def iterative_PGA_with_dict(width):
'''
Iterative permutation generation algorithm according
to dict order.
'''
total_numbers = math.factorial(width)
for i in range(total_numbers):
asc_number = integer_to_ascending_system_number(i)
asc_number += (width - len(asc_number)) * [0] # align
ret = []
ordered_index = list(range(width))
for n in reversed(asc_number):
ret.append(ordered_index[n])
del ordered_index[n]
yield list(ret)
def PGA_with_ascending_system_number(width):
'''
permutation generation algorithm by mapping index to ascending
system number and then mapping it to sequence.
'''
total_numbers = math.factorial(width)
for i in range(total_numbers):
asc_number = integer_to_ascending_system_number(i)
asc_number += (width - len(asc_number)) * [0] # align
ret = [None, ] * width
for index, n in enumerate(reversed(asc_number)):
for pos in reversed(range(width)):
if ret[pos] is None:
n -= 1
if n < 0:
ret[pos] = width - index - 1
break
yield ret
