[Tutor] global variables & recursion

[Alan Gauld]

> Particularly I'm not sure if using global variables is a good idea.

Its hardly ever a good idea. Much better to pass them in as
arguments to the function

> def gcd(a,b):
>    ...

No probs there

> # global variables (is this bad programming style?)

Usually

> _eulen = 0  # recursion depth
> _rem = []   # list of remainders
>
> def st(a,b):

Change to:

def st(a,b,c,d):
    eulen = c
    rem = d

    # 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
       rem = []

    else:              # not finished.

       # we will need this information later:
       eulen += 1
       rem.append(a)
       rem.append(b)

       # function calls itself:
       st(b,r,eulen,rem)



That uses the same algorithm but avoids the global variables by
simply passing them in as arguments.

Now as to whether the basic algorithm can be improved, and I think
it can, I'll leave to someone else, like Danny - who seems to
particularly enjoy these little mathematical games... :-)

Alan G.