Efficient Divide-and-Conquer using compression over little endian

divide-and-conquer.py

from functools import reduce
from itertools import compress
from operator import mul

def iterate(f, initial):
  """Keeps applying function `f` to accumulated state, yielding each intermediate result.
  
  E.g. iterate(lambda k: k*k, 2) -> 2,4,16,64,256,65536,..."""
  state = initial
  while True:
    yield state
    state = f(state)

def little_endian(n):
  """Generates bit in a little-endian order, e.g. little_endian(8) -> [0,0,0,1]"""
  state = n
  while state > 0:
    yield state % 2
    state = state // 2
 
In [1]: 2 ** 8
Out[1]: 256
  
In [2]: reduce(mul, compress(iterate(lambda k: k*k, 2), little_endian(8)), 1)
Out[2]: 256