Challenge: to come up with a sorting task that cannot be achieved
by passing to the sort method (or sorted function) suitable values
for its key and reverse parameters, but instead *require* giving
a value to its cmp parameter.
For example,
from random import random
scrambled = some_list.sort(cmp=lambda x, y: cmp(random(), 0.5))
can be achieved (to a very good approximation at least) with
scrambled = some_list.sort(key=lambda x: random())
Is there a real-life sorting task that requires (or is far more
efficient with) cmp and can't be easily achieved with key and
reverse?
Many thanks in advance,
G.
P.S. I guess that, if sort is going to produce a non-trivial,
*consistent* order, a function CMP passed as the value of its cmp
parameter must satisfy the following properties:
0. CMP(x, y) must be non-zero for some elements x, y of the list;
1. anti-symmetry: sign(CMP(x, y)) must be equal to -sign(CMP(y, x));
2. transitivity: if sign(CMP(x, y)) equals sign(CMP(y, z)), then
sign(CMP(x, z)) must be equal to sign(CMP(x, y)).
In (1) and (2), sign() stands for the function
-1 if x < 0
sign(x) = 0 if x == 0
1 if x > 0
I suppose that all bets are off if these properties are not satisfied,
though the documentation does not make this entirely clear, as far
as I can tell. (If I'm wrong about this alleged omission, please
point me to the part of the docs that I missed.)
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