def _unsliced_length(self):
'''
The number of perms in the space, ignoring any slicing.
This is used as an interim step in calculating the actual length of the
space with the slice taken into account.
'''
if self.n_elements > self.sequence_length:
return 0
if self.is_degreed:
assert not self.is_recurrent and not self.is_partial and \
not self.is_combination
return sum(
math_tools.abs_stirling(
self.sequence_length - len(self.fixed_map),
self.sequence_length - degree -
self._n_cycles_in_fixed_items_of_just_fixed
) for degree in self.degrees
)
elif self.is_fixed:
assert not self.is_degreed and not self.is_combination
if self.is_recurrent:
return calculate_length_of_recurrent_perm_space(
self.n_elements - len(self.fixed_map),
nifty_collections.FrozenBagBag(
collections.Counter(self.free_values).values()
)
)
else:
return math_tools.factorial(
len(self.free_indices),
start=(len(self.free_indices) -
(self.n_elements - len(self.fixed_map)) + 1)
)
else:
assert not self.is_degreed and not self.is_fixed
if self.is_recurrent:
if self.is_combination:
return calculate_length_of_recurrent_comb_space(
self.n_elements,
self._frozen_bag_bag
)
else:
return calculate_length_of_recurrent_perm_space(
self.n_elements,
self._frozen_bag_bag
)
else:
return math_tools.factorial(
self.sequence_length,
start=(self.sequence_length - self.n_elements + 1)
) // (math_tools.factorial(self.n_elements) if
self.is_combination else 1)
def test_abs_stirling():
assert tuple(abs_stirling(0, i) for i in range(-1, 2)) == (0, 1, 0, )
assert tuple(abs_stirling(1, i) for i in range(-1, 3)) == (0, 0, 1, 0, )
assert tuple(abs_stirling(2, i) for i in range(-1, 4)) == (0, 0, 1, 1, 0)
assert tuple(abs_stirling(3, i) for i in range(-1, 5)) == (0, 0, 2, 3, 1,
0)
assert tuple(abs_stirling(4, i) for i in range(-1, 6)) == (0, 0, 6, 11, 6,
1, 0)
assert tuple(abs_stirling(5, i) for i in range(-1, 7)) == (0, 0, 24, 50,
35, 10, 1, 0)
assert abs_stirling(200, 50) == 525010571470323062300307763288024029929662200077890908912803398279686186838073914722860457474159887042512346530620756231465891831828236378945598188429630326359716300315479010640625526167635598138598969330736141913019490812196987045505021083120744610946447254207252791218757775609887718753072629854788563118348792912143712216969484697600
def _unsliced_length(self):
'''
The number of perms in the space, ignoring any slicing.
This is used as an interim step in calculating the actual length of the
space with the slice taken into account.
'''
if self.n_elements > self.sequence_length:
return 0
if self.is_degreed:
assert not self.is_recurrent and not self.is_partial and \
not self.is_combination
return sum(
math_tools.abs_stirling(
self.sequence_length -
len(self.fixed_map), self.sequence_length - degree -
self._n_cycles_in_fixed_items_of_just_fixed)
for degree in self.degrees)
elif self.is_fixed:
assert not self.is_degreed and not self.is_combination
if self.is_recurrent:
return calculate_length_of_recurrent_perm_space(
self.n_elements - len(self.fixed_map),
nifty_collections.FrozenBagBag(
nifty_collections.Bag(self.free_values).values()))
else:
return math_tools.factorial(
len(self.free_indices),
start=(len(self.free_indices) -
(self.n_elements - len(self.fixed_map)) + 1))
else:
assert not self.is_degreed and not self.is_fixed
if self.is_recurrent:
if self.is_combination:
return calculate_length_of_recurrent_comb_space(
self.n_elements, self._frozen_bag_bag)
else:
return calculate_length_of_recurrent_perm_space(
self.n_elements, self._frozen_bag_bag)
else:
return math_tools.factorial(
self.sequence_length,
start=(self.sequence_length - self.n_elements +
1)) // (math_tools.factorial(self.n_elements)
if self.is_combination else 1)
def test_abs_stirling():
assert tuple(abs_stirling(0, i) for i in range(-1, 2)) == (
0,
1,
0,
)
assert tuple(abs_stirling(1, i) for i in range(-1, 3)) == (
0,
0,
1,
0,
)
assert tuple(abs_stirling(2, i) for i in range(-1, 4)) == (0, 0, 1, 1, 0)
assert tuple(abs_stirling(3, i)
for i in range(-1, 5)) == (0, 0, 2, 3, 1, 0)
assert tuple(abs_stirling(4, i)
for i in range(-1, 6)) == (0, 0, 6, 11, 6, 1, 0)
assert tuple(abs_stirling(5, i)
for i in range(-1, 7)) == (0, 0, 24, 50, 35, 10, 1, 0)
assert abs_stirling(
200, 50
) == 525010571470323062300307763288024029929662200077890908912803398279686186838073914722860457474159887042512346530620756231465891831828236378945598188429630326359716300315479010640625526167635598138598969330736141913019490812196987045505021083120744610946447254207252791218757775609887718753072629854788563118348792912143712216969484697600
def __getitem__(self, i):
if isinstance(i, (slice, sequence_tools.CanonicalSlice)):
canonical_slice = sequence_tools.CanonicalSlice(
i, self.length, offset=self.canonical_slice.start)
return PermSpace(self.sequence,
domain=self.domain,
n_elements=self.n_elements,
fixed_map=self.fixed_map,
degrees=self.degrees,
is_combination=self.is_combination,
slice_=canonical_slice,
perm_type=self.perm_type)
assert isinstance(i, numbers.Integral)
if i <= -1:
i += self.length
if not (0 <= i < self.length):
raise IndexError
elif self.is_sliced:
return self.unsliced[i + self.canonical_slice.start]
elif self.is_dapplied:
return self.perm_type(self.undapplied[i], perm_space=self)
#######################################################################
elif self.is_degreed:
if self.is_rapplied:
assert not self.is_recurrent and \
not self.is_partial and not self.is_combination and \
not self.is_dapplied and not self.is_sliced
return self.perm_type(map(self.sequence.__getitem__,
self.unrapplied[i]),
perm_space=self)
assert not self.is_rapplied and not self.is_recurrent and \
not self.is_partial and not self.is_combination and \
not self.is_dapplied and not self.is_sliced
# If that wasn't an example of asserting one's dominance, I don't
# know what is.
available_values = list(self.free_values)
wip_perm_sequence_dict = dict(self.fixed_map)
wip_n_cycles_in_fixed_items = \
self._n_cycles_in_fixed_items_of_just_fixed
wip_i = i
for j in self.sequence:
if j in wip_perm_sequence_dict:
continue
for unused_value in available_values:
candidate_perm_sequence_dict = dict(wip_perm_sequence_dict)
candidate_perm_sequence_dict[j] = unused_value
### Checking whether we closed a cycle: ###################
# #
if j == unused_value:
closed_cycle = True
else:
current = j
while True:
current = candidate_perm_sequence_dict[current]
if current == j:
closed_cycle = True
break
elif current not in candidate_perm_sequence_dict:
closed_cycle = False
break
# #
### Finished checking whether we closed a cycle. ##########
candidate_n_cycles_in_fixed_items = \
wip_n_cycles_in_fixed_items + closed_cycle
candidate_fixed_perm_space_length = sum(
math_tools.abs_stirling(
self.sequence_length -
len(candidate_perm_sequence_dict),
self.sequence_length - degree -
candidate_n_cycles_in_fixed_items)
for degree in self.degrees)
if wip_i < candidate_fixed_perm_space_length:
available_values.remove(unused_value)
wip_perm_sequence_dict[j] = unused_value
wip_n_cycles_in_fixed_items = \
candidate_n_cycles_in_fixed_items
break
wip_i -= candidate_fixed_perm_space_length
else:
raise RuntimeError
assert wip_i == 0
return self.perm_type(
(wip_perm_sequence_dict[k] for k in self.domain), self)
#######################################################################
elif self.is_recurrent:
assert not self.is_dapplied and not self.is_degreed and \
not self.is_sliced
available_values = list(self.sequence)
reserved_values = nifty_collections.Bag(self.fixed_map.values())
wip_perm_sequence_dict = dict(self.fixed_map)
wip_i = i
shit_set = set()
for j in range(self.n_elements):
if j in self.fixed_map:
available_values.remove(self.fixed_map[j])
reserved_values[self.fixed_map[j]] -= 1
continue
unused_values = [
item for item in
nifty_collections.OrderedBag(available_values) -
reserved_values if item not in shit_set
]
for unused_value in unused_values:
wip_perm_sequence_dict[j] = unused_value
candidate_sub_perm_space = \
PermSpace._create_with_cut_prefix(
self.sequence,
n_elements=self.n_elements,
fixed_map=wip_perm_sequence_dict,
is_combination=self.is_combination,
shit_set=shit_set, perm_type=self.perm_type
)
if wip_i < candidate_sub_perm_space.length:
available_values.remove(unused_value)
break
else:
wip_i -= candidate_sub_perm_space.length
if self.is_combination:
shit_set.add(wip_perm_sequence_dict[j])
del wip_perm_sequence_dict[j]
else:
raise RuntimeError
assert wip_i == 0
return self.perm_type(
dict_tools.get_tuple(wip_perm_sequence_dict, self.domain),
self)
#######################################################################
elif self.is_fixed:
free_values_perm = self._free_values_unsliced_perm_space[i]
free_values_perm_iterator = iter(free_values_perm)
return self.perm_type(
tuple((self._undapplied_fixed_map[m] if (
m in self.fixed_indices
) else next(free_values_perm_iterator))
for m in self.indices), self)
#######################################################################
elif self.is_combination:
wip_number = self.length - 1 - i
wip_perm_sequence = []
for i in range(self.n_elements, 0, -1):
for j in range(self.sequence_length, i - 2, -1):
candidate = math_tools.binomial(j, i)
if candidate <= wip_number:
wip_perm_sequence.append(self.sequence[-(j + 1)])
wip_number -= candidate
break
else:
raise RuntimeError
result = tuple(wip_perm_sequence)
assert len(result) == self.n_elements
return self.perm_type(result, self)
#######################################################################
else:
factoradic_number = math_tools.to_factoradic(
i * math.factorial(self.n_unused_elements),
n_digits_pad=self.sequence_length)
if self.is_partial:
factoradic_number = factoradic_number[:-self.n_unused_elements]
unused_numbers = list(self.sequence)
result = tuple(
unused_numbers.pop(factoradic_digit)
for factoradic_digit in factoradic_number)
assert sequence_tools.get_length(result) == self.n_elements
return self.perm_type(result, self)
def __getitem__(self, i):
if isinstance(i, (slice, sequence_tools.CanonicalSlice)):
canonical_slice = sequence_tools.CanonicalSlice(
i, self.length, offset=self.canonical_slice.start
)
return PermSpace(
self.sequence, domain=self.domain, n_elements=self.n_elements,
fixed_map=self.fixed_map, degrees=self.degrees,
is_combination=self.is_combination, slice_=canonical_slice,
perm_type=self.perm_type
)
assert isinstance(i, numbers.Integral)
if i <= -1:
i += self.length
if not (0 <= i < self.length):
raise IndexError
elif self.is_sliced:
return self.unsliced[i + self.canonical_slice.start]
elif self.is_dapplied:
return self.perm_type(self.undapplied[i], perm_space=self)
#######################################################################
elif self.is_degreed:
if self.is_rapplied:
assert not self.is_recurrent and \
not self.is_partial and not self.is_combination and \
not self.is_dapplied and not self.is_sliced
return self.perm_type(map(self.sequence.__getitem__,
self.unrapplied[i]),
perm_space=self)
assert not self.is_rapplied and not self.is_recurrent and \
not self.is_partial and not self.is_combination and \
not self.is_dapplied and not self.is_sliced
# If that wasn't an example of asserting one's dominance, I don't
# know what is.
available_values = list(self.free_values)
wip_perm_sequence_dict = dict(self.fixed_map)
wip_n_cycles_in_fixed_items = \
self._n_cycles_in_fixed_items_of_just_fixed
wip_i = i
for j in self.sequence:
if j in wip_perm_sequence_dict:
continue
for unused_value in available_values:
candidate_perm_sequence_dict = dict(wip_perm_sequence_dict)
candidate_perm_sequence_dict[j] = unused_value
### Checking whether we closed a cycle: ###################
# #
if j == unused_value:
closed_cycle = True
else:
current = j
while True:
current = candidate_perm_sequence_dict[current]
if current == j:
closed_cycle = True
break
elif current not in candidate_perm_sequence_dict:
closed_cycle = False
break
# #
### Finished checking whether we closed a cycle. ##########
candidate_n_cycles_in_fixed_items = \
wip_n_cycles_in_fixed_items + closed_cycle
candidate_fixed_perm_space_length = sum(
math_tools.abs_stirling(
self.sequence_length -
len(candidate_perm_sequence_dict),
self.sequence_length - degree -
candidate_n_cycles_in_fixed_items
) for degree in self.degrees
)
if wip_i < candidate_fixed_perm_space_length:
available_values.remove(unused_value)
wip_perm_sequence_dict[j] = unused_value
wip_n_cycles_in_fixed_items = \
candidate_n_cycles_in_fixed_items
break
wip_i -= candidate_fixed_perm_space_length
else:
raise RuntimeError
assert wip_i == 0
return self.perm_type((wip_perm_sequence_dict[k] for k in
self.domain), self)
#######################################################################
elif self.is_recurrent:
assert not self.is_dapplied and not self.is_degreed and \
not self.is_sliced
available_values = list(self.sequence)
reserved_values = nifty_collections.Bag(self.fixed_map.values())
wip_perm_sequence_dict = dict(self.fixed_map)
wip_i = i
shit_set = set()
for j in range(self.n_elements):
if j in self.fixed_map:
available_values.remove(self.fixed_map[j])
reserved_values[self.fixed_map[j]] -= 1
continue
unused_values = [
item for item in
nifty_collections.OrderedBag(available_values) -
reserved_values if item not in shit_set
]
for unused_value in unused_values:
wip_perm_sequence_dict[j] = unused_value
candidate_sub_perm_space = \
PermSpace._create_with_cut_prefix(
self.sequence,
n_elements=self.n_elements,
fixed_map=wip_perm_sequence_dict,
is_combination=self.is_combination,
shit_set=shit_set, perm_type=self.perm_type
)
if wip_i < candidate_sub_perm_space.length:
available_values.remove(unused_value)
break
else:
wip_i -= candidate_sub_perm_space.length
if self.is_combination:
shit_set.add(wip_perm_sequence_dict[j])
del wip_perm_sequence_dict[j]
else:
raise RuntimeError
assert wip_i == 0
return self.perm_type(
dict_tools.get_tuple(wip_perm_sequence_dict, self.domain),
self
)
#######################################################################
elif self.is_fixed:
free_values_perm = self._free_values_unsliced_perm_space[i]
free_values_perm_iterator = iter(free_values_perm)
return self.perm_type(
tuple(
(self._undapplied_fixed_map[m] if
(m in self.fixed_indices) else
next(free_values_perm_iterator))
for m in range(self.sequence_length)
),
self
)
#######################################################################
elif self.is_combination:
wip_number = self.length - 1 - i
wip_perm_sequence = []
for i in range(self.n_elements, 0, -1):
for j in range(self.sequence_length, i - 2, -1):
candidate = math_tools.binomial(j, i)
if candidate <= wip_number:
wip_perm_sequence.append(
self.sequence[-(j+1)]
)
wip_number -= candidate
break
else:
raise RuntimeError
result = tuple(wip_perm_sequence)
assert len(result) == self.n_elements
return self.perm_type(result, self)
#######################################################################
else:
factoradic_number = math_tools.to_factoradic(
i * math.factorial(
self.n_unused_elements),
n_digits_pad=self.sequence_length
)
if self.is_partial:
factoradic_number = factoradic_number[:-self.n_unused_elements]
unused_numbers = list(self.sequence)
result = tuple(unused_numbers.pop(factoradic_digit) for
factoradic_digit in factoradic_number)
assert sequence_tools.get_length(result) == self.n_elements
return self.perm_type(result, self)