def partition_to_avoid_octave_adjacencies(l, direction):
'''Partition to avoid octave adjacencies.
'''
assert direction in ('left', 'right')
result = [[]]
part = result[-1]
for x in l:
if not isinstance(x, (int, float, Fraction)):
raise ValueError
if x % 12 in [y % 12 for y in part]:
first_value = [y for y in part if y % 12 == x % 12][0]
first_index = part.index(first_value)
## partition current part into left and middle subparts
old_part = part[:first_index+1]
disputed_part = part[first_index+1:]
new_part = []
## divvy up disputed part
left, right = mathtools.partition_integer_into_halves(
len(disputed_part), bigger = direction)
disputed_parts = sequencetools.partition_sequence_by_counts(
disputed_part, [left, right], cyclic=False, overhang=False)
left_disputed_part, right_disputed_part = disputed_parts
assert len(left_disputed_part) == left
assert len(right_disputed_part) == right
old_part.extend(left_disputed_part)
new_part.extend(right_disputed_part)
## replace last sublist in result with old, trimmed part
result[-1] = old_part
## append new part to result
result.append(new_part)
part = result[-1]
part.append(x)
result = [tuple(x) for x in result]
return result
def test_mathtools_partition_integer_into_halves_03():
r'''Partition zero into halves.
'''
assert mathtools.partition_integer_into_halves(0, bigger='left') == (0, 0)
assert mathtools.partition_integer_into_halves(0, bigger='right') == (0, 0)
def test_mathtools_partition_integer_into_halves_01():
assert mathtools.partition_integer_into_halves(7, bigger='left') == (4, 3)
assert mathtools.partition_integer_into_halves(7, bigger='right') == (3, 4)
def test_mathtools_partition_integer_into_halves_02():
assert mathtools.partition_integer_into_halves(8, bigger='left') == (4, 4)
assert mathtools.partition_integer_into_halves(8, bigger='right') == (4, 4)
assert mathtools.partition_integer_into_halves(8, bigger='left', even='disallowed') == (5, 3)
assert mathtools.partition_integer_into_halves(8, bigger='right', even='disallowed') == (3, 5)