PyEuler

[bearophileHUGS@lycos.com]

This is the first time I write something that looks like a little
rant :-) Surely I'll be wrong in many points, but I presume this isn't
going to damage people, so...

Here there are some functional Python solutions to some Euler
problems:

http://pyeuler.wikidot.com/

Some pieces of that code:

def takenth(n, iterable):
"Returns the nth item"
return list(islice(ite rable, n, n+1))[0]

def euler1(end, nums):
isanymultiple = lambda x: any((x % y == 0) for y in nums)
return sum(filter(isan ymultiple, xrange(end)))

euler1(1000, [3,5])

#Find the sum of all the even-valued terms in the Fibonacci sequence
which do not exceed one million.

def fibonacci(n):
"""Return nth element of the fibonacci serie"""
if n == 0 or n == 1:
return n
return fibonacci(n-1) + fibonacci(n-2)

def euler2(end):
genfib = imap(fibonacci, count())
candidates = takewhile(lambd a n: n<end, genfib)
return sum(ifilter(lam bda n: n%2, candidates))


def least_common_mu ltiple(nums):
"""Return least common multiples of nums"""
factorized = dict((n, dict(factorize( n))) for n in nums)
union = lambda lst: reduce(set.unio n, map(set, lst))
all_factors = union(factorize d.values())
getexponent = lambda factor: (factorized[n].get(factor, 0) for n
in nums)
return mul(factor**(ma x(getexponent(f actor))) for factor in
all_factors)

What I think about such code:
- It's not much readable (but usually it can be read).
- it's not much Pythonic. Python is only partially functional, if you
try to use it in a very functional way you go against the language,
its coding practices, and the net result may be slow/little readable.
If you want to write almost fully functional code it's better to use a
fitter language, like Haskell.
- In some situations it seems to just show lack of knowledge of
Python.
- In various points it's not much efficient in speed and/or space.
- It's not even short, there are many ways to shorten that code, often
keeping or even increasing its readability; one of the most common
ways is to use generators and list comps more often.
- It lacks tests, like doctests.
- It has small pedagogical value too, because this is a bad way to
learn Python, and programming in general too.
- It has shown me when to use takewhile(), and some of the
mathematical insights it contains are interesting :-)

Bye,
bearophile

[Mark Dickinson]

Re: PyEuler

On Feb 25, 11:25 am, bearophileH...@ lycos.com wrote:

This is the first time I write something that looks like a little
rant :-) Surely I'll be wrong in many points, but I presume this isn't
going to damage people, so...

Agreed on all points. :-) This looks a lot like someone trying to
write
Haskell in Python. And that's a truly horrible way of finding a least
common multiple: much better to do lcm(a, b) = a*(b//gcd(a, b)), with
gcd computed using the usual algorithm (written *iteratively*, not
recursively).

Mark

[Paul Rubin]

Re: PyEuler

bearophileHUGS@ lycos.com writes:

def takenth(n, iterable):
"Returns the nth item"
return list(islice(ite rable, n, n+1))[0]
>

return islice(iterable , n).next()

isanymultiple = lambda x: any((x % y == 0) for y in nums)
return sum(filter(isan ymultiple, xrange(end)))

This isn't so good, you really want to apply the filters recursively.

def fibonacci(n):
"""Return nth element of the fibonacci serie"""
if n == 0 or n == 1:
return n
return fibonacci(n-1) + fibonacci(n-2)

uggh!!!! exponential blowup!

def euler2(end):
genfib = imap(fibonacci, count())

Are you kidding?
def ggenfib():
a,b = 1,2
while True:
yield a
a,b = b, a=b

What I think about such code:
- It's not much readable (but usually it can be read). ...

Your observations are generally good; I'd say it was done
without enough attention to the math too.

There is a full set of solutions on the haskell wiki, if anyone cares.

[Arnaud Delobelle]

Re: PyEuler

On Feb 25, 7:25 pm, Paul Rubin <http://phr...@NOSPAM.i nvalidwrote:

Are you kidding?
    def ggenfib():
      a,b = 1,2
      while True:
         yield a
         a,b = b, a=b

Or:

def genfib(a=0, b=1):
for a, b in iter(lambda:(b, a+b), None):
yield a

;-)

Ahem. I admit that somehow, I am proud of this.

--
Arnaud

[Mark Dickinson]

Re: PyEuler

On Feb 25, 4:24 pm, Arnaud Delobelle <arno...@google mail.comwrote:

def genfib(a=0, b=1):
    for a, b in iter(lambda:(b, a+b), None):
        yield a
>
;-)
>
Ahem.  I admit that somehow, I am proud of this.

You're one sick puppy dog. :-)
(P.S. Your mother was a hamster, and your father smelt of
elderberries.)

Gratuitous insulting'ly yours,

Mark

[Arnaud Delobelle]

Re: PyEuler

On Feb 25, 10:25 pm, bearophileH...@ lycos.com wrote:

Paul Rubin:
>

    def ggenfib():
      a,b = 1,2
      while True:
         yield a
         a,b = b, a=b

>
Your version is the nice basic generator version (the last line
contains a +, I presume), but I like this other version too:
>
def xfibonacci():
    a = b = 1
    yield a
    yield b
    while True:
        a = a + b
        yield a
        b = b + a
        yield b
>
It's a bit faster, longer, and I find it a bit more readable.

In this case why not:

def xfib(a=1, b=1):
while True:
yield a
a += b
yield b
b += a

--
Arnaud

[bearophileHUGS@lycos.com]

Re: PyEuler

Arnaud Delobelle:

In this case why not:
>
def xfib(a=1, b=1):
while True:
yield a
a += b
yield b
b += a

That's a bit less easy to understand than my version, for me.
In my version is easy to see the values of the variables. And using a
longer function name is better.

Bye,
bearophile

[Arnaud Delobelle]

Re: PyEuler

On Feb 25, 10:52 pm, bearophileH...@ lycos.com wrote:

Arnaud Delobelle:
>

In this case why not:

>

def xfib(a=1, b=1):
    while True:
        yield a
        a += b
        yield b
        b += a

>
That's a bit less easy to understand than my version, for me.
In my version is easy to see the values of the variables.

I disagree; the generator function has no right to keep a and b to
itself. a and b cry out to be function parameters. The user may want
to start a fibonacci sequence with any two initial values. IMHO one
of the great qualities of Python is that it makes this very easy in
most cases.

And using a
longer function name is better.

Up to a certain length :-)

--
Arnaud

[bearophileHUGS@lycos.com]

Re: PyEuler

Arnaud Delobelle:

I disagree; the generator function has no right to keep a and b to
itself. a and b cry out to be function parameters.

I see. Then that's a generator for a generalized Fibonacci
sequence :-)
Your version too is useful.

Bye,
bearophile