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Calculate edit distance with simple (memoized) recursive algorithm
def distance(s, t, cache=None):
"""Return minimum edit distance between s and t, where an edit
is a character substitution, deletion, or addition.
if not s:
return len(t)
if not t:
return len(s)
if cache is None:
cache = {}
key = (s, t)
if key in cache:
return cache[key]
if s[0] == t[0]:
# First chars equal, return edit distance of the rest
d = distance(s[1:], t[1:], cache)
# First chars not equal, it's 1 + edit distance of the rest
d = 1 + min(
distance(s[1:], t[1:], cache), # substitution of first chars
distance(s[1:], t, cache), # delete first char of s
distance(s, t[1:], cache), # delete first char of t (addition)
cache[key] = d
return d
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