On Dec 27, 9:48 pm, rgalgon <[EMAIL PROTECTED]> wrote:
> I'm new to Python and have been putting my mind to learning it over my
> holiday break. I've been looking over the functional programming
> aspects of Python and I'm stuck trying to come up with some concise
> code to find Taxicab numbers (http://mathworld.wolfram.com/
> TaxicabNumber.html).
>
> "Taxicab(n), is defined as the smallest number that can be expressed
> as a sum of two positive cubes in n distinct ways"
>
> In Haskell something like this could easily be done with:
> cube x = x * x * x
>
> taxicab n = [(cube a + cube b, (a, b), (c, d))
> | a <- [1..n],
> b <- [(a+1)..n],
> c <- [(a+1)..n],
> d <- [(c+1)..n],
> (cube a + cube b) == (cube c + cube d)]
>
> Output::
> *Main> taxicab 10
> []
> *Main> taxicab 12
> [(1729,(1,12),(9,10))]
> *Main> taxicab 20
> [(1729,(1,12),(9,10)),(4104,(2,16),(9,15))]
>
> I'm looking for a succinct way of doing this in Python. I've been
> toying around with filter(),map(), and reduce() but haven't gotten
> anything half-way decent yet.
>
> So, how would you implement this taxicab(n) function in Python?
> Thanks in advance :-)
Python's list comprehensions are quite similar to haskell's, so this
code can be translated almost word-for-word.
def cube(x):
return x * x * x
def taxicab(n):
return [(cube(a) + cube(b), (a, b), (c, d))
for a in range(1, n + 1)
for b in range(a + 1, n + 1)
for c in range(a + 1, n + 1)
for d in range(c + 1, n + 1)
if cube(a) + cube(b) == cube(c) + cube(d)]
for n in (10, 12, 20):
print list(taxicab(n))
--
Paul Hankin
--
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