131 lines
2.7 KiB
Python
131 lines
2.7 KiB
Python
'''Tau numbers'''
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from operator import mul
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from math import floor, sqrt
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from functools import reduce
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from itertools import (
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accumulate, chain, count,
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groupby, islice, product
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)
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# tauNumbers :: Generator [Int]
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def tauNumbers():
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'''Positive integers divisible by the
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count of their positive divisors.
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'''
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return (
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n for n in count(1)
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if 0 == n % len(divisors(n))
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)
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# ------------------------- TEST -------------------------
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# main :: IO ()
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def main():
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'''The first hundred Tau numbers.
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'''
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xs = take(100)(
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tauNumbers()
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)
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w = len(str(xs[-1]))
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print('\n'.join([
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' '.join([
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str(cell).rjust(w, ' ') for cell in row
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])
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for row in chunksOf(10)(xs)
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]))
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# ----------------------- GENERIC ------------------------
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# chunksOf :: Int -> [a] -> [[a]]
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def chunksOf(n):
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'''A series of lists of length n, subdividing the
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contents of xs. Where the length of xs is not evenly
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divible, the final list will be shorter than n.
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'''
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def go(xs):
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return (
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xs[i:n + i] for i in range(0, len(xs), n)
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) if 0 < n else None
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return go
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# divisors :: Int -> [Int]
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def divisors(n):
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'''The ordered divisors of n.
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'''
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def go(a, x):
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return [a * b for a, b in product(
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a,
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accumulate(chain([1], x), 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
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in groupby(primeFactors(n))
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], [1])
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) if 1 < n else [1]
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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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# take :: Int -> [a] -> [a]
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# take :: Int -> String -> String
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def take(n):
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'''The prefix of xs of length n,
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or xs itself if n > length xs.
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'''
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def go(xs):
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return (
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xs[0:n]
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if isinstance(xs, (list, tuple))
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else list(islice(xs, n))
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)
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return go
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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):
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def g(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 g
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return go
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# MAIN ---
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if __name__ == '__main__':
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main()
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