Inverse Image pattern (remarkably useful)

gistfile1.py

def inv_image(f, collection):
    """Returns the inverse image (in the mathematical sense)
    of the function applied to the collection.
    """
    result = {}
    for x in collection:
        img = f(x)
        if result.has_key(img):
            result[img].add(x)
        else:
            result[img] = set([x,])
    return result

assert(inv_image(lambda x: x % 3, range(15)) == {
    0: set([0, 9, 3, 12, 6]),
    1: set([1, 10, 4, 13, 7]),
    2: set([8, 2, 11, 5, 14])
    } )

students_with_grade = [("Joe", 'F'), ("Bill", "B"), ("Eve", "B"), ("Josh", "A") ]
assert( inv_image(lambda x: x[1], students_with_grade) ==
        {'A': set([('Josh', 'A')]),
         'B': set([('Bill', 'B'), ('Eve', 'B')]),
         'F': set([('Joe', 'F')])
         } )