[Tutor] global variables & recursion

[Gregor Lingl]

Hi Alice! (Hi Robin Hood?)

alice schrieb:

>I would like some advice.
>  
>
I'll try. As your second problem, determioning s and t is a generaliziation
of  the simplecomputation of gcd, I'll concentrate on  this.  (Although  
there
are 'famous' versions of euclids algorithm which are well worth discussing.
So if you are interested in it,  feel fre to ask more ...)

>Is there a better way of doing this?
>Particularly I'm not sure if using global variables is a good idea.
>  
>
Generally you should avoid using global variables, if it can easily be done.

># Find integers s and t such that as + bt = gcd(a,b):
>
># global variables (is this bad programming style?)
>  
>
A standard way to do so is passing them as parameters with
default arguments.

>## _eulen = 0  # recursion depth
>## _rem = []   # list of remainders
>
>def st(a,b,_eulen=0, _rem=[]):
>
>##    global _eulen
>##    global _rem
>
>    # a should be bigger than b:
>    if (b > a):
>       a, b = b, a
>
>    # find remainder:
>    r = a % b
>
>    if (r == 0):        # finished
>
>       # find s and t:
>       s = 1
>       t = 1 - (a / b)
>       for i in range(_eulen):
>           b = _rem.pop()
>           a = _rem.pop()
>           s,t = t, s - (a/b)*t
>
>       # show results:
>       print "gcd(%d,%d) = (%d)(%d) + (%d)(%d) = %d" % (a,b,a,s,b,t,a*s+b*t)
>
>       # reset _eulen and _rem:
>##       _eulen = 0
>  
>
## Interestingly it is not necessary to reset :eulen, as it is set to 0
## when st() is defined, and cannot be changed, because integers are
## immutable python objects
## the contrary is true for _rem, which as a list is a mutable python 
object *and*
## will be changed during the run of this version of your function.
## (This issue is a bit tricky)

>       _rem = []
>
>    else:              # not finished.
>
>       # we will need this information later:
>##       _eulen += 1  ## will be passed as argument (see below)
>       _rem.append(a)
>       _rem.append(b)
>
>       # function calls itself:
>       st(b,r,_eulen+1)
>  
>
## Here _rem need not be inserted as argument as it si the default value 
of this
## fourth parameter.

I'll show you some more 'amendments in a follow up posting

Regards, Gregor