On 10-03-18 02:13, Steven D'Aprano wrote:
> I am trying to enumerate all the three-tuples (x, y, z) where each of x,
> y, z can range from 1 to ∞ (infinity).
>
> This is clearly unhelpful:
>
> for x in itertools.count(1):
> for y in itertools.count(1):
> for z in itertools.count(1):
> print(x, y, z)
>
> as it never advances beyond x=1, y=1 since the innermost loop never
> finishes.
>
> Georg Cantor to the rescue! (Well, almost...)
>
> https://en.wikipedia.org/wiki/Pairing_function
I came up with the following generalisation:
from itertools import count
def summation2(total):
for n in range(1, total):
yield n, total - n
def summation(total, n):
if n == 2:
yield from summation2(total)
else:
for i in range(1, total - n + 2):
for tail in summation(total - i, n - 1):
yield (i,) + tail
def cantor(n):
for total in count(n):
yield from summation(total, n)
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