module LCS

How `Diff` Works (by Mark-Jason Dominus)¶ ↑

I once read an article written by the authors of diff; they said that they hard worked very hard on the algorithm until they found the right one.

I think what they ended up using (and I hope someone will correct me, because I am not very confident about this) was the ‘longest common subsequence’ method. In the LCS problem, you have two sequences of items:

a b c d f g h j q z
a b c d e f g i j k r x y z

and you want to find the longest sequence of items that is present in both original sequences in the same order. That is, you want to find a new sequence S which can be obtained from the first sequence by deleting some items, and from the second sequence by deleting other items. You also want S to be as long as possible. In this case S is:

a b c d f g j z

From there it’s only a small step to get diff-like output:

e   h i   k   q r x y
+   - +   +   - + + +

This module solves the LCS problem. It also includes a canned function to generate diff-like output.

It might seem from the example above that the LCS of two sequences is always pretty obvious, but that’s not always the case, especially when the two sequences have many repeated elements. For example, consider

a x b y c z p d q
a b c a x b y c z

A naive approach might start by matching up the a and b that appear at the beginning of each sequence, like this:

a x b y c         z p d q
a   b   c a b y c z

This finds the common subsequence +a b c z+. But actually, the LCS is +a x b y c z+:

      a x b y c z p d q
a b c a x b y c z

Constants

BalancedCallbacks

This callback object implements the default set of callback events, which only returns the event itself. Note that finished_a and finished_b are not implemented – I haven’t yet figured out where they would be useful.

Note that this is intended to be called as is, e.g.,

Diff::LCS.LCS(seq1, seq2, Diff::LCS::DefaultCallbacks)

SequenceCallbacks

Note that this is intended to be called as is, e.g.,

Diff::LCS.LCS(seq1, seq2, Diff::LCS::DefaultCallbacks)

VERSION

Public Class Methods

LCS (seq1, seq2)

Alias for: lcs

callbacks_for (callbacks)

Source

# File lib/diff/lcs/callbacks.rb, line 52
def self.callbacks_for(callbacks)
  callbacks.new
rescue
  callbacks
end

diff (seq1, seq2, callbacks = nil) { |diff changes| ... }

Source

# File lib/diff/lcs.rb, line 169
def diff(seq1, seq2, callbacks = nil, &block) # :yields: diff changes
  diff_traversal(:diff, seq1, seq2, callbacks || Diff::LCS::DiffCallbacks, &block)
end

diff computes the smallest set of additions and deletions necessary to turn the first sequence into the second, and returns a description of these changes.

See Diff::LCS::DiffCallbacks for the default behaviour. An alternate behaviour may be implemented with Diff::LCS::ContextDiffCallbacks. If a Class argument is provided for callbacks, diff will attempt to initialise it. If the callbacks object (possibly initialised) responds to finish, it will be called.

lcs (seq1, seq2) { |seq1 for each matched| ... }

Source

# File lib/diff/lcs.rb, line 145
def lcs(seq1, seq2, &block) # :yields: seq1[i] for each matched
  matches = Diff::LCS::Internals.lcs(seq1, seq2)
  ret = []
  string = seq1.is_a? String
  matches.each_index do |i|
    next if matches[i].nil?

    v = string ? seq1[i, 1] : seq1[i]
    v = block[v] if block
    ret << v
  end
  ret
end

Also aliased as: LCS

patch (src, patchset, direction = nil)

Source

# File lib/diff/lcs.rb, line 627
def patch(src, patchset, direction = nil)
  # Normalize the patchset.
  has_changes, patchset = Diff::LCS::Internals.analyze_patchset(patchset)

  return src.respond_to?(:dup) ? src.dup : src unless has_changes

  string = src.is_a?(String)
  # Start with a new empty type of the source's class
  res = src.class.new

  direction ||= Diff::LCS::Internals.intuit_diff_direction(src, patchset)

  ai = bj = 0

  patch_map = PATCH_MAP[direction]

  patchset.each do |change|
    # Both Change and ContextChange support #action
    action = patch_map[change.action]

    case change
    when Diff::LCS::ContextChange
      case direction
      when :patch
        el = change.new_element
        op = change.old_position
        np = change.new_position
      when :unpatch
        el = change.old_element
        op = change.new_position
        np = change.old_position
      end

      case action
      when "-" # Remove details from the old string
        while ai < op
          res << (string ? src[ai, 1] : src[ai])
          ai += 1
          bj += 1
        end
        ai += 1
      when "+"
        while bj < np
          res << (string ? src[ai, 1] : src[ai])
          ai += 1
          bj += 1
        end

        res << el
        bj += 1
      when "="
        # This only appears in sdiff output with the SDiff callback.
        # Therefore, we only need to worry about dealing with a single
        # element.
        res << el

        ai += 1
        bj += 1
      when "!"
        while ai < op
          res << (string ? src[ai, 1] : src[ai])
          ai += 1
          bj += 1
        end

        bj += 1
        ai += 1

        res << el
      end
    when Diff::LCS::Change
      case action
      when "-"
        while ai < change.position
          res << (string ? src[ai, 1] : src[ai])
          ai += 1
          bj += 1
        end
        ai += 1
      when "+"
        while bj < change.position
          res << (string ? src[ai, 1] : src[ai])
          ai += 1
          bj += 1
        end

        bj += 1

        res << change.element
      end
    end
  end

  while ai < src.size
    res << (string ? src[ai, 1] : src[ai])
    ai += 1
    bj += 1
  end

  res
end

Applies a patchset to the sequence src according to the direction (:patch or :unpatch), producing a new sequence.

If the direction is not specified, Diff::LCS::patch will attempt to discover the direction of the patchset.

A patchset can be considered to apply forward (:patch) if the following expression is true:

patch(s1, diff(s1, s2)) -> s2

A patchset can be considered to apply backward (:unpatch) if the following expression is true:

patch(s2, diff(s1, s2)) -> s1

If the patchset contains no changes, the src value will be returned as either src.dup or src. A patchset can be deemed as having no changes if the following predicate returns true:

patchset.empty? or
  patchset.flatten(1).all? { |change| change.unchanged? }

Patchsets¶ ↑

A patchset is always an enumerable sequence of changes, hunks of changes, or a mix of the two. A hunk of changes is an enumerable sequence of changes:

[ # patchset
  # change
  [ # hunk
    # change
  ]
]

The patch method accepts patchsets that are enumerable sequences containing either Diff::LCS::Change objects (or a subclass) or the array representations of those objects. Prior to application, array representations of Diff::LCS::Change objects will be reified.

patch! (src, patchset)

Source

# File lib/diff/lcs.rb, line 737
def patch!(src, patchset)
  patch(src, patchset, :patch)
end

Given a set of patchset, convert the current version to the next version. Does no auto-discovery.

sdiff (seq1, seq2, callbacks = nil) { |diff changes| ... }

Source

# File lib/diff/lcs.rb, line 201
def sdiff(seq1, seq2, callbacks = nil, &block) # :yields: diff changes
  diff_traversal(:sdiff, seq1, seq2, callbacks || Diff::LCS::SDiffCallbacks, &block)
end

sdiff computes all necessary components to show two sequences and their minimized differences side by side, just like the Unix utility sdiff does:

old        <     -
same             same
before     |     after
-          >     new

See Diff::LCS::SDiffCallbacks for the default behaviour. An alternate behaviour may be implemented with Diff::LCS::ContextDiffCallbacks. If a Class argument is provided for callbacks, diff will attempt to initialise it. If the callbacks object (possibly initialised) responds to finish, it will be called.

Each element of a returned array is a Diff::LCS::ContextChange object, which can be implicitly converted to an array.

Diff::LCS.sdiff(a, b).each do |action, (old_pos, old_element), (new_pos, new_element)|
  case action
  when '!'
    # replace
  when '-'
    # delete
  when '+'
    # insert
  end
end

traverse_balanced (seq1, seq2, callbacks = Diff::LCS::BalancedCallbacks) { |event| ... }

Source

# File lib/diff/lcs.rb, line 476
def traverse_balanced(seq1, seq2, callbacks = Diff::LCS::BalancedCallbacks)
  matches = Diff::LCS::Internals.lcs(seq1, seq2)
  a_size = seq1.size
  b_size = seq2.size
  ai = bj = mb = 0
  ma = -1
  string = seq1.is_a?(String)

  # Process all the lines in the match vector.
  loop do
    # Find next match indexes +ma+ and +mb+
    loop do
      ma += 1
      break unless ma < matches.size && matches[ma].nil?
    end

    break if ma >= matches.size # end of matches?

    mb = matches[ma]

    # Change(seq2)
    while (ai < ma) || (bj < mb)
      ax = string ? seq1[ai, 1] : seq1[ai]
      bx = string ? seq2[bj, 1] : seq2[bj]

      case [(ai < ma), (bj < mb)]
      when [true, true]
        if callbacks.respond_to?(:change)
          event = Diff::LCS::ContextChange.new("!", ai, ax, bj, bx)
          event = yield event if block_given?
          callbacks.change(event)
          ai += 1
        else
          event = Diff::LCS::ContextChange.new("-", ai, ax, bj, bx)
          event = yield event if block_given?
          callbacks.discard_a(event)
          ai += 1
          ax = string ? seq1[ai, 1] : seq1[ai]
          event = Diff::LCS::ContextChange.new("+", ai, ax, bj, bx)
          event = yield event if block_given?
          callbacks.discard_b(event)
        end

        bj += 1
      when [true, false]
        event = Diff::LCS::ContextChange.new("-", ai, ax, bj, bx)
        event = yield event if block_given?
        callbacks.discard_a(event)
        ai += 1
      when [false, true]
        event = Diff::LCS::ContextChange.new("+", ai, ax, bj, bx)
        event = yield event if block_given?
        callbacks.discard_b(event)
        bj += 1
      end
    end

    # Match
    ax = string ? seq1[ai, 1] : seq1[ai]
    bx = string ? seq2[bj, 1] : seq2[bj]
    event = Diff::LCS::ContextChange.new("=", ai, ax, bj, bx)
    event = yield event if block_given?
    callbacks.match(event)
    ai += 1
    bj += 1
  end

  while (ai < a_size) || (bj < b_size)
    ax = string ? seq1[ai, 1] : seq1[ai]
    bx = string ? seq2[bj, 1] : seq2[bj]

    case [(ai < a_size), (bj < b_size)]
    when [true, true]
      if callbacks.respond_to?(:change)
        event = Diff::LCS::ContextChange.new("!", ai, ax, bj, bx)
        event = yield event if block_given?
        callbacks.change(event)
        ai += 1
      else
        event = Diff::LCS::ContextChange.new("-", ai, ax, bj, bx)
        event = yield event if block_given?
        callbacks.discard_a(event)
        ai += 1
        ax = string ? seq1[ai, 1] : seq1[ai]
        event = Diff::LCS::ContextChange.new("+", ai, ax, bj, bx)
        event = yield event if block_given?
        callbacks.discard_b(event)
      end

      bj += 1
    when [true, false]
      event = Diff::LCS::ContextChange.new("-", ai, ax, bj, bx)
      event = yield event if block_given?
      callbacks.discard_a(event)
      ai += 1
    when [false, true]
      event = Diff::LCS::ContextChange.new("+", ai, ax, bj, bx)
      event = yield event if block_given?
      callbacks.discard_b(event)
      bj += 1
    end
  end
end

traverse_balanced is an alternative to traverse_sequences. It uses a different algorithm to iterate through the entries in the computed longest common subsequence. Instead of viewing the changes as insertions or deletions from one of the sequences, traverse_balanced will report changes between the sequences.

The arguments to traverse_balanced are the two sequences to traverse and a callback object, like this:

traverse_balanced(seq1, seq2, Diff::LCS::ContextDiffCallbacks.new)

sdiff is implemented with traverse_balanced.

Callback Methods¶ ↑

Optional callback methods are emphasized.

callbacks#match: Called when a and b are pointing to common elements in A and B.
callbacks#discard_a: Called when a is pointing to an element not in B.
callbacks#discard_b: Called when b is pointing to an element not in A.
callbacks#change: Called when a and b are pointing to the same relative position, but A[a] and B[b] are not the same; a change has occurred.

traverse_balanced might be a bit slower than traverse_sequences, noticeable only while processing huge amounts of data.

Algorithm¶ ↑

a---+
    v
A = a b c e h j l m n p
B = b c d e f j k l m r s t
    ^
b---+

Matches¶ ↑

If there are two arrows (a and b) pointing to elements of sequences A and B, the arrows will initially point to the first elements of their respective sequences. traverse_sequences will advance the arrows through the sequences one element at a time, calling a method on the user-specified callback object before each advance. It will advance the arrows in such a way that if there are elements A[i] and B[j] which are both equal and part of the longest common subsequence, there will be some moment during the execution of traverse_sequences when arrow a is pointing to A[i] and arrow b is pointing to B[j]. When this happens, traverse_sequences will call callbacks#match and then it will advance both arrows.

Discards¶ ↑

Changes¶ ↑

If both a and b point to elements that are not part of the longest common subsequence, then traverse_sequences will try to call callbacks#change and advance both arrows. If callbacks#change is not implemented, then callbacks#discard_a and callbacks#discard_b will be called in turn.

The methods for callbacks#match, callbacks#discard_a, callbacks#discard_b, and callbacks#change are invoked with an event comprising the action (“=”, “+”, “-”, or “!”, respectively), the indexes i and j, and the elements A[i] and B[j]. Return values are discarded by traverse_balanced.

Context¶ ↑

Note that i and j may not be the same index position, even if a and b are considered to be pointing to matching or changed elements.

traverse_sequences (seq1, seq2, callbacks = Diff::LCS::SequenceCallbacks) { |change events| ... }

Source

# File lib/diff/lcs.rb, line 286
def traverse_sequences(seq1, seq2, callbacks = Diff::LCS::SequenceCallbacks) # :yields: change events
  callbacks ||= Diff::LCS::SequenceCallbacks
  matches = Diff::LCS::Internals.lcs(seq1, seq2)

  run_finished_a = run_finished_b = false
  string = seq1.is_a?(String)

  a_size = seq1.size
  b_size = seq2.size
  ai = bj = 0

  matches.each do |b_line|
    if b_line.nil?
      unless seq1[ai].nil?
        ax = string ? seq1[ai, 1] : seq1[ai]
        bx = string ? seq2[bj, 1] : seq2[bj]

        event = Diff::LCS::ContextChange.new("-", ai, ax, bj, bx)
        event = yield event if block_given?
        callbacks.discard_a(event)
      end
    else
      ax = string ? seq1[ai, 1] : seq1[ai]

      loop do
        break unless bj < b_line

        bx = string ? seq2[bj, 1] : seq2[bj]
        event = Diff::LCS::ContextChange.new("+", ai, ax, bj, bx)
        event = yield event if block_given?
        callbacks.discard_b(event)
        bj += 1
      end
      bx = string ? seq2[bj, 1] : seq2[bj]
      event = Diff::LCS::ContextChange.new("=", ai, ax, bj, bx)
      event = yield event if block_given?
      callbacks.match(event)
      bj += 1
    end
    ai += 1
  end

  # The last entry (if any) processed was a match. +ai+ and +bj+ point just
  # past the last matching lines in their sequences.
  while (ai < a_size) || (bj < b_size)
    # last A?
    if ai == a_size && bj < b_size
      if callbacks.respond_to?(:finished_a) && !run_finished_a
        ax = string ? seq1[-1, 1] : seq1[-1]
        bx = string ? seq2[bj, 1] : seq2[bj]
        event = Diff::LCS::ContextChange.new(">", (a_size - 1), ax, bj, bx)
        event = yield event if block_given?
        callbacks.finished_a(event)
        run_finished_a = true
      else
        ax = string ? seq1[ai, 1] : seq1[ai]
        loop do
          bx = string ? seq2[bj, 1] : seq2[bj]
          event = Diff::LCS::ContextChange.new("+", ai, ax, bj, bx)
          event = yield event if block_given?
          callbacks.discard_b(event)
          bj += 1
          break unless bj < b_size
        end
      end
    end

    # last B?
    if bj == b_size && ai < a_size
      if callbacks.respond_to?(:finished_b) && !run_finished_b
        ax = string ? seq1[ai, 1] : seq1[ai]
        bx = string ? seq2[-1, 1] : seq2[-1]
        event = Diff::LCS::ContextChange.new("<", ai, ax, (b_size - 1), bx)
        event = yield event if block_given?
        callbacks.finished_b(event)
        run_finished_b = true
      else
        bx = string ? seq2[bj, 1] : seq2[bj]
        loop do
          ax = string ? seq1[ai, 1] : seq1[ai]
          event = Diff::LCS::ContextChange.new("-", ai, ax, bj, bx)
          event = yield event if block_given?
          callbacks.discard_a(event)
          ai += 1
          break unless bj < b_size
        end
      end
    end

    if ai < a_size
      ax = string ? seq1[ai, 1] : seq1[ai]
      bx = string ? seq2[bj, 1] : seq2[bj]
      event = Diff::LCS::ContextChange.new("-", ai, ax, bj, bx)
      event = yield event if block_given?
      callbacks.discard_a(event)
      ai += 1
    end

    if bj < b_size
      ax = string ? seq1[ai, 1] : seq1[ai]
      bx = string ? seq2[bj, 1] : seq2[bj]
      event = Diff::LCS::ContextChange.new("+", ai, ax, bj, bx)
      event = yield event if block_given?
      callbacks.discard_b(event)
      bj += 1
    end
  end
end

traverse_sequences is the most general facility provided by this module; diff and lcs are implemented as calls to it.

The arguments to traverse_sequences are the two sequences to traverse, and a callback object, like this:

traverse_sequences(seq1, seq2, Diff::LCS::ContextDiffCallbacks.new)

Callback Methods¶ ↑

Optional callback methods are emphasized.

callbacks#match: Called when a and b are pointing to common elements in A and B.
callbacks#discard_a: Called when a is pointing to an element not in B.
callbacks#discard_b: Called when b is pointing to an element not in A.
callbacks#finished_a: Called when a has reached the end of sequence A.
callbacks#finished_b: Called when b has reached the end of sequence B.

Algorithm¶ ↑

a---+
    v
A = a b c e h j l m n p
B = b c d e f j k l m r s t
    ^
b---+

Otherwise, one of the arrows is pointing to an element of its sequence that is not part of the longest common subsequence. traverse_sequences will advance that arrow and will call callbacks#discard_a or callbacks#discard_b, depending on which arrow it advanced. If both arrows point to elements that are not part of the longest common subsequence, then traverse_sequences will advance arrow a and call the appropriate callback, then it will advance arrow b and call the appropriate callback.

The methods for callbacks#match, callbacks#discard_a, and callbacks#discard_b are invoked with an event comprising the action (“=”, “+”, or “-”, respectively), the indexes i and j, and the elements A[i] and B[j]. Return values are discarded by traverse_sequences.

End of Sequences¶ ↑

If arrow a reaches the end of its sequence before arrow b does, traverse_sequence will try to call callbacks#finished_a with the last index and element of A (A[-1]) and the current index and element of B (B[j]). If callbacks#finished_a does not exist, then callbacks#discard_b will be called on each element of B until the end of the sequence is reached (the call will be done with A[-1] and B[j] for each element).

If b reaches the end of B before a reaches the end of A, callbacks#finished_b will be called with the current index and element of A (A[i]) and the last index and element of B (A[-1]). Again, if callbacks#finished_b does not exist on the callback object, then callbacks#discard_a will be called on each element of A until the end of the sequence is reached (A[i] and B[-1]).

There is a chance that one additional callbacks#discard_a or callbacks#discard_b will be called after the end of the sequence is reached, if a has not yet reached the end of A or b has not yet reached the end of B.

unpatch! (src, patchset)

Source

# File lib/diff/lcs.rb, line 731
def unpatch!(src, patchset)
  patch(src, patchset, :unpatch)
end

Given a set of patchset, convert the current version to the prior version. Does no auto-discovery.

Public Instance Methods

diff (other, callbacks = nil, &block)

Source

# File lib/diff/lcs.rb, line 76
def diff(other, callbacks = nil, &block)
  Diff::LCS.diff(self, other, callbacks, &block)
end

Returns the difference set between self and other. See Diff::LCS#diff.

lcs (other) { |self| ... }

Source

# File lib/diff/lcs.rb, line 71
def lcs(other, &block) # :yields: self[i] if there are matched subsequences
  Diff::LCS.lcs(self, other, &block)
end

Returns an Array containing the longest common subsequence(s) between self and other. See Diff::LCS#lcs.

lcs = seq1.lcs(seq2)

A note when using objects: Diff::LCS only works properly when each object can be used as a key in a Hash. This means that those objects must implement the methods hash and eql? such that two objects containing identical values compare identically for key purposes. That is:

O.new('a').eql?(O.new('a')) == true &&
O.new('a').hash == O.new('a').hash

patch (patchset)

Source

# File lib/diff/lcs.rb, line 102
def patch(patchset)
  Diff::LCS.patch(self, patchset)
end

Attempts to patch self with the provided patchset. A new sequence based on self and the patchset will be created. See Diff::LCS#patch. Attempts to autodiscover the direction of the patch.

Also aliased as: unpatch

patch! (patchset)

Source

# File lib/diff/lcs.rb, line 110
def patch!(patchset)
  Diff::LCS.patch!(self, patchset)
end

Attempts to patch self with the provided patchset. A new sequence based on self and the patchset will be created. See Diff::LCS#patch. Does no patch direction autodiscovery.

patch_me (patchset)

Source

# File lib/diff/lcs.rb, line 124
def patch_me(patchset)
  if respond_to? :replace
    replace(patch!(patchset))
  else
    patch!(patchset)
  end
end

Attempts to patch self with the provided patchset, using patch!. If the sequence this is used on supports replace, the value of self will be replaced. See Diff::LCS#patch. Does no patch direction autodiscovery.

sdiff (other, callbacks = nil, &block)

Source

# File lib/diff/lcs.rb, line 82
def sdiff(other, callbacks = nil, &block)
  Diff::LCS.sdiff(self, other, callbacks, &block)
end

Returns the balanced (“side-by-side”) difference set between self and other. See Diff::LCS#sdiff.

traverse_balanced (other, callbacks = nil, &block)

Source

# File lib/diff/lcs.rb, line 95
def traverse_balanced(other, callbacks = nil, &block)
  Diff::LCS.traverse_balanced(self, other, callbacks || Diff::LCS::BalancedCallbacks, &block)
end

Traverses the discovered longest common subsequences between self and other using the alternate, balanced algorithm. See Diff::LCS#traverse_balanced.

traverse_sequences (other, callbacks = nil, &block)

Source

# File lib/diff/lcs.rb, line 88
def traverse_sequences(other, callbacks = nil, &block)
  Diff::LCS.traverse_sequences(self, other, callbacks || Diff::LCS::SequenceCallbacks, &block)
end

Traverses the discovered longest common subsequences between self and other. See Diff::LCS#traverse_sequences.

unpatch (patchset)

Alias for: patch

unpatch! (patchset)

Source

# File lib/diff/lcs.rb, line 117
def unpatch!(patchset)
  Diff::LCS.unpatch!(self, patchset)
end

Attempts to unpatch self with the provided patchset. A new sequence based on self and the patchset will be created. See Diff::LCS#unpatch. Does no patch direction autodiscovery.

unpatch_me (patchset)

Source

# File lib/diff/lcs.rb, line 135
def unpatch_me(patchset)
  if respond_to? :replace
    replace(unpatch!(patchset))
  else
    unpatch!(patchset)
  end
end

Attempts to unpatch self with the provided patchset, using unpatch!. If the sequence this is used on supports replace, the value of self will be replaced. See Diff::LCS#unpatch. Does no patch direction autodiscovery.

module LCS

How Diff Works (by Mark-Jason Dominus)¶ ↑

Patchsets¶ ↑

Callback Methods¶ ↑

Algorithm¶ ↑

Matches¶ ↑

Discards¶ ↑

Changes¶ ↑

Context¶ ↑

Callback Methods¶ ↑

Algorithm¶ ↑

End of Sequences¶ ↑

How `Diff` Works (by Mark-Jason Dominus)¶ ↑