115 lines
2.6 KiB
Python
115 lines
2.6 KiB
Python
'''Proper divisors'''
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from itertools import accumulate, chain, groupby, product
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from functools import reduce
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from math import floor, sqrt
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from operator import mul
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# properDivisors :: Int -> [Int]
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def properDivisors(n):
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'''The ordered divisors of n, excluding n itself.
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'''
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def go(a, group):
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return [x * y for x, y in product(
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a,
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accumulate(chain([1], group), mul)
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)]
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return sorted(
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reduce(go, [
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list(g) for _, g in groupby(primeFactors(n))
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], [1])
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)[:-1] if 1 < n else []
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# --------------------------TEST---------------------------
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# main :: IO ()
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def main():
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'''Tests'''
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print(
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fTable('Proper divisors of [1..10]:')(str)(str)(
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properDivisors
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)(range(1, 1 + 10))
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)
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print('\nExample of maximum divisor count in the range [1..20000]:')
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print(
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max(
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[(n, len(properDivisors(n))) for n in range(1, 1 + 20000)],
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key=snd
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)
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)
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# -------------------------DISPLAY-------------------------
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# fTable :: String -> (a -> String) ->
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# (b -> String) -> (a -> b) -> [a] -> String
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def fTable(s):
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'''Heading -> x display function -> fx display function ->
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f -> xs -> tabular string.
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'''
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def go(xShow, fxShow, f, xs):
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ys = [xShow(x) for x in xs]
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w = max(map(len, ys))
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return s + '\n' + '\n'.join(map(
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lambda x, y: y.rjust(w, ' ') + ' -> ' + fxShow(f(x)),
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xs, ys
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))
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return lambda xShow: lambda fxShow: lambda f: lambda xs: go(
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xShow, fxShow, f, xs
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)
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# -------------------------GENERIC-------------------------
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# primeFactors :: Int -> [Int]
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def primeFactors(n):
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'''A list of the prime factors of n.
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'''
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def f(qr):
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r = qr[1]
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return step(r), 1 + r
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def step(x):
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return 1 + (x << 2) - ((x >> 1) << 1)
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def go(x):
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root = floor(sqrt(x))
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def p(qr):
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q = qr[0]
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return root < q or 0 == (x % q)
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q = until(p)(f)(
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(2 if 0 == x % 2 else 3, 1)
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)[0]
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return [x] if q > root else [q] + go(x // q)
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return go(n)
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# snd :: (a, b) -> b
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def snd(tpl):
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'''Second member of a pair.'''
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return tpl[1]
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# until :: (a -> Bool) -> (a -> a) -> a -> a
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def until(p):
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'''The result of repeatedly applying f until p holds.
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The initial seed value is x.
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'''
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def go(f, x):
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v = x
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while not p(v):
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v = f(v)
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return v
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return lambda f: lambda x: go(f, x)
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# MAIN ---
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if __name__ == '__main__':
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main()
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