# gives all possible integer vectors between two endpoints, inclusively.  For example:
# IntVectorRange([0,0,2], [1,1,3]) yields:
#   [0, 0, 2]
#   [1, 0, 2]
#   [0, 1, 2]
#   [1, 1, 2]
#   [0, 0, 3]
#   [1, 0, 3]
#   [0, 1, 3]
#   [1, 1, 3]
# if only one argument is given to __init__, then the range goes from [0,0,...,0] to the vector given
class IntVectorRange(object):
    def __init__(self,start,end=None):
        if end is None:
            end=start
            start=[0] * len(end)
 
        self.start=start
        self.end=end
        self.size = len(start)
        self.delta = [end[i]-start[i]+1  for  i in xrange(self.size)]
        self.len = reduce(lambda x,y: x*y, self.delta, 1)
 
    def __getitem__(self,index): 
        if index >= self.len: raise IndexError
        r = [0] * self.size
        for i in xrange(self.size):
            r[i] = index % self.delta[i] + self.start[i]
            index /= self.delta[i]
        return r
 
    def __len__(self): return self.len
 
# Provides a list with all possible subsets of the given list
# (based on a binary IntVectorRange object)
#
# Example: AllSubsets(['alpha','beta','gamma']) yields:
#   []
#   ['alpha']
#   ['beta']
#   ['alpha', 'beta']
#   ['gamma']
#   ['alpha', 'gamma']
#   ['beta', 'gamma']
#   ['alpha', 'beta', 'gamma']
class AllSubsets:
    def __init__(self,items):
        self.vector_range = IntVectorRange([1] * len(items))
        self.items = items
 
    def __getitem__(self,index):
        v = self.vector_range[index]
        return [self.items[i] for i in xrange(len(v)) if v[i]]
 
    def __len__(self): return len(self.vector_range)
 
# for academic purposes only, here's the same class based on inheritence instead of composition
class AllSubsets2(IntVectorRange):
	def __init__(self,items):
		super(AllCombinations2,self).__init__([1] * len(items))
		self.items = items
 
	def __getitem__(self,index):
		v = super(AllCombinations2,self).__getitem__(index)
		return [self.items[i] for i in xrange(len(v)) if v[i]]
 
 
# Provides a list with all possible "choices" of the sublists of the input list
#
# Example: AllCombinations(["abc","123"]) yields:
#   ['a', '1']
#   ['b', '1']
#   ['c', '1']
#   ['a', '2']
#   ['b', '2']
#   ['c', '2']
#   ['a', '3']
#   ['b', '3']
#   ['c', '3']
class AllCombinations:
    def __init__(self,choices):
        self.vector_range = IntVectorRange([len(choice)-1 for choice in choices])
        self.choices = choices
 
    def __getitem__(self,index):
        c_indices = self.vector_range[index]
        return [self.choices[i][c_indices[i]] for i in xrange(len(self.choices))]
 
    def __len__(self): return len(self.vector_range)

This can be used to build a simple combinatorial optimizer:

import operator
 
# Optimize the return value of the given function func(), comparing return values with the is_this_better() function (which defaults to greater-than).
# All parameters must be named parameters, and come after all other arguments. Options:
# - Print out the latest best answer if print_on_better is True
# - If return_choices_only is True, then the best_inputs part of the return will only have the choices, not the fixed values
# Returns the tuple: (best_inputs,best_value)
#
# Example:
#   def f(x,y,z): return x**2+x+5-y**3+z
#   print optimize(f, x=Choice(range(-3,5)), y=Choice(range(-3,5)), z=2)
# 
# This finds the best x and y to maximize f(x,y,z) with the given choices, with z fixed at 2.
class Choice(list): pass
def optimize(func, is_this_better=operator.gt, print_on_better=False, return_choices_only=False, **vargs):
    choices = {}
    fixed_values = {}
    for k,v in vargs.items():
        if isinstance(v,Choice): choices[k] = v
        else:                    fixed_values[k] = v
    c_keys = choices.keys()
    c_value_choices = [choices[k] for k in c_keys]
 
    best_value = None
    best_inputs = None
    for c_values in AllCombinations(c_value_choices):
        chosen = dict((k,c_values[i]) for i,k in enumerate(c_keys))
        all_values = chosen.copy()
        all_values.update(fixed_values)
        value = func(**all_values)
        if best_value is None or is_this_better(value,best_value):
            best_inputs = chosen if return_choices_only else all_values
            best_value = value
            if print_on_better: print best_inputs,best_value
    return (best_inputs,best_value)