["8","81","82","829"]
print(sortArr(ls))

the output is

82 829 82829 82982 False
81 82 8182 8281 False
8 81 881 818 True
8 82 882 828 True
8 829 8829 8298 True
88298281

Apparently the second sort function is what's needed ( the final string 88182829 < 88298281 ). the first function didn't do all comparing use first element.

So why the first comparing function didn't work?

It's unclear why you might expect the first function to work. An old-style comparison function has to work like so:

• cmp(x, y) is negative if and only if x < y.
• cmp(x, y) is 0 if and only if x == y.
• cmp(x, y) is strictly positive (> 0) if and only if x > y.

Given that, your return (a+b)>(b+a) doesn't appear to make sense. It can only return True or False, which act like 1 and 0, respectively. So it's impossible for it to return a result which will be interpreted as meaning a is less than b.