# [Python-bugs-list] [ python-Bugs-645629 ] SequenceMatcher finds suboptimal sequenc

Fri, 29 Nov 2002 20:15:40 -0800

```Bugs item #645629, was opened at 2002-11-29 10:54
You can respond by visiting:
https://sourceforge.net/tracker/?func=detail&atid=105470&aid=645629&group_id=5470

Category: Python Library
Group: Python 2.2.2
Status: Open
Resolution: None
>Priority: 3
Submitted By: David Necas (yeti-dn)
Assigned to: Tim Peters (tim_one)
Summary: SequenceMatcher finds suboptimal sequenc

Initial Comment:
The algorithm used for approximate string matching
doesn't find the optimal edit sequence (it finds

Example:

>>> from difflib import SequenceMatcher
>>> sm = SequenceMatcher()
>>> sm.set_seqs('axfot', 'aoftax')
>>> sm.ratio()
0.36363636363636365
>>> sm.get_matching_blocks()
[(0, 4, 2), (5, 6, 0)]
>>> sm.get_opcodes()
[('insert', 0, 0, 0, 4), ('equal', 0, 2, 4, 6),
('delete', 2, 5, 6, 6)]

What's wrong?

Levenshtein distance with weight 2 for item replacement
is only 5 (the weight 2 corresponds to what ratio() is
supposed to compute, the classic Levenshtein distance
is 4), so one would expect to get similarity (i.e.
ratio()) (11-5)/11 = 6/11 = 0.545454545454..., and not
only 4/11.

And really, the maximal matching blocks are:
[(0, 0, 1), (2, 2, 1), (4, 3, 1)]
and the minimal edit sequence is:
[('equal', 0, 1, 0, 1), ('replace', 1, 2, 1, 2),
('equal', 2, 3, 2, 3), ('delete', 3, 4, 3, 3),
('equal', 4, 5, 3, 4), ('insert', 5, 5, 4, 6)]

The impact of this ``feature'' on diff-like
applications may be even positive, beause the edit
sequence then consists of smaller number of operations
on lager chunks.  Thus I'm not sure if this is
something which should be fixed.  However, it should be
at least noted in the documentation the ratio()
function gives only a lower bound of the string
similarity (so people like me won't be tempted to use
it to check results of their own Levenshtein
distance/string similarity implementation).

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>Comment By: David Necas (yeti-dn)
Date: 2002-11-30 04:15

Message:
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OK, I know it's not Levenshtein because I've read the
source, and I agree I should really read the docs first and
the source after, it's actually written in the docs.

However, the docs say

`This does not yield minimal edit sequences, but does tend
to yield matches that ``look right'' to people.'

This is not true -- see my last posting.  Or perhaps you
really think matching `Observation' looks better to people
than matching the smaller parts from the rest of the string
matches it finds can be arbitrarily bad, at least (e.g., the
ratio between optimal and difflib's best match can be as big
as (N-1)^2/4N, where N is sequence length (of both sequecnes)).

Thank you.

----------------------------------------------------------------------

Comment By: Tim Peters (tim_one)
Date: 2002-11-29 16:03

Message:
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user_id=31435

algorithm, and it doesn't care about finding minimal edit
distance.

----------------------------------------------------------------------

Comment By: David Necas (yeti-dn)
Date: 2002-11-29 12:58

Message:
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user_id=658986

Sorry, I've changed my mind.  This definitely should be
fixed.  In following strings finding `Observation'
effectively inhibits finding the much better match:

sm.set_seqs('Observation: What seems as a small glitch at
the first sight may have large impact',
'What-seems-as-a-small-glitch-at-the-first-sight-may-have-large-impact
(Observation)')

Unfortunately this probably means complete rewrite, I can't
see how the current algorithm could be changed to work in
this case (but I don't understand it 100%, so maybe...).

----------------------------------------------------------------------

You can respond by visiting:
https://sourceforge.net/tracker/?func=detail&atid=105470&aid=645629&group_id=5470

```