The Computer Language
Benchmarks Game

fannkuch-redux Python 3 #4 program

source code

# The Computer Language Benchmarks Game
# http://benchmarksgame.alioth.debian.org/
#
# 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

def task(n, start, size):
    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)

        task_count = cpu_count()
        total = factorial(n)
        task_size = (total + task_count - 1) // task_count

        if task_size < 20000:
            task_size = total
            task_count = 1

        assert(task_size % 2 == 0)

        task_args = [(n, i * task_size, task_size) for i in range(task_count)]

        if task_count > 1:
            with Pool() as pool:
                checksums, maximums = zip(*pool.starmap(task, task_args))
        else:
            checksums, maximums = zip(*starmap(task, task_args))

        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:
64-bit Ubuntu quad core
Python 3.6.0 (default, Feb  5 2017, 10:29:14)
[GCC 5.4.0 20160609] on linux
--enable-optimizations
make profile-opt


Sun, 05 Feb 2017 20:25:07 GMT

MAKE:
mv fannkuchredux.python3-4.python3 fannkuchredux.python3-4.py
0.02s to complete and log all make actions

COMMAND LINE:
/usr/local/src/Python-3.6.0/bin/python3.6 -OO fannkuchredux.python3-4.py 12

PROGRAM OUTPUT:
3968050
Pfannkuchen(12) = 65