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\section{\module{difflib} ---
Helpers for computing deltas}
\declaremodule{standard}{difflib}
\modulesynopsis{Helpers for computing differences between objects.}
\moduleauthor{Tim Peters}{tim_one@users.sourceforge.net}
\sectionauthor{Tim Peters}{tim_one@users.sourceforge.net}
% LaTeXification by Fred L. Drake, Jr. <fdrake@acm.org>.
\versionadded{2.1}
\begin{classdesc*}{SequenceMatcher}
This is a flexible class for comparing pairs of sequences of any
type, so long as the sequence elements are hashable. The basic
algorithm predates, and is a little fancier than, an algorithm
published in the late 1980's by Ratcliff and Obershelp under the
hyperbolic name ``gestalt pattern matching.'' The idea is to find
the longest contiguous matching subsequence that contains no
``junk'' elements (the Ratcliff and Obershelp algorithm doesn't
address junk). The same idea is then applied recursively to the
pieces of the sequences to the left and to the right of the matching
subsequence. This does not yield minimal edit sequences, but does
tend to yield matches that ``look right'' to people.
\strong{Timing:} The basic Ratcliff-Obershelp algorithm is cubic
time in the worst case and quadratic time in the expected case.
\class{SequenceMatcher} is quadratic time for the worst case and has
expected-case behavior dependent in a complicated way on how many
elements the sequences have in common; best case time is linear.
\end{classdesc*}
\begin{classdesc*}{Differ}
This is a class for comparing sequences of lines of text, and
producing human-readable differences or deltas. Differ uses
\class{SequenceMatcher} both to compare sequences of lines, and to
compare sequences of characters within similar (near-matching)
lines.
Each line of a \class{Differ} delta begins with a two-letter code:
\begin{tableii}{l|l}{code}{Code}{Meaning}
\lineii{'- '}{line unique to sequence 1}
\lineii{'+ '}{line unique to sequence 2}
\lineii{' '}{line common to both sequences}
\lineii{'? '}{line not present in either input sequence}
\end{tableii}
Lines beginning with `\code{?~}' attempt to guide the eye to
intraline differences, and were not present in either input
sequence. These lines can be confusing if the sequences contain tab
characters.
\end{classdesc*}
\begin{classdesc*}{HtmlDiff}
This class can be used to create an HTML table (or a complete HTML file
containing the table) showing a side by side, line by line comparision
of text with inter-line and intra-line change highlights. The table can
be generated in either full or contextual difference mode.
The constructor for this class is:
\begin{funcdesc}{__init__}{
\optional{, tabsize
\optional{, wrapcolumn
\optional{, linejunk
\optional{, charjunk}}}}}
Initializes instance of \class{HtmlDiff}.
\var{tabsize} is an optional keyword argument to specify tab stop spacing
and defaults to \code{8}.
\var{wrapcolumn} is an optional keyword to specify column number where
lines are broken and wrapped, defaults to \code{None} where lines are not
wrapped.
\var{linejunk} and \var{charjunk} are optional keyword arguments passed
into \code{ndiff()} (used to by \class{HtmlDiff} to generate the
side by side HTML differences). See \code{ndiff()} documentation for
argument default values and descriptions.
\end{funcdesc}
The following methods are public:
\begin{funcdesc}{make_file}{fromlines, tolines
\optional{, fromdesc
\optional{, todesc
\optional{, context
\optional{, numlines}}}}}
Compares \var{fromlines} and \var{tolines} (lists of strings) and returns
a string which is a complete HTML file containing a table showing line by
line differences with inter-line and intra-line changes highlighted.
\var{fromdesc} and \var{todesc} are optional keyword arguments to specify
from/to file column header strings (both default to an empty string).
\var{context} and \var{numlines} are both optional keyword arguments.
Set \var{context} to \code{True} when contextual differences are to be
shown, else the default is \code{False} to show the full files.
\var{numlines} defaults to \code{5}. When \var{context} is \code{True}
\var{numlines} controls the number of context lines which surround the
difference highlights. When \var{context} is \code{False} \var{numlines}
controls the number of lines which are shown before a difference
highlight when using the "next" hyperlinks (setting to zero would cause
the "next" hyperlinks to place the next difference highlight at the top of
the browser without any leading context).
\end{funcdesc}
\begin{funcdesc}{make_table}{fromlines, tolines
\optional{, fromdesc
\optional{, todesc
\optional{, context}}}}
Compares \var{fromlines} and \var{tolines} (lists of strings) and returns
a string which is a complete HTML table showing line by line differences
with inter-line and intra-line changes highlighted.
The arguments of this method are a subset of those for the
\code{make_file} method. Refer to the \code{make_file} method
documentation.
\end{funcdesc}
\file{Tools/scripts/ndiff.py} is a command-line front-end to this class
and contains a good example of its use.
\end{classdesc*}
\begin{funcdesc}{context_diff}{a, b\optional{, fromfile\optional{, tofile
\optional{, fromfiledate\optional{, tofiledate\optional{, n
\optional{, lineterm}}}}}}}
Compare \var{a} and \var{b} (lists of strings); return a
delta (a generator generating the delta lines) in context diff
format.
Context diffs are a compact way of showing just the lines that have
changed plus a few lines of context. The changes are shown in a
before/after style. The number of context lines is set by \var{n}
which defaults to three.
By default, the diff control lines (those with \code{***} or \code{---})
are created with a trailing newline. This is helpful so that inputs created
from \function{file.readlines()} result in diffs that are suitable for use
with \function{file.writelines()} since both the inputs and outputs have
trailing newlines.
For inputs that do not have trailing newlines, set the \var{lineterm}
argument to \code{""} so that the output will be uniformly newline free.
The context diff format normally has a header for filenames and
modification times. Any or all of these may be specified using strings for
\var{fromfile}, \var{tofile}, \var{fromfiledate}, and \var{tofiledate}.
The modification times are normally expressed in the format returned by
\function{time.ctime()}. If not specified, the strings default to blanks.
\file{Tools/scripts/diff.py} is a command-line front-end for this
function.
\versionadded{2.3}
\end{funcdesc}
\begin{funcdesc}{get_close_matches}{word, possibilities\optional{,
n\optional{, cutoff}}}
Return a list of the best ``good enough'' matches. \var{word} is a
sequence for which close matches are desired (typically a string),
and \var{possibilities} is a list of sequences against which to
match \var{word} (typically a list of strings).
Optional argument \var{n} (default \code{3}) is the maximum number
of close matches to return; \var{n} must be greater than \code{0}.
Optional argument \var{cutoff} (default \code{0.6}) is a float in
the range [0, 1]. Possibilities that don't score at least that
similar to \var{word} are ignored.
The best (no more than \var{n}) matches among the possibilities are
returned in a list, sorted by similarity score, most similar first.
\begin{verbatim}
>>> get_close_matches('appel', ['ape', 'apple', 'peach', 'puppy'])
['apple', 'ape']
>>> import keyword
>>> get_close_matches('wheel', keyword.kwlist)
['while']
>>> get_close_matches('apple', keyword.kwlist)
[]
>>> get_close_matches('accept', keyword.kwlist)
['except']
\end{verbatim}
\end{funcdesc}
\begin{funcdesc}{ndiff}{a, b\optional{, linejunk\optional{,
charjunk}}}
Compare \var{a} and \var{b} (lists of strings); return a
\class{Differ}-style delta (a generator generating the delta lines).
Optional keyword parameters \var{linejunk} and \var{charjunk} are
for filter functions (or \code{None}):
\var{linejunk}: A function that accepts a single string
argument, and returns true if the string is junk, or false if not.
The default is (\code{None}), starting with Python 2.3. Before then,
the default was the module-level function
\function{IS_LINE_JUNK()}, which filters out lines without visible
characters, except for at most one pound character (\character{\#}).
As of Python 2.3, the underlying \class{SequenceMatcher} class
does a dynamic analysis of which lines are so frequent as to
constitute noise, and this usually works better than the pre-2.3
default.
\var{charjunk}: A function that accepts a character (a string of
length 1), and returns if the character is junk, or false if not.
The default is module-level function \function{IS_CHARACTER_JUNK()},
which filters out whitespace characters (a blank or tab; note: bad
idea to include newline in this!).
\file{Tools/scripts/ndiff.py} is a command-line front-end to this
function.
\begin{verbatim}
>>> diff = ndiff('one\ntwo\nthree\n'.splitlines(1),
... 'ore\ntree\nemu\n'.splitlines(1))
>>> print ''.join(diff),
- one
? ^
+ ore
? ^
- two
- three
? -
+ tree
+ emu
\end{verbatim}
\end{funcdesc}
\begin{funcdesc}{restore}{sequence, which}
Return one of the two sequences that generated a delta.
Given a \var{sequence} produced by \method{Differ.compare()} or
\function{ndiff()}, extract lines originating from file 1 or 2
(parameter \var{which}), stripping off line prefixes.
Example:
\begin{verbatim}
>>> diff = ndiff('one\ntwo\nthree\n'.splitlines(1),
... 'ore\ntree\nemu\n'.splitlines(1))
>>> diff = list(diff) # materialize the generated delta into a list
>>> print ''.join(restore(diff, 1)),
one
two
three
>>> print ''.join(restore(diff, 2)),
ore
tree
emu
\end{verbatim}
\end{funcdesc}
\begin{funcdesc}{unified_diff}{a, b\optional{, fromfile\optional{, tofile
\optional{, fromfiledate\optional{, tofiledate\optional{, n
\optional{, lineterm}}}}}}}
Compare \var{a} and \var{b} (lists of strings); return a
delta (a generator generating the delta lines) in unified diff
format.
Unified diffs are a compact way of showing just the lines that have
changed plus a few lines of context. The changes are shown in a
inline style (instead of separate before/after blocks). The number
of context lines is set by \var{n} which defaults to three.
By default, the diff control lines (those with \code{---}, \code{+++},
or \code{@@}) are created with a trailing newline. This is helpful so
that inputs created from \function{file.readlines()} result in diffs
that are suitable for use with \function{file.writelines()} since both
the inputs and outputs have trailing newlines.
For inputs that do not have trailing newlines, set the \var{lineterm}
argument to \code{""} so that the output will be uniformly newline free.
The context diff format normally has a header for filenames and
modification times. Any or all of these may be specified using strings for
\var{fromfile}, \var{tofile}, \var{fromfiledate}, and \var{tofiledate}.
The modification times are normally expressed in the format returned by
\function{time.ctime()}. If not specified, the strings default to blanks.
\file{Tools/scripts/diff.py} is a command-line front-end for this
function.
\versionadded{2.3}
\end{funcdesc}
\begin{funcdesc}{IS_LINE_JUNK}{line}
Return true for ignorable lines. The line \var{line} is ignorable
if \var{line} is blank or contains a single \character{\#},
otherwise it is not ignorable. Used as a default for parameter
\var{linejunk} in \function{ndiff()} before Python 2.3.
\end{funcdesc}
\begin{funcdesc}{IS_CHARACTER_JUNK}{ch}
Return true for ignorable characters. The character \var{ch} is
ignorable if \var{ch} is a space or tab, otherwise it is not
ignorable. Used as a default for parameter \var{charjunk} in
\function{ndiff()}.
\end{funcdesc}
\begin{seealso}
\seetitle[http://www.ddj.com/documents/s=1103/ddj8807c/]
{Pattern Matching: The Gestalt Approach}{Discussion of a
similar algorithm by John W. Ratcliff and D. E. Metzener.
This was published in
\citetitle[http://www.ddj.com/]{Dr. Dobb's Journal} in
July, 1988.}
\end{seealso}
\subsection{SequenceMatcher Objects \label{sequence-matcher}}
The \class{SequenceMatcher} class has this constructor:
\begin{classdesc}{SequenceMatcher}{\optional{isjunk\optional{,
a\optional{, b}}}}
Optional argument \var{isjunk} must be \code{None} (the default) or
a one-argument function that takes a sequence element and returns
true if and only if the element is ``junk'' and should be ignored.
Passing \code{None} for \var{b} is equivalent to passing
\code{lambda x: 0}; in other words, no elements are ignored. For
example, pass:
\begin{verbatim}
lambda x: x in " \t"
\end{verbatim}
if you're comparing lines as sequences of characters, and don't want
to synch up on blanks or hard tabs.
The optional arguments \var{a} and \var{b} are sequences to be
compared; both default to empty strings. The elements of both
sequences must be hashable.
\end{classdesc}
\class{SequenceMatcher} objects have the following methods:
\begin{methoddesc}{set_seqs}{a, b}
Set the two sequences to be compared.
\end{methoddesc}
\class{SequenceMatcher} computes and caches detailed information about
the second sequence, so if you want to compare one sequence against
many sequences, use \method{set_seq2()} to set the commonly used
sequence once and call \method{set_seq1()} repeatedly, once for each
of the other sequences.
\begin{methoddesc}{set_seq1}{a}
Set the first sequence to be compared. The second sequence to be
compared is not changed.
\end{methoddesc}
\begin{methoddesc}{set_seq2}{b}
Set the second sequence to be compared. The first sequence to be
compared is not changed.
\end{methoddesc}
\begin{methoddesc}{find_longest_match}{alo, ahi, blo, bhi}
Find longest matching block in \code{\var{a}[\var{alo}:\var{ahi}]}
and \code{\var{b}[\var{blo}:\var{bhi}]}.
If \var{isjunk} was omitted or \code{None},
\method{get_longest_match()} returns \code{(\var{i}, \var{j},
\var{k})} such that \code{\var{a}[\var{i}:\var{i}+\var{k}]} is equal
to \code{\var{b}[\var{j}:\var{j}+\var{k}]}, where
\code{\var{alo} <= \var{i} <= \var{i}+\var{k} <= \var{ahi}} and
\code{\var{blo} <= \var{j} <= \var{j}+\var{k} <= \var{bhi}}.
For all \code{(\var{i'}, \var{j'}, \var{k'})} meeting those
conditions, the additional conditions
\code{\var{k} >= \var{k'}},
\code{\var{i} <= \var{i'}},
and if \code{\var{i} == \var{i'}}, \code{\var{j} <= \var{j'}}
are also met.
In other words, of all maximal matching blocks, return one that
starts earliest in \var{a}, and of all those maximal matching blocks
that start earliest in \var{a}, return the one that starts earliest
in \var{b}.
\begin{verbatim}
>>> s = SequenceMatcher(None, " abcd", "abcd abcd")
>>> s.find_longest_match(0, 5, 0, 9)
(0, 4, 5)
\end{verbatim}
If \var{isjunk} was provided, first the longest matching block is
determined as above, but with the additional restriction that no
junk element appears in the block. Then that block is extended as
far as possible by matching (only) junk elements on both sides.
So the resulting block never matches on junk except as identical
junk happens to be adjacent to an interesting match.
Here's the same example as before, but considering blanks to be junk.
That prevents \code{' abcd'} from matching the \code{' abcd'} at the
tail end of the second sequence directly. Instead only the
\code{'abcd'} can match, and matches the leftmost \code{'abcd'} in
the second sequence:
\begin{verbatim}
>>> s = SequenceMatcher(lambda x: x==" ", " abcd", "abcd abcd")
>>> s.find_longest_match(0, 5, 0, 9)
(1, 0, 4)
\end{verbatim}
If no blocks match, this returns \code{(\var{alo}, \var{blo}, 0)}.
\end{methoddesc}
\begin{methoddesc}{get_matching_blocks}{}
Return list of triples describing matching subsequences.
Each triple is of the form \code{(\var{i}, \var{j}, \var{n})}, and
means that \code{\var{a}[\var{i}:\var{i}+\var{n}] ==
\var{b}[\var{j}:\var{j}+\var{n}]}. The triples are monotonically
increasing in \var{i} and \var{j}.
The last triple is a dummy, and has the value \code{(len(\var{a}),
len(\var{b}), 0)}. It is the only triple with \code{\var{n} == 0}.
% Explain why a dummy is used!
\begin{verbatim}
>>> s = SequenceMatcher(None, "abxcd", "abcd")
>>> s.get_matching_blocks()
[(0, 0, 2), (3, 2, 2), (5, 4, 0)]
\end{verbatim}
\end{methoddesc}
\begin{methoddesc}{get_opcodes}{}
Return list of 5-tuples describing how to turn \var{a} into \var{b}.
Each tuple is of the form \code{(\var{tag}, \var{i1}, \var{i2},
\var{j1}, \var{j2})}. The first tuple has \code{\var{i1} ==
\var{j1} == 0}, and remaining tuples have \var{i1} equal to the
\var{i2} from the preceeding tuple, and, likewise, \var{j1} equal to
the previous \var{j2}.
The \var{tag} values are strings, with these meanings:
\begin{tableii}{l|l}{code}{Value}{Meaning}
\lineii{'replace'}{\code{\var{a}[\var{i1}:\var{i2}]} should be
replaced by \code{\var{b}[\var{j1}:\var{j2}]}.}
\lineii{'delete'}{\code{\var{a}[\var{i1}:\var{i2}]} should be
deleted. Note that \code{\var{j1} == \var{j2}} in
this case.}
\lineii{'insert'}{\code{\var{b}[\var{j1}:\var{j2}]} should be
inserted at \code{\var{a}[\var{i1}:\var{i1}]}.
Note that \code{\var{i1} == \var{i2}} in this
case.}
\lineii{'equal'}{\code{\var{a}[\var{i1}:\var{i2}] ==
\var{b}[\var{j1}:\var{j2}]} (the sub-sequences are
equal).}
\end{tableii}
For example:
\begin{verbatim}
>>> a = "qabxcd"
>>> b = "abycdf"
>>> s = SequenceMatcher(None, a, b)
>>> for tag, i1, i2, j1, j2 in s.get_opcodes():
... print ("%7s a[%d:%d] (%s) b[%d:%d] (%s)" %
... (tag, i1, i2, a[i1:i2], j1, j2, b[j1:j2]))
delete a[0:1] (q) b[0:0] ()
equal a[1:3] (ab) b[0:2] (ab)
replace a[3:4] (x) b[2:3] (y)
equal a[4:6] (cd) b[3:5] (cd)
insert a[6:6] () b[5:6] (f)
\end{verbatim}
\end{methoddesc}
\begin{methoddesc}{get_grouped_opcodes}{\optional{n}}
Return a generator of groups with up to \var{n} lines of context.
Starting with the groups returned by \method{get_opcodes()},
this method splits out smaller change clusters and eliminates
intervening ranges which have no changes.
The groups are returned in the same format as \method{get_opcodes()}.
\versionadded{2.3}
\end{methoddesc}
\begin{methoddesc}{ratio}{}
Return a measure of the sequences' similarity as a float in the
range [0, 1].
Where T is the total number of elements in both sequences, and M is
the number of matches, this is 2.0*M / T. Note that this is
\code{1.0} if the sequences are identical, and \code{0.0} if they
have nothing in common.
This is expensive to compute if \method{get_matching_blocks()} or
\method{get_opcodes()} hasn't already been called, in which case you
may want to try \method{quick_ratio()} or
\method{real_quick_ratio()} first to get an upper bound.
\end{methoddesc}
\begin{methoddesc}{quick_ratio}{}
Return an upper bound on \method{ratio()} relatively quickly.
This isn't defined beyond that it is an upper bound on
\method{ratio()}, and is faster to compute.
\end{methoddesc}
\begin{methoddesc}{real_quick_ratio}{}
Return an upper bound on \method{ratio()} very quickly.
This isn't defined beyond that it is an upper bound on
\method{ratio()}, and is faster to compute than either
\method{ratio()} or \method{quick_ratio()}.
\end{methoddesc}
The three methods that return the ratio of matching to total characters
can give different results due to differing levels of approximation,
although \method{quick_ratio()} and \method{real_quick_ratio()} are always
at least as large as \method{ratio()}:
\begin{verbatim}
>>> s = SequenceMatcher(None, "abcd", "bcde")
>>> s.ratio()
0.75
>>> s.quick_ratio()
0.75
>>> s.real_quick_ratio()
1.0
\end{verbatim}
\subsection{SequenceMatcher Examples \label{sequencematcher-examples}}
This example compares two strings, considering blanks to be ``junk:''
\begin{verbatim}
>>> s = SequenceMatcher(lambda x: x == " ",
... "private Thread currentThread;",
... "private volatile Thread currentThread;")
\end{verbatim}
\method{ratio()} returns a float in [0, 1], measuring the similarity
of the sequences. As a rule of thumb, a \method{ratio()} value over
0.6 means the sequences are close matches:
\begin{verbatim}
>>> print round(s.ratio(), 3)
0.866
\end{verbatim}
If you're only interested in where the sequences match,
\method{get_matching_blocks()} is handy:
\begin{verbatim}
>>> for block in s.get_matching_blocks():
... print "a[%d] and b[%d] match for %d elements" % block
a[0] and b[0] match for 8 elements
a[8] and b[17] match for 6 elements
a[14] and b[23] match for 15 elements
a[29] and b[38] match for 0 elements
\end{verbatim}
Note that the last tuple returned by \method{get_matching_blocks()} is
always a dummy, \code{(len(\var{a}), len(\var{b}), 0)}, and this is
the only case in which the last tuple element (number of elements
matched) is \code{0}.
If you want to know how to change the first sequence into the second,
use \method{get_opcodes()}:
\begin{verbatim}
>>> for opcode in s.get_opcodes():
... print "%6s a[%d:%d] b[%d:%d]" % opcode
equal a[0:8] b[0:8]
insert a[8:8] b[8:17]
equal a[8:14] b[17:23]
equal a[14:29] b[23:38]
\end{verbatim}
See also the function \function{get_close_matches()} in this module,
which shows how simple code building on \class{SequenceMatcher} can be
used to do useful work.
\subsection{Differ Objects \label{differ-objects}}
Note that \class{Differ}-generated deltas make no claim to be
\strong{minimal} diffs. To the contrary, minimal diffs are often
counter-intuitive, because they synch up anywhere possible, sometimes
accidental matches 100 pages apart. Restricting synch points to
contiguous matches preserves some notion of locality, at the
occasional cost of producing a longer diff.
The \class{Differ} class has this constructor:
\begin{classdesc}{Differ}{\optional{linejunk\optional{, charjunk}}}
Optional keyword parameters \var{linejunk} and \var{charjunk} are
for filter functions (or \code{None}):
\var{linejunk}: A function that accepts a single string
argument, and returns true if the string is junk. The default is
\code{None}, meaning that no line is considered junk.
\var{charjunk}: A function that accepts a single character argument
(a string of length 1), and returns true if the character is junk.
The default is \code{None}, meaning that no character is
considered junk.
\end{classdesc}
\class{Differ} objects are used (deltas generated) via a single
method:
\begin{methoddesc}{compare}{a, b}
Compare two sequences of lines, and generate the delta (a sequence
of lines).
Each sequence must contain individual single-line strings ending
with newlines. Such sequences can be obtained from the
\method{readlines()} method of file-like objects. The delta generated
also consists of newline-terminated strings, ready to be printed as-is
via the \method{writelines()} method of a file-like object.
\end{methoddesc}
\subsection{Differ Example \label{differ-examples}}
This example compares two texts. First we set up the texts, sequences
of individual single-line strings ending with newlines (such sequences
can also be obtained from the \method{readlines()} method of file-like
objects):
\begin{verbatim}
>>> text1 = ''' 1. Beautiful is better than ugly.
... 2. Explicit is better than implicit.
... 3. Simple is better than complex.
... 4. Complex is better than complicated.
... '''.splitlines(1)
>>> len(text1)
4
>>> text1[0][-1]
'\n'
>>> text2 = ''' 1. Beautiful is better than ugly.
... 3. Simple is better than complex.
... 4. Complicated is better than complex.
... 5. Flat is better than nested.
... '''.splitlines(1)
\end{verbatim}
Next we instantiate a Differ object:
\begin{verbatim}
>>> d = Differ()
\end{verbatim}
Note that when instantiating a \class{Differ} object we may pass
functions to filter out line and character ``junk.'' See the
\method{Differ()} constructor for details.
Finally, we compare the two:
\begin{verbatim}
>>> result = list(d.compare(text1, text2))
\end{verbatim}
\code{result} is a list of strings, so let's pretty-print it:
\begin{verbatim}
>>> from pprint import pprint
>>> pprint(result)
[' 1. Beautiful is better than ugly.\n',
'- 2. Explicit is better than implicit.\n',
'- 3. Simple is better than complex.\n',
'+ 3. Simple is better than complex.\n',
'? ++ \n',
'- 4. Complex is better than complicated.\n',
'? ^ ---- ^ \n',
'+ 4. Complicated is better than complex.\n',
'? ++++ ^ ^ \n',
'+ 5. Flat is better than nested.\n']
\end{verbatim}
As a single multi-line string it looks like this:
\begin{verbatim}
>>> import sys
>>> sys.stdout.writelines(result)
1. Beautiful is better than ugly.
- 2. Explicit is better than implicit.
- 3. Simple is better than complex.
+ 3. Simple is better than complex.
? ++
- 4. Complex is better than complicated.
? ^ ---- ^
+ 4. Complicated is better than complex.
? ++++ ^ ^
+ 5. Flat is better than nested.
\end{verbatim}
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