[PATCH 3/4] diff-highlight: match up lines before highlighting

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As mentioned in the README, one of the current limitations of
diff-highlight is that it only calculates highlights when the hunk
contains the same number of removed lines as added lines.

A further limitation upon this is that diff-highlight assumes that the
first line removed matches the first line added, similarly with the
second, the third, etc... As was demonstrated in the "Bugs" section of
the README, this poses limitations since that assumption does not always
give the best result.

With this patch, we eliminate those limitations by trying to match up
the removed and added lines before highlighting them. This is done using
a recursive algorithm.

Note that I did not bother with some common optimizations such as
memoization since the usual number of removed/added lines in a single
hunk are small. In practice, I have not felt any lag at all during
paging.

Signed-off-by: Jonathan Lebon <jonathan.lebon@xxxxxxxxx>
---
 contrib/diff-highlight/README         | 61 +------------------------
 contrib/diff-highlight/diff-highlight | 83 +++++++++++++++++++++++++++++------
 2 files changed, 70 insertions(+), 74 deletions(-)

diff --git a/contrib/diff-highlight/README b/contrib/diff-highlight/README
index bbbfdda..885ff2f 100644
--- a/contrib/diff-highlight/README
+++ b/contrib/diff-highlight/README
@@ -14,17 +14,7 @@ Instead, this script post-processes the line-oriented diff, finds pairs
 of lines, and highlights the differing segments.  It's currently very
 simple and stupid about doing these tasks. In particular:
 
-  1. It will only highlight hunks in which the number of removed and
-     added lines is the same, and it will pair lines within the hunk by
-     position (so the first removed line is compared to the first added
-     line, and so forth). This is simple and tends to work well in
-     practice. More complex changes don't highlight well, so we tend to
-     exclude them due to the "same number of removed and added lines"
-     restriction. Or even if we do try to highlight them, they end up
-     not highlighting because of our "don't highlight if the whole line
-     would be highlighted" rule.
-
-  2. It will find the common prefix and suffix of two lines, and
+  1. It will find the common prefix and suffix of two lines, and
      consider everything in the middle to be "different". It could
      instead do a real diff of the characters between the two lines and
      find common subsequences. However, the point of the highlight is to
@@ -142,52 +132,3 @@ heuristics.
 -----------------------------------------------------
 
    which is less readable than the current output.
-
-2. The multi-line matching assumes that lines in the pre- and post-image
-   match by position. This is often the case, but can be fooled when a
-   line is removed from the top and a new one added at the bottom (or
-   vice versa). Unless the lines in the middle are also changed, diffs
-   will show this as two hunks, and it will not get highlighted at all
-   (which is good). But if the lines in the middle are changed, the
-   highlighting can be misleading. Here's a pathological case:
-
------------------------------------------------------
--one
--two
--three
--four
-+two 2
-+three 3
-+four 4
-+five 5
------------------------------------------------------
-
-   which gets highlighted as:
-
------------------------------------------------------
--one
--t-{wo}
--three
--f-{our}
-+two 2
-+t+{hree 3}
-+four 4
-+f+{ive 5}
------------------------------------------------------
-
-   because it matches "two" to "three 3", and so forth. It would be
-   nicer as:
-
------------------------------------------------------
--one
--two
--three
--four
-+two +{2}
-+three +{3}
-+four +{4}
-+five 5
------------------------------------------------------
-
-   which would probably involve pre-matching the lines into pairs
-   according to some heuristic.
diff --git a/contrib/diff-highlight/diff-highlight b/contrib/diff-highlight/diff-highlight
index a332f86..46556fc 100755
--- a/contrib/diff-highlight/diff-highlight
+++ b/contrib/diff-highlight/diff-highlight
@@ -88,24 +88,79 @@ sub show_hunk {
 		return;
 	}
 
-	# If we have mismatched numbers of lines on each side, we could try to
-	# be clever and match up similar lines. But for now we are simple and
-	# stupid, and only handle multi-line hunks that remove and add the same
-	# number of lines.
-	if (@$a != @$b) {
-		print @$a, @$b;
-		return;
-	}
-
 	my @queue;
-	for (my $i = 0; $i < @$a; $i++) {
-		my ($rm, $add) = highlight_pair($a->[$i], $b->[$i]);
-		print $rm;
-		push @queue, $add;
-	}
+	match_and_highlight_pairs($a, 0, scalar @$a, $b, 0, scalar @$b, \@queue);
 	print @queue;
 }
 
+# Here, we try to be clever and match up similar lines. I.e. we try to
+# find which lines in the `rem` lines (array a) became which other lines
+# in the `add` lines (array b). To do this, we use a recursive algorithm
+# that works as follow:
+# 	1. Find the most similar pair of lines in all possible pairs
+# 	2. Do a recursive call to find the most similar pair of lines in all
+# 	   pairs, restricted to lower indices
+# 	3. Print the `rem` line of the best pair
+# 	4. Queue the `add` line of the best pair
+# 	5. Do a recursive call to find the most similar pair of lines in all
+# 	   pairs, restricted to higher indices
+sub match_and_highlight_pairs {
+	my ($a, $a_first, $a_last, $b,  $b_first, $b_last, $queue) = @_;
+
+	# base case: no more rem or add lines to pair up
+	if ($a_first >= $a_last || $b_first >= $b_last) {
+
+		# flush out any remaining rem lines
+		for (my $i = $a_first; $i < $a_last; $i++) {
+			print $a->[$i];
+		}
+
+		# queue up any remaining add lines
+		for (my $i = $b_first; $i < $b_last; $i++) {
+			push @$queue, $b->[$i];
+		}
+
+		return;
+	}
+
+	# prime the loop
+	my ($besti, $bestj) = ($a_first, $b_first);
+	my $bestn = calculate_match($a->[$a_first], $b->[$b_first]) + 1;
+
+	for (my $i = $a_first; $i < $a_last; $i++) {
+		for (my $j = $b_first; $j < $b_last; $j++) {
+			my $n = calculate_match($a->[$i], $b->[$j]);
+			if ($n < $bestn) {
+				($besti, $bestj, $bestn) = ($i, $j, $n);
+			}
+		}
+	}
+
+	# find the best matches in the lower pairs
+	match_and_highlight_pairs($a, $a_first, $besti, $b, $b_first, $bestj, $queue);
+
+	my ($rm, $add) = highlight_pair($a->[$besti], $b->[$bestj]);
+	print $rm;
+	push @$queue, $add;
+
+	# find the best matches in the higher pairs
+	match_and_highlight_pairs($a, $besti+1, $a_last, $b, $bestj+1, $b_last, $queue);
+}
+
+# A measure of how well the two lines passed match up. The smaller the
+# returned value, the better the match. The current implementation uses
+# a simple heuristic which tries to minimize the overall diff between
+# the two lines considering only their common prefix and suffix.
+sub calculate_match {
+	my @a = split_line(shift);
+	my @b = split_line(shift);
+
+	my ($pa, $pb) = find_common_prefix(\@a, \@b);
+	my ($sa, $sb) = find_common_suffix(\@a, $pa, \@b, $pb);
+
+	return ($sa - $pa) + ($sb - $pb);
+}
+
 sub highlight_pair {
 	my @a = split_line(shift);
 	my @b = split_line(shift);
-- 
2.6.0

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