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===Composition of pure functions===
With Python type hints.
====Using compiler type hints, at the expense of clarity for the reader====
On clear comments vs noisy and misleading compiler hints,
and on an utterly disgraceful (deletionary) attack on Rosetta Code and PEP8, see the discussion page.
<lang python>'''Practical numbers'''
from operator import mul
from functools import reduce
from typing import AnyCallable, List, Callable
))
# Note: Although mypy compliant, type Any below could be improved.
def sumOfAnySubset(xs: List[int]) -> Callable[[Anyint], Anybool]:
'''True if any subset of xs sums to n.
'''
# ----------------------- GENERIC ------------------------
def chunksOf(n: int) -> Callable[[AnyList[str]], AnyList[List[str]]]:
'''A series of lists of length n, subdividing the
contents of xs. Where the length of xs is not evenly
def listTranspose(xss: List[List[intstr]]) -> List[List[intstr]]:
'''Transposed matrix'''
def go(xss):
def until(p: Callable[[int], bool]) -> AnyCallable[[int], bool]:
'''The result of repeatedly applying f until p holds.
The initial seed value is x.
# ---------------------- FORMATTING ----------------------
def spacedTable(rows: List[List[intstr]]) -> str:
'''Tabulation with right-aligned cells'''
columnWidths = [
len(str(row[-1])) for row in listTranspose(rows)
]
def aligned(s, w):
return s.rjust(w, ' ')
return '\n'.join(
' '.join(
map(aligned, row, columnWidths)
) for row in rows
)
# MAIN ---
if __name__ == '__main__':
main()
</lang>
{{Out}}
<pre>77 OEIS A005153 numbers in [1..333]
1 2 4 6 8 12 16 18 20 24
28 30 32 36 40 42 48 54 56 60
64 66 72 78 80 84 88 90 96 100
104 108 112 120 126 128 132 140 144 150
156 160 162 168 176 180 192 196 198 200
204 208 210 216 220 224 228 234 240 252
256 260 264 270 272 276 280 288 294 300
304 306 308 312 320 324 330
666 is practical :: True</pre>
====Clearer original draft, with comments on types for the reader====
See the discussion page. There has been a spate of unilateral deletions here,
in a shameless and apparently obsessional attempt to "discourage" differing approaches,
undermine the Rosetta Code principle of showing different approaches side by side,
and completely tear up the PEP8 emphasis on clarity.
Issues of compliance can be delegated to the widely used linters.
There is no need for a terrorist campaign, and extending "compliance"
to the angry policing of clarifying comments seems barely sane.
<lang python>'''Practical numbers'''
from itertools import accumulate, chain, groupby, product
from math import floor, sqrt
from operator import mul
from functools import reduce
# isPractical :: Int -> Bool
def isPractical(n):
'''True if n is a Practical number
(a member of OEIS A005153)
'''
ds = properDivisors(n)
return all(map(
sumOfAnySubset(ds),
range(1, n)
))
# sumOfAnySubset :: [Int] -> Int -> Bool
def sumOfAnySubset(xs):
'''True if any subset of xs sums to n.
'''
def go(n):
if n in xs:
return True
else:
total = sum(xs)
if n == total:
return True
elif n < total:
h, *t = reversed(xs)
d = n - h
return d in t or (
d > 0 and sumOfAnySubset(t)(d)
) or sumOfAnySubset(t)(n)
else:
return False
return go
# ------------------------- TEST -------------------------
# main :: IO ()
def main():
'''Practical numbers in the range [1..333],
and the OEIS A005153 membership of 666.
'''
xs = [x for x in range(1, 334) if isPractical(x)]
print(
f'{len(xs)} OEIS A005153 numbers in [1..333]\n\n' + (
spacedTable(
chunksOf(10)([
str(x) for x in xs
])
)
)
)
print("\n")
for n in [666]:
print(
f'{n} is practical :: {isPractical(n)}'
)
# ----------------------- GENERIC ------------------------
# chunksOf :: Int -> [a] -> [[a]]
def chunksOf(n):
'''A series of lists of length n, subdividing the
contents of xs. Where the length of xs is not evenly
divible, the final list will be shorter than n.
'''
def go(xs):
return [
xs[i:n + i] for i in range(0, len(xs), n)
] if 0 < n else None
return go
# primeFactors :: Int -> [Int]
def primeFactors(n):
'''A list of the prime factors of n.
'''
def f(qr):
r = qr[1]
return step(r), 1 + r
def step(x):
return 1 + (x << 2) - ((x >> 1) << 1)
def go(x):
root = floor(sqrt(x))
def p(qr):
q = qr[0]
return root < q or 0 == (x % q)
q = until(p)(f)(
(2 if 0 == x % 2 else 3, 1)
)[0]
return [x] if q > root else [q] + go(x // q)
return go(n)
# properDivisors :: Int -> [Int]
def properDivisors(n):
'''The ordered divisors of n, excluding n itself.
'''
def go(a, x):
return [a * b for a, b in product(
a,
accumulate(chain([1], x), mul)
)]
return sorted(
reduce(go, [
list(g) for _, g in groupby(primeFactors(n))
], [1])
)[:-1] if 1 < n else []
# listTranspose :: [[a]] -> [[a]]
def listTranspose(xss):
'''Transposed matrix'''
def go(xss):
if xss:
h, *t = xss
return (
[[h[0]] + [xs[0] for xs in t if xs]] + (
go([h[1:]] + [xs[1:] for xs in t])
)
) if h and isinstance(h, list) else go(t)
else:
return []
return go(xss)
# until :: (a -> Bool) -> (a -> a) -> a -> a
def until(p):
'''The result of repeatedly applying f until p holds.
The initial seed value is x.
'''
def go(f):
def g(x):
v = x
while not p(v):
v = f(v)
return v
return g
return go
# ---------------------- FORMATTING ----------------------
# spacedTable :: [[String]] -> String
def spacedTable(rows):
'''Tabulation with right-aligned cells'''
columnWidths = [
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