You've got tree paths encoded as integers such as: 10030201. Your code would much easier to write if instead they tuples like: (10, 03, 02, 01). If at all possible, you should change your dictionary to always use tuples. If not possible, have a function to convert the integers to tuples when you need them. If you do that, you'll find its fairly easy to devise a general implementation of your BACKS logic.
On the stylistic front: We typically use ALL_CAPS only for constants. We use lowercase_with_underscores for local variables which all of your stuff appears to be.
My solution:
def calculate_backs(source, destination):
"""
Return how many "resets" are required to transform source into destination
"""
def as_tuple(id_number):
"""
Converts the id_number into a path sequence:
10010200 becomes (10, 1, 2)
"""
pieces = []
while id_number:
pieces.append(id_number % 100)
id_number /= 100
pieces.reverse()
# position 0 denotes a root node in the tree, so remove any trailing
# zeros.
while pieces[-1] == 0:
pieces.pop()
return tuple(pieces)
def calculate(source, destination):
if source and destination and source[0] == destination[0]:
# If both source and destination agree for the first piece of the
# path, drop that piece and determine the number of resets required
# for the rest.
return calculate(source[1:], destination[1:])
else:
# If the path disagrees on the first piece, we have to reset
# everything remaining in both paths.
return len(source) + len(destination)
return calculate(as_tuple(source), as_tuple(destination))