Question

On one hand it is easy to see given a key function, one can easily implement a sort that does the same thing using a compare function. The reduction is as follows:

def compare(x,y):
    return key(x) - key(y)

On the other, how do we know for sure we are not losing potential sortings by restricting every kinds of sort by a map of elements using key? For instance, suppose I want to sort a list of length 2 tuples (x,y) where I insist the following compare method:

def compare(tup1,tup2):
    if (tup1[1] < tup2[0]):
       return -1
    if (tup1[0] % 2 == 0):
       return 1
    if (tup1[0] - tup2[1] < 4):
       return 0
    else:
       return 1

Now tell me how do I translate this compare into a corresponding “key” function such that my sorting algorithm proceed the same way? This is not a contrived example as these kinds of customised sorting show up in symmetry breaking algorithms during a search, and is very important.

Answer 1

Use functools.cmp_to_key, this will guarantee the same sorting behavior as your compare function. The source for this function can be found on Python’s Sorting How To document.