Iteration for Factorials

[Roberto Bonvallet]

Re: Iteration for Factorials

On Oct 22, 11:45 am, Ant <ant...@gmail.c omwrote:

Er, no. And neither is mine. You may want to google for the definition
of factorial!

Don't google for the definition... google for the answer!

import urllib
import re
urllib.URLopene r.version = "Mozilla/4.0"

def fact(x):
r = re.compile(r"%d ! = (\d+)" % x)
for line in urllib.urlopen( "http://www.google.cl/search?q=%d%%21 "
% x):
m = r.search(line)
if m:
return int(m.group(1))

--
Roberto Bonvallet

[Hendrik van Rooyen]

Re: Iteration for Factorials

"Dennis Lee Bieber" <wlfraed@ix.net com.comwrote:

Heh... the one saving grace of taking a CS major in a period where
the primary languages taught were FORTRAN (IV), COBOL (74), and
something close to K&K BASIC. Heck, even the assembler class followed
the FORTRAN parameter handling scheme (argument addresses copied to
static locals and used via one level of indirection) -- It would take me
some time, today, to figure out how to even create a "stack" (even the
return address was passed via a reserved register and saved locally):
>
call,2 sub-address
data arg1-address
data arg2-address
do-something
.
.
.
sub-address: store,2 my-return
load,9 *my-return,1 ;indexed access
store,9 param1
load,9 *my-return,2
store,9 param2
do-stuff
load,2 my-return
addimmediate,2 2 ;number of args to
adjust return
return,2
>
(format:
label command,registe r argument
*argument ;indirection
argument,x ;indexed )
--

Yuk. Reminds me of one of the Hitachi processors that
has a single depth hardware "link register" that tells a
subroutine where it was called from.

I was thinking of a stack that grows when you call or push,
and shrinks when you return or pop.

When there are only 128 or so bytes, and an address is two bytes,
recursive calling soon runs into trouble. Especially so if you also
use the stack to pass params...

- Hendrik

[Jon Ribbens]

Re: Iteration for Factorials

On 2007-10-23, Hendrik van Rooyen <mail@microcorp .co.zawrote:

Yuk. Reminds me of one of the Hitachi processors that
has a single depth hardware "link register" that tells a
subroutine where it was called from.

That's how ARM processors work, and they're everywhere these days.

[Marco Mariani]

Re: Iteration for Factorials

Roberto Bonvallet wrote:

import urllib
import re
urllib.URLopene r.version = "Mozilla/4.0"
>
def fact(x):
r = re.compile(r"%d ! = (\d+)" % x)
for line in urllib.urlopen( "http://www.google.cl/search?q=%d%%21 " % x):
m = r.search(line)
if m:
return int(m.group(1))

You solution reminds me the web-based WTF calculator.

http://worsethanfailure.com/Articles/OMGWTF-Finalist-05-WTF-Web-Calc.aspx

[mensanator@aol.com]

Re: Iteration for Factorials

On Oct 23, 6:58 am, tokl...@gmail.c om wrote:

On 22 oct, 23:39, "mensana...@aol .com" <mensana...@aol .comwrote:
>

Nope, still doesn't work:

>

def fact(x):
return reduce(operator .mul,xrange(1,x +1),1)

>

fact() should raise an exception if x is negative.

>
So, where is the problem?

The fact that it returns 1 for negative x?

And didn't you see my followup message? About how the
example, as posted, doesn't even produce correct answers
for legal values of x?

if not allowing negative numbers is so
important for you,

Mathematical consistency is only important to _me_?

add a if statement and raise a ValueError exception.

Not necessary when done correctly. Didn't you see my example?

[mensanator@aol.com]

Re: Iteration for Factorials

On Oct 23, 5:55 am, Marco Mariani <ma...@sferacar ta.comwrote:

Tim Chase wrote:

>>fact = lambda i: i 1 and reduce(mul, xrange(1, i+1)) or not

i and 1 or None

>

Stunts like this would get a person fired around here if they
were found in production code :)

>
eheh, indeed.
>
def fact(n):
try:
return eval('*'.join(s tr(x) for x in range(1,n+1)))
except:
return 1

Needs work.

IDLE 1.2

>>def fact(n):

try:
return eval('*'.join(s tr(x) for x in range(1,n+1)))
except:
return 1

>>fact(3)

6

>>fact(2)

2

>>fact(1)

1

>>fact(0)

1

>>fact(-1)

1

>>fact(-2)

1

[Marco Mariani]

Re: Iteration for Factorials

mensanator@aol. com wrote:

Needs work.

Uh... ok.. this one gives an exception ;-)


def fact(n):
try:
return eval('*'.join(s tr(x) for x in range(1,n+1)))
except:
return n>=0 or ValueError



print fact(-1)
<type 'exceptions.Val ueError'>

[Hendrik van Rooyen]

Re: Iteration for Factorials

"Jon Ribbens" <jon+use...quiv ocal.co.ukwrote :

On 2007-10-23, Hendrik van Rooyen <mail@microcorp .co.zawrote:

Yuk. Reminds me of one of the Hitachi processors that
has a single depth hardware "link register" that tells a
subroutine where it was called from.

>
That's how ARM processors work, and they're everywhere these days.

Yes, worse luck. The market has chosen...

- Hendrik

[Nick Craig-Wood]

Re: Iteration for Factorials

Py-Fun <lorna.burns@gm ail.comwrote:

I'm stuck trying to write a function that generates a factorial of a
number using iteration and not recursion. Any simple ideas would be
appreciated.

Here is the math geek answer ;-)

import math

def factorial(i):
n = i + 1
return math.exp(-n)*(n**(n-0.5))*math.sqrt (2*math.pi)*(1. + 1./12/n + 1./288/n**2 - 139./51840/n**3)

Works for non integer factorials also...

See here for background

http://mathworld.wolfram.com/StirlingsSeries.html

--
Nick Craig-Wood <nick@craig-wood.com-- http://www.craig-wood.com/nick

[Lou Pecora]

Re: Iteration for Factorials

In article <slrnfhvalj.67s .nick@irishsea. home.craig-wood.com>,
Nick Craig-Wood <nick@craig-wood.comwrote:

Py-Fun <lorna.burns@gm ail.comwrote:

I'm stuck trying to write a function that generates a factorial of a
number using iteration and not recursion. Any simple ideas would be
appreciated.

>
Here is the math geek answer ;-)
>
import math
>
def factorial(i):
n = i + 1
return math.exp(-n)*(n**(n-0.5))*math.sqrt (2*math.pi)*(1. + 1./12/n +
1./288/n**2 - 139./51840/n**3)
>
Works for non integer factorials also...
>
See here for background
>
http://mathworld.wolfram.com/StirlingsSeries.html

Well, that's Sterling's formula. You do have to worry about
convergence/accuracy.

How about (for intergers - simple-minded version):

def factorial(i):
fact=1.0
for n in xrange(i):
fact=n*fact
return fact

There might even be an array method that can be adapted to get the
product. Is there a product method? (analogous to a sum method)

Then you could use,

arr=arange(i)+1
fact=arr.produc t() # or something like that

--
-- Lou Pecora

[mensanator@aol.com]

Re: Iteration for Factorials

On Oct 24, 4:05 pm, Lou Pecora <pec...@anvil.n rl.navy.milwrot e:

In article <slrnfhvalj.67s .n...@irishsea. home.craig-wood.com>,
Nick Craig-Wood <n...@craig-wood.comwrote:
>
>
>
>
>

Py-Fun <lorna.bu...@gm ail.comwrote:

I'm stuck trying to write a function that generates a factorial of a
number using iteration and not recursion. Any simple ideas would be
appreciated.

>

Here is the math geek answer ;-)

>

import math

>

def factorial(i):
n = i + 1
return math.exp(-n)*(n**(n-0.5))*math.sqrt (2*math.pi)*(1. + 1./12/n +
1./288/n**2 - 139./51840/n**3)

>

Works for non integer factorials also...

>

See here for background

>

http://mathworld.wolfram.com/StirlingsSeries.html

>
Well, that's Sterling's formula. You do have to worry about
convergence/accuracy.
>
How about (for intergers - simple-minded version):
>
def factorial(i):
fact=1.0
for n in xrange(i):
fact=n*fact
return fact

Simple minded indeed.

>>factorial(3 )

0.0

>
There might even be an array method that can be adapted to get the
product. Is there a product method? (analogous to a sum method)
>
Then you could use,
>
arr=arange(i)+1
fact=arr.produc t() # or something like that
>
--
-- Lou Pecora- Hide quoted text -
>
- Show quoted text -

[marek.rocki@wp.pl]

Re: Iteration for Factorials

Tim Golden napisa (a):

It's only a moment before the metaclass and
the Twisted solution come along. :)

I couldn't resist. It's not as elegant as I hoped, but hey, at least
it memoizes the intermediate classes :-)


class fact_0(object):
value = 1

class fact_meta(objec t):
def __new__(cls, name, bases, attrs):
n = attrs['n']
class_name = 'fact_%i' % n
try:
return globals()[class_name]
except KeyError:
new_class = type(class_name , bases, {})
new_class.value = n * fact(n - 1).value
new_class.__str __ = lambda self: str(self.value)
globals()[class_name] = new_class
return new_class

class fact(object):
def __new__(self, n_):
class spanish_inquisi tion(object):
__metaclass__ = fact_meta
n = n_
return spanish_inquisi tion()

print fact(5)
print fact(3)
print fact(1)

[mensanator@aol.com]

Re: Iteration for Factorials

On Oct 24, 5:19 pm, marek.ro...@wp. pl wrote:

Tim Golden napisa (a):
>

It's only a moment before the metaclass and
the Twisted solution come along. :)

>
I couldn't resist. It's not as elegant as I hoped, but hey, at least
it memoizes the intermediate classes :-)
>
class fact_0(object):
value = 1
>
class fact_meta(objec t):
def __new__(cls, name, bases, attrs):
n = attrs['n']
class_name = 'fact_%i' % n
try:
return globals()[class_name]
except KeyError:
new_class = type(class_name , bases, {})
new_class.value = n * fact(n - 1).value
new_class.__str __ = lambda self: str(self.value)
globals()[class_name] = new_class
return new_class
>
class fact(object):
def __new__(self, n_):
class spanish_inquisi tion(object):
__metaclass__ = fact_meta
n = n_
return spanish_inquisi tion()
>
print fact(5)
print fact(3)
print fact(1)

Dare I add fact(0)?

120
6
1
<__main__.fact_ 0 object at 0x011729F0>

Hmm..not sure what that means, but I bet I can't calculate
combinations.

What about fact(-1)?

120
6
1
<__main__.fact_ 0 object at 0x011729F0>

Traceback (most recent call last):
File "C:/Program Files/PyGTK/Python/user/yet_another_fac torial.py",
line 31, in <module>
print fact(-1)
File "C:/Program Files/PyGTK/Python/user/yet_another_fac torial.py",
line 21, in __new__
class spanish_inquisi tion(object):
File "C:/Program Files/PyGTK/Python/user/yet_another_fac torial.py",
line 13, in __new__
new_class.value = n * fact(n - 1).value
File "C:/Program Files/PyGTK/Python/user/yet_another_fac torial.py",
line 21, in __new__
class spanish_inquisi tion(object):
File "C:/Program Files/PyGTK/Python/user/yet_another_fac torial.py",
line 13, in __new__
new_class.value = n * fact(n - 1).value
File "C:/Program Files/PyGTK/Python/user/yet_another_fac torial.py",
line 21, in __new__
class spanish_inquisi tion(object):
File "C:/Program Files/PyGTK/Python/user/yet_another_fac torial.py",
line 13, in __new__
new_class.value = n * fact(n - 1).value
File "C:/Program Files/PyGTK/Python/user/yet_another_fac torial.py",
line 21, in __new__
class spanish_inquisi tion(object):
File "C:/Program Files/PyGTK/Python/user/yet_another_fac torial.py",
line 13, in __new__
new_class.value = n * fact(n - 1).value
File "C:/Program Files/PyGTK/Python/user/yet_another_fac torial.py",
line 21, in __new__
class spanish_inquisi tion(object):
File "C:/Program Files/PyGTK/Python/user/yet_another_fac torial.py",
line 13, in __new__
new_class.value = n * fact(n - 1).value
File "C:/Program Files/PyGTK/Python/user/yet_another_fac torial.py",
line 21, in __new__
class spanish_inquisi tion(object):
File "C:/Program Files/PyGTK/Python/user/yet_another_fac torial.py",
line 13, i

Wow! An infinite loop in the Traceback. Not quite the exception
I was looking for.

[Paul Rubin]

Re: Iteration for Factorials

Lou Pecora <pecora@anvil.n rl.navy.milwrit es:

There might even be an array method that can be adapted to get the
product. Is there a product method? (analogous to a sum method)

The "reduce" function which is being removed from python in 3.0.

import operator
def factorial(n):
return reduce(operator .mul, xrange(1,n+1))

[Paul Rubin]

Re: Iteration for Factorials

marek.rocki@wp. pl writes:

It's only a moment before the metaclass and
the Twisted solution come along. :)

>
I couldn't resist. It's not as elegant as I hoped, but hey, at least
it memoizes the intermediate classes :-)

It gets even weirder in Haskell.

http://www.willamette.edu/~fruehr/haskell/evolution.html