deletion distance between words

Question

I'm trying to find how many characters I would need to delete to make the two words the same. For instance "at", "cat" would be 1 because I could delete the c, "boat" and "got" would be 3 because I could delete the b,a and g to make it ot. I put the words into a dictionary with their count as the value. Then I iterate over the dictionary and see if that key exists in the other dictionary otherwise I add 1 to the difference. Is this a very inefficient algorithm?

But it is overestimating the number of deletions I need.

def deletiondistance(firstword, secondword):
dfw = {}
dsw = {}
diff = 0
for i in range(len(firstword)):
    print firstword[i]
    if firstword[i] in dfw:
        dfw[firstword[i]]+=1
    else:
        dfw[firstword[i]]=1
for j in range(len(secondword)):
    if secondword[j] in dsw:
        dsw[secondword[j]] +=1
    else:
        dsw[secondword[j]]=1

for key, value in dfw.iteritems():

    if key in dsw:
        #print "key exists"
        pass

    else:
        diff +=1

print "diff",diff

Answer 1

As @Hulk mentioned this is similar to levenshtein distance. The only difference is that substitutions are not allowed but that can be rectified by using substitution cost of 2 which is the same as removing character from both strings. Example:

def dist(s1, s2):
    cur = list(range(len(s2) + 1))
    prev = [0] * (len(s2) + 1)
    for i in range(len(s1)):
        cur, prev = prev, cur
        cur[0] = i + 1
        for j in range(len(s2)):
            # Substitution is same as two deletions
            sub = 0 if s1[i] == s2[j] else 2
            cur[j+1] = min(prev[j] + sub, cur[j] + 1, prev[j+1] + 1)

    return cur[-1]

cases=[('cat','bat'),
       ('bat','cat'),
       ('broom', 'ballroom'),
       ('boat','got'),
       ('foo', 'bar'),
       ('foobar', '')]

for s1, s2 in cases:
    print('{} & {} = {}'.format(s1, s2, dist(s1, s2)))

Output:

cat & bat = 2
bat & cat = 2
broom & ballroom = 3
boat & got = 3
foo & bar = 6
foobar &  = 6

Answer 2

I think your goal is similar to levenshtein distance.

Levenshtein distance is a metric for measuring distance between 2 strings.

Here is a wiki-link. https://en.wikipedia.org/wiki/Levenshtein_distance

And here is pypi package for levenshtein distance. https://pypi.python.org/pypi/python-Levenshtein