Sometimes you need quick and dirty implementation of greatest common divisor and its extended variant. Actually, because the fractions module comes gcd function, probably the implementation of the exteded greatest common divisor algorithm is more useful. Both implementations are recursive, but work nonetheless even for comparatively large integers.

# simply returns the gcd
gcd = lambda a,b: gcd(b, a % b) if b else a

# egcd(a,b) returns (d,x,y) where d == a*x + b*y
egcd = lambda a,b: (lambda d,x,y: (d, y, x - (a // b) * y))(*egcd(b, a % b)) if b else (a, 1, 0)

The code above is Python 2 and 3 compatible.

I’ve been using python to write various bots and crawler for a long time. Few days ago I needed to write some simple bot to remove some 400+ spam pages in Sikumuna, I took an old script of mine (from 2006) in order to modify it. The script used ClientForm, a python module that allows you to easily parse and fill html forms using python. I quickly found that ClientForm is now deprecated in favor of mechanize. In the beginning I was partly set back by the change, as ClientForm was pretty easy to use, and mechanize‘s documentation could use some improvement. However, I quickly changed my mind about mechanize. The basic interface for mechanize is a simple browser object, that litteraly allows you to browse using python. It takes care of handling cookies and such and it got similar form-filling abilities to ClientForm, but this time they are integrated into the browser object.

For future reference for myself, and as another code example to mechanizes sparse documentation I’m giving below the gist of the simple bot I wrote:

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Damerau-Levenshtein Distance is a metric for measuring how far two given strings are, in terms of 4 basic operations:

• deletion
• insertion
• substitution
• transposition

The distance of two strings are the minimal number of such operations needed to transform the first string to the second. The algorithm can be used to create spelling correction suggestions, by finding the closest word from a given list to the users input. See Damerau–Levenshtein distance (Wikipedia) for more info on the subject.

Here is an of the algorithm (restricted edit distance version) in Python. While this implementation isn’t perfect (performance wise) it is well suited for many applications.

"""
Compute the Damerau-Levenshtein distance between two given
strings (s1 and s2)
"""
def damerau_levenshtein_distance(s1, s2):
    d = {}
    lenstr1 = len(s1)
    lenstr2 = len(s2)
    for i in xrange(-1,lenstr1+1):
        d[(i,-1)] = i+1
    for j in xrange(-1,lenstr2+1):
        d[(-1,j)] = j+1

    for i in xrange(lenstr1):
        for j in xrange(lenstr2):
            if s1[i] == s2[j]:
                cost = 0
            else:
                cost = 1
            d[(i,j)] = min(
                           d[(i-1,j)] + 1, # deletion
                           d[(i,j-1)] + 1, # insertion
                           d[(i-1,j-1)] + cost, # substitution
                          )
            if i and j and s1[i]==s2[j-1] and s1[i-1] == s2[j]:
                d[(i,j)] = min (d[(i,j)], d[i-2,j-2] + cost) # transposition

    return d[lenstr1-1,lenstr2-1]

Update 24 Mar, 2012: Fixed the error in computing transposition at the beginning of the strings.