fannkuch-redux Python 3 #4 program

source code

```# The Computer Language Benchmarks Game
# https://salsa.debian.org/benchmarksgame-team/benchmarksgame/
#
# contributed by Joerg Baumann
# many thanks to Oleg Mazurov for his helpful description

from sys import argv
from math import factorial
from multiprocessing import cpu_count, Pool
from itertools import islice, starmap

def permutations(n, start, size):
p = bytearray(range(n))
count = bytearray(n)

remainder = start
for v in range(n - 1, 0, -1):
count[v], remainder = divmod(remainder, factorial(v))
for _ in range(count[v]):
p[:v], p[v] = p[1:v + 1], p[0]

assert(count[1] == 0)
assert(size < 2 or (size % 2 == 0))

if size < 2:
yield p[:]
else:
rotation_swaps = [None] * n
for i in range(1, n):
r = list(range(n))
for v in range(1, i + 1):
r[:v], r[v] = r[1:v + 1], r[0]
swaps = []
for dst, src in enumerate(r):
if dst != src:
swaps.append((dst, src))
rotation_swaps[i] = tuple(swaps)

while True:
yield p[:]
p[0], p[1] = p[1], p[0]
yield p[:]
i = 2
while count[i] >= i:
count[i] = 0
i += 1
else:
count[i] += 1
t = p[:]
for dst, src in rotation_swaps[i]:
p[dst] = t[src]

def alternating_flips_generator(n, start, size):
maximum_flips = 0
alternating_factor = 1
for permutation in islice(permutations(n, start, size), size):
first = permutation[0]
if first:
flips_count = 1
while True:
permutation[:first + 1] = permutation[first::-1]
first = permutation[0]
if not first: break
flips_count += 1
if maximum_flips < flips_count:
maximum_flips = flips_count
yield flips_count * alternating_factor
else:
yield 0
alternating_factor = -alternating_factor
yield maximum_flips

alternating_flips = alternating_flips_generator(n, start, size)
return sum(islice(alternating_flips, size)), next(alternating_flips)

def fannkuch(n):
if n < 0:
for data in islice(permutations(-n, 0, factorial(-n)), factorial(-n)):
print(''.join(map(lambda n: str(n + 1), data)))
else:
assert(n > 0)

total = factorial(n)

with Pool() as pool:
else:

checksum, maximum = sum(checksums), max(maximums)
print("{0}\nPfannkuchen({1}) = {2}".format(checksum, n, maximum))

if __name__ == "__main__":
fannkuch(int(argv[1]))
```

notes, command-line, and program output

```NOTES:
Python 3.8.0

Tue, 15 Oct 2019 05:09:03 GMT

MAKE:
mv fannkuchredux.python3-4.python3 fannkuchredux.python3-4.py
pytype .
[1/1] check fannkuchredux.python3-4
Python versions > 3.7 are not yet supported.
ninja: build stopped: subcommand failed.
Computing dependencies
Analyzing 1 sources with 0 local dependencies
make: [/home/dunham/8000-benchmarksgame/nanobench/makefiles/u64q.programs.Makefile:513: fannkuchredux.python3-4.python3_run] Error 1 (ignored)

5.08s to complete and log all make actions

COMMAND LINE:
/opt/src/Python-3.8.0/bin/python3 -OO fannkuchredux.python3-4.py 12

PROGRAM OUTPUT:
3968050
Pfannkuchen(12) = 65
```