Iteration for Factorials

[Paul McGuire]

Re: Iteration for Factorials

On Oct 22, 8:02 am, vimal <cool.vimalsm.. .@gmail.comwrot e:

On Oct 22, 5:43 pm, Marco Mariani <ma...@sferacar ta.comwrote:
>

Py-Fun wrote:

def itforfact(n):
while n<100:
print n
n+1
n = input("Please enter a number below 100")

>

You function should probably return something. After that, you can see
what happens with the result you get.

>
i am just suggesting u an idea
but i dont know it satisfies ur needs
>
x=10
def cal_range(10)
for i in range(10):
print 2**i

Maybe a little math refresher would be good for those trying to post
suggestions.

"Factorial of N" means "the product of 1 x 2 x 3 x ... x N", and is
shown symbolically as "N!".

(Factorial is only defined for nonnegative numbers, and for reasons
that go beyond this little note, just know that 0! = 1.)

In Python, a fully expanded factorial for values >= 1 would be:

2! = 1 * 2
5! = 1 * 2 * 3 * 4 * 5
8! = 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8

Here is an example routine showing iteration, that prints these
expressions:


def print_factorial (n):
print str(n)+"! =",
print "1",
t = 2
while t <= n:
print "*",t,
t += 1
print

Perhaps this example will give you some ideas on how to approach your
problem.


-- Paul

[Tim Golden]

Re: Iteration for Factorials

Marco Mariani wrote:

Tim Golden wrote:
>

>> From the cookbook, this time.
>>It satisfies the requirements nicely ;)
>>>
>>http://aspn.activestate.com/ASPN/Coo.../Recipe/496691

>[... snip the ultimate general-purpose answer to the OP's question ...
>>
>I really hope that's a wink up there, Marco.

>
The wink is in the second line of my post...

I did see it :)

>The poor guy was just trying to get his homework done!

>
I don't see how my answer is in any way worse than those based on
lambda.

Nor do I. I was just joking with a colleague that the guy
just wanted a bit of help (which he did get, in fact from
several sources) and then out came the lambda and the
decorator. It's only a moment before the metaclass and
the Twisted solution come along. :)
(It's like watching a convention of lisp programmers --
ducks, runs for cover)

TJG

[mensanator@aol.com]

Re: Iteration for Factorials

On Oct 22, 7:50 am, Duncan Booth <duncan.bo...@i nvalid.invalidw rote:

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.

>
This version avoids doing anything fancier than adding 1, so it should be
simple enough for anyone:
>
def factorial(e):
a = 1
for b in range(e):
c = 0
for j in range(b, -1, -1):
for d in range(a):
c += 1
a = c
return a

Not simple enough for my taste:

>>import gmpy
>>gmpy.fac(10 )

mpz(3628800)

[Paul Rudin]

Re: Iteration for Factorials

"mensanator@aol .com" <mensanator@aol .comwrites:

On Oct 22, 7:50 am, Duncan Booth <duncan.bo...@i nvalid.invalidw rote:

>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.

>>
>This version avoids doing anything fancier than adding 1, so it should be
>simple enough for anyone:
>>
>def factorial(e):
> a = 1
> for b in range(e):
> c = 0
> for j in range(b, -1, -1):
> for d in range(a):
> c += 1
> a = c
> return a

>
Not simple enough for my taste:
>

>>>import gmpy
>>>gmpy.fac(1 0)

mpz(3628800)

I haven't followed all this thread, but has anyone yet done:

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

[mensanator@aol.com]

Re: Iteration for Factorials

On Oct 22, 1:35 pm, Paul Rudin <paul.nos...@ru din.co.ukwrote:

"mensana...@aol .com" <mensana...@aol .comwrites:

On Oct 22, 7:50 am, Duncan Booth <duncan.bo...@i nvalid.invalidw rote:

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.

>

This version avoids doing anything fancier than adding 1, so it should be
simple enough for anyone:

>

def factorial(e):
a = 1
for b in range(e):
c = 0
for j in range(b, -1, -1):
for d in range(a):
c += 1
a = c
return a

>

Not simple enough for my taste:

>

>>import gmpy
>>gmpy.fac(10 )

mpz(3628800)

>
I haven't followed all this thread, but has anyone yet done:
>
import operator
def fact(x):
return reduce(operator .mul, xrange(1,x))

I hope not.

>>import operator
>>def fact(x):

return reduce(operator .mul,xrange(1,x ))

>>fact(3)

2

>>fact(2)

1

>>fact(1)

Traceback (most recent call last):
File "<pyshell#1 0>", line 1, in <module>
fact(1)
File "<pyshell#7 >", line 2, in fact
return reduce(operator .mul,xrange(1,x ))
TypeError: reduce() of empty sequence with no initial value

>>fact(0)

Traceback (most recent call last):
File "<pyshell#1 1>", line 1, in <module>
fact(0)
File "<pyshell#7 >", line 2, in fact
return reduce(operator .mul,xrange(1,x ))
TypeError: reduce() of empty sequence with no initial value

I think you need to make it a bit more complicated.

[tokland@gmail.com]

Re: Iteration for Factorials

On 22 oct, 20:35, Paul Rudin <paul.nos...@ru din.co.ukwrote:

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

Maybe:

import operator
def fact(x):
return reduce(operator .mul, xrange(2, x+1), 1)

fact(0)
1
fact(4)
24

[Paul Rudin]

Re: Iteration for Factorials

tokland@gmail.c om writes:

On 22 oct, 20:35, Paul Rudin <paul.nos...@ru din.co.ukwrote:
>

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

>
Maybe:
>
import operator
def fact(x):
return reduce(operator .mul, xrange(2, x+1), 1)

Or just:

reduce(operator .mul, xrange(1, x), 1)

[mensanator@aol.com]

Re: Iteration for Factorials

On Oct 22, 3:38 pm, Paul Rudin <paul.nos...@ru din.co.ukwrote:

tokl...@gmail.c om writes:

On 22 oct, 20:35, Paul Rudin <paul.nos...@ru din.co.ukwrote:

>

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

>

Maybe:

>

import operator
def fact(x):
return reduce(operator .mul, xrange(2, x+1), 1)

>
Or just:
>
reduce(operator .mul, xrange(1, x), 1)

Nope, still doesn't work:

>>def fact(x):

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

>>fact(3)

6

>>fact(2)

2

>>fact(1)

1

>>fact(0)

1

>>fact(-1)

1

>>fact(-2)

1

>>fact(-3)

1

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

My variant of your original (same as Tim Chase's except the
test for x==1 is not necessary):

>>def fact(x):

if x==0:
return 1
else:
return reduce(operator .mul,xrange(1,x +1))

>>fact(3)

6

>>fact(2)

2

>>fact(1)

1

>>fact(0)

1

>>fact(-1)

Traceback (most recent call last):
File "<pyshell#4 0>", line 1, in <module>
fact(-1)
File "<pyshell#3 5>", line 5, in fact
return reduce(operator .mul,xrange(1,x +1))
TypeError: reduce() of empty sequence with no initial value

[mensanator@aol.com]

Re: Iteration for Factorials

On Oct 22, 4:39 pm, "mensana...@aol .com" <mensana...@aol .comwrote:

On Oct 22, 3:38 pm, Paul Rudin <paul.nos...@ru din.co.ukwrote:
>
>
>
>
>

tokl...@gmail.c om writes:

On 22 oct, 20:35, Paul Rudin <paul.nos...@ru din.co.ukwrote:

>

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

>

Maybe:

>

import operator
def fact(x):
return reduce(operator .mul, xrange(2, x+1), 1)

>

Or just:

>

reduce(operator .mul, xrange(1, x), 1)

>
Nope, still doesn't work:
>

>def fact(x):

>
return reduce(operator .mul,xrange(1,x +1),1)

Excuse me, I mistyped your proposed solution. You had
xrange(1,x) not xrange(1,x+1). The former only returns
correct factorials for x==0 and x==1.

Sorry for the confusion.

>

>fact(3)

6

>fact(2)

2

>fact(1)

1

>fact(0)

1

>fact(-1)

1

>fact(-2)

1

>fact(-3)

>
1
>
fact() should raise an exception if x is negative.
>
My variant of your original (same as Tim Chase's except the
test for x==1 is not necessary):
>

>def fact(x):

>
if x==0:
return 1
else:
return reduce(operator .mul,xrange(1,x +1))
>
>
>

>fact(3)

6

>fact(2)

2

>fact(1)

1

>fact(0)

1

>fact(-1)

>
Traceback (most recent call last):
File "<pyshell#4 0>", line 1, in <module>
fact(-1)
File "<pyshell#3 5>", line 5, in fact
return reduce(operator .mul,xrange(1,x +1))
TypeError: reduce() of empty sequence with no initial value- Hide quoted text -
>
- Show quoted text -

[Tim Chase]

Re: Iteration for Factorials

Still, why do you want None instead of raisng an exception

(as is the case in other factorial implementations )?

A null value is as good/bad as raising an exception in my book.
Since you can't do math on a None object, any attempt to do so
will raise an exception:

>>42 + fact(-1)

I generally prefer my functions to return semi-sensible results
(in this case, None makes sense to me, as there isn't really a
definition of "negative-one factorial"). It also fits in my head
alongside my SQL where NULL values/expressions can be returned
and evaluated without the whole query falling over.

I suppose if you really wanted to throw an exception using this
lambda craziness, you could wrap the whole result in "0 +
([body])" which, if the body returned Null, would push up
exception daisies (with slightly misleading exception information).

-tkc

[Hendrik van Rooyen]

Re: Iteration for Factorials

"Marco Mariani" <marc....arta.c omwrote:

I don't see how my answer is in any way worse than those based on
lambda. Maybe I'm just envious because when I was his age I couldn't
google for answers. He should at least be able to do that, shouldn't he?
But wait. That would mean understanding what a factorial is. That would
require a second search, or a textbook, or an understanding of
arithmetics before programming with or without recursion. Should we
blame the teachers?

Yes. And burn their cars to get their attention!

Asking someone to write a factorial algorithm before he knows WTF a
factorial "is", is either insane, or the ultimate demonstration of deliberate
lack of cooperation and coordination between departments.
I feel kind of strongly about this ever since, as a student, the physics people
expected me to use mathematics that I had not been taught yet...

;-)

I shall try to refrain from commenting on the concept of introducing
recursion into a first course in CS - I am too much tainted by my ability
to mentally "see" the stack growth in a small processor to be qualified
to comment.

- Hendrik

[cokofreedom@gmail.com]

Re: Iteration for Factorials

On Oct 23, 8:53 am, "Hendrik van Rooyen" <m...@microcorp .co.zawrote:

"Marco Mariani" <marc....arta.c omwrote:
>

I don't see how my answer is in any way worse than those based on
lambda. Maybe I'm just envious because when I was his age I couldn't
google for answers. He should at least be able to do that, shouldn't he?
But wait. That would mean understanding what a factorial is. That would
require a second search, or a textbook, or an understanding of
arithmetics before programming with or without recursion. Should we
blame the teachers?

>
Yes. And burn their cars to get their attention!
>
Asking someone to write a factorial algorithm before he knows WTF a
factorial "is", is either insane, or the ultimate demonstration of deliberate
lack of cooperation and coordination between departments.
I feel kind of strongly about this ever since, as a student, the physics people
expected me to use mathematics that I had not been taught yet...
>
;-)
>
I shall try to refrain from commenting on the concept of introducing
recursion into a first course in CS - I am too much tainted by my ability
to mentally "see" the stack growth in a small processor to be qualified
to comment.
>
- Hendrik

Completely agree with this point of view. After being on the receiving
end of such problems when first introduced to Haskell and told to look
at a database written in it and work my way through it (without having
started the course on databases, locks, or any of that jargon) you
find yourself almost helpless at times.

Hard to google for something you don't know about.

Recursive calling is a fun, and yet painful, thing...

[Marco Mariani]

Re: Iteration for Factorials

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

[tokland@gmail.com]

Re: Iteration for Factorials

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? if not allowing negative numbers is so
important for you, add a if statement and raise a ValueError exception.

[cokofreedom@gmail.com]

Re: Iteration for Factorials

On Oct 23, 1:58 pm, 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? if not allowing negative numbers is so
important for you, add a if statement and raise a ValueError exception.

indeed, especially considering that fact(x) is essentially just a
lambda statement as Marco Mariani said.