Variation of finding edit distance with only insertions and deletions?

Question

I need to find the edit distance between a word and its sorted word (ex: apple and aelpp), using only insertions and deletions recursively.

I have found some sources that used insertions, deletions, and substitutions, but I am not sure how to only use insertion and deletion.

This is the code I found:

def ld(s, t):
    if not s: return len(t)
    if not t: return len(s)
    if s[0] == t[0]: return ld(s[1:], t[1:])
    l1 = ld(s, t[1:])
    l2 = ld(s[1:], t)
    l3 = ld(s[1:], t[1:])
    return 1 + min(l1, l2, l3)

What edits would need to be made to only find the number of insertions and deletions?

Answer 1

Remove l3, which computes substitutions like so

def ld2(s, t):
    if not s: return len(t)
    if not t: return len(s)
    if s[0] == t[0]: return ld2(s[1:], t[1:])
    l1 = ld2(s, t[1:])
    l2 = ld2(s[1:], t)
    return 1 + min(l1, l2)

You can see that ld('apple', 'applx') is equal to 1, while ld2 with the same parameters evaluates to 2.