Is there a more pythonic way to build this dictionary?

Question

What is the "most pythonic" way to build a dictionary where I have the values in a sequence and each key will be a function of its value? I'm currently using the following, but I feel like I'm just missing a cleaner way. NOTE: values is a list that is not related to any dictionary.

for value in values:
    new_dict[key_from_value(value)] = value

Answer 1

At least it's shorter:

dict((key_from_value(value), value) for value in values)

Answer 2

>>> l = [ 1, 2, 3, 4 ]
>>> dict( ( v, v**2 ) for v in l )
{1: 1, 2: 4, 3: 9, 4: 16}

In Python 3.0 you can use a "dict comprehension" which is basically a shorthand for the above:

{ v : v**2 for v in l }