If you are familiar with some builtin high-order functions and methods such as sorted(), filter, min(), max(), reduce(), etc, you might already be familiar with how key function works.

A key function allows you to define a specific criteria to be used for  establishing order in a collection of items.  Typically,  key functions takes a single argument and returns a value that the sorting or ordering algorithm will use to compare elements in the collection.   

ExampleEdit & Run

compare elements by their absolute values

def absolute(x):
    return x if x > 0 else -x 

L = [0, -2, 5, 1, -4, 3]

#get the smallest item by absolute value
print(min(L, key = absolute))

#get the largest item by absolute value
print(max(L, key = absolute))

#sort the elements based on their absolute values
print(sorted(L, key = absolute))
 Visualize 
Output:
0
5
[0, 1, -2, 3, -4, 5]
[Finished in 0.01121069397777319s]

How cmp_to_key() function works

The cmp_to_key() function converts a comparison function to a key function which can be used as an ordering criteria. Typically, a comparison function takes two arguments and returns a negative( usually -1), zero, or positive( usually 1) number depending on whether the comparison operation  evaluates to False, equal, or True, respectively.

Syntax: 
@cmp_to_key
def cmp_func(x, y):
    #statements

     or

def cmp_func(x, y):
    #statements
key_func = cmp_to_key(func)
copy
ExampleEdit & Run
from functools import cmp_to_key

#function to get the larger item by absolute value
@cmp_to_key
def absolute_larger(x, y):
    if abs(x) > abs(y): 
        return 1
    elif abs(x) < abs(y): 
        return -1 
    return 0  

L = [-1, 5, -2, 3, -8, 0,  7]

print(min(L, key= absolute_larger ))
print(max(L, key= absolute_larger ))
print(sorted(L, key= absolute_larger ))
 Visualize 
copy
Output:
0
-8
[0, -1, -2, 3, 5, 7, -8]
[Finished in 0.013285364024341106s]

If the comparison function has already been defined or for some reason you do not want to use the @ decorator syntax, you can  achive the same as shown below.

ExampleEdit & Run
from functools import cmp_to_key

#function to get the larger item by absolute value
def absolute_larger(x, y):
    if abs(x) > abs(y): 
        return 1
    elif abs(x) < abs(y): 
        return -1 
    return 0  

L = [-1, 5, -2, 3, -8, 0,  7]

print(min(L, key= cmp_to_key(absolute_larger) ))
print(max(L, key= cmp_to_key(absolute_larger) ))
print(sorted(L, key= cmp_to_key(absolute_larger) ))
 Visualize 
copy
Output:
0
-8
[0, -1, -2, 3, 5, 7, -8]
[Finished in 0.013083614874631166s]