373 lines
12 KiB
Go
373 lines
12 KiB
Go
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// Copyright 2017, The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE.md file.
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// Package diff implements an algorithm for producing edit-scripts.
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// The edit-script is a sequence of operations needed to transform one list
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// of symbols into another (or vice-versa). The edits allowed are insertions,
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// deletions, and modifications. The summation of all edits is called the
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// Levenshtein distance as this problem is well-known in computer science.
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//
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// This package prioritizes performance over accuracy. That is, the run time
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// is more important than obtaining a minimal Levenshtein distance.
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package diff
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// EditType represents a single operation within an edit-script.
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type EditType uint8
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const (
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// Identity indicates that a symbol pair is identical in both list X and Y.
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Identity EditType = iota
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// UniqueX indicates that a symbol only exists in X and not Y.
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UniqueX
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// UniqueY indicates that a symbol only exists in Y and not X.
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UniqueY
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// Modified indicates that a symbol pair is a modification of each other.
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Modified
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)
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// EditScript represents the series of differences between two lists.
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type EditScript []EditType
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// String returns a human-readable string representing the edit-script where
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// Identity, UniqueX, UniqueY, and Modified are represented by the
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// '.', 'X', 'Y', and 'M' characters, respectively.
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func (es EditScript) String() string {
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b := make([]byte, len(es))
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for i, e := range es {
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switch e {
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case Identity:
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b[i] = '.'
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case UniqueX:
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b[i] = 'X'
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case UniqueY:
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b[i] = 'Y'
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case Modified:
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b[i] = 'M'
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default:
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panic("invalid edit-type")
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}
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}
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return string(b)
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}
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// stats returns a histogram of the number of each type of edit operation.
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func (es EditScript) stats() (s struct{ NI, NX, NY, NM int }) {
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for _, e := range es {
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switch e {
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case Identity:
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s.NI++
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case UniqueX:
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s.NX++
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case UniqueY:
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s.NY++
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case Modified:
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s.NM++
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default:
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panic("invalid edit-type")
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}
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}
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return
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}
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// Dist is the Levenshtein distance and is guaranteed to be 0 if and only if
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// lists X and Y are equal.
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func (es EditScript) Dist() int { return len(es) - es.stats().NI }
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// LenX is the length of the X list.
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func (es EditScript) LenX() int { return len(es) - es.stats().NY }
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// LenY is the length of the Y list.
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func (es EditScript) LenY() int { return len(es) - es.stats().NX }
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// EqualFunc reports whether the symbols at indexes ix and iy are equal.
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// When called by Difference, the index is guaranteed to be within nx and ny.
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type EqualFunc func(ix int, iy int) Result
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// Result is the result of comparison.
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// NumSame is the number of sub-elements that are equal.
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// NumDiff is the number of sub-elements that are not equal.
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type Result struct{ NumSame, NumDiff int }
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// BoolResult returns a Result that is either Equal or not Equal.
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func BoolResult(b bool) Result {
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if b {
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return Result{NumSame: 1} // Equal, Similar
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} else {
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return Result{NumDiff: 2} // Not Equal, not Similar
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}
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}
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// Equal indicates whether the symbols are equal. Two symbols are equal
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// if and only if NumDiff == 0. If Equal, then they are also Similar.
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func (r Result) Equal() bool { return r.NumDiff == 0 }
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// Similar indicates whether two symbols are similar and may be represented
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// by using the Modified type. As a special case, we consider binary comparisons
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// (i.e., those that return Result{1, 0} or Result{0, 1}) to be similar.
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//
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// The exact ratio of NumSame to NumDiff to determine similarity may change.
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func (r Result) Similar() bool {
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// Use NumSame+1 to offset NumSame so that binary comparisons are similar.
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return r.NumSame+1 >= r.NumDiff
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}
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// Difference reports whether two lists of lengths nx and ny are equal
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// given the definition of equality provided as f.
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//
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// This function returns an edit-script, which is a sequence of operations
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// needed to convert one list into the other. The following invariants for
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// the edit-script are maintained:
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// • eq == (es.Dist()==0)
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// • nx == es.LenX()
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// • ny == es.LenY()
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//
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// This algorithm is not guaranteed to be an optimal solution (i.e., one that
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// produces an edit-script with a minimal Levenshtein distance). This algorithm
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// favors performance over optimality. The exact output is not guaranteed to
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// be stable and may change over time.
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func Difference(nx, ny int, f EqualFunc) (es EditScript) {
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// This algorithm is based on traversing what is known as an "edit-graph".
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// See Figure 1 from "An O(ND) Difference Algorithm and Its Variations"
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// by Eugene W. Myers. Since D can be as large as N itself, this is
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// effectively O(N^2). Unlike the algorithm from that paper, we are not
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// interested in the optimal path, but at least some "decent" path.
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//
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// For example, let X and Y be lists of symbols:
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// X = [A B C A B B A]
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// Y = [C B A B A C]
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//
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// The edit-graph can be drawn as the following:
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// A B C A B B A
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// ┌─────────────┐
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// C │_|_|\|_|_|_|_│ 0
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// B │_|\|_|_|\|\|_│ 1
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// A │\|_|_|\|_|_|\│ 2
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// B │_|\|_|_|\|\|_│ 3
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// A │\|_|_|\|_|_|\│ 4
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// C │ | |\| | | | │ 5
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// └─────────────┘ 6
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// 0 1 2 3 4 5 6 7
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//
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// List X is written along the horizontal axis, while list Y is written
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// along the vertical axis. At any point on this grid, if the symbol in
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// list X matches the corresponding symbol in list Y, then a '\' is drawn.
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// The goal of any minimal edit-script algorithm is to find a path from the
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// top-left corner to the bottom-right corner, while traveling through the
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// fewest horizontal or vertical edges.
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// A horizontal edge is equivalent to inserting a symbol from list X.
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// A vertical edge is equivalent to inserting a symbol from list Y.
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// A diagonal edge is equivalent to a matching symbol between both X and Y.
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// Invariants:
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// • 0 ≤ fwdPath.X ≤ (fwdFrontier.X, revFrontier.X) ≤ revPath.X ≤ nx
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// • 0 ≤ fwdPath.Y ≤ (fwdFrontier.Y, revFrontier.Y) ≤ revPath.Y ≤ ny
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//
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// In general:
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// • fwdFrontier.X < revFrontier.X
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// • fwdFrontier.Y < revFrontier.Y
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// Unless, it is time for the algorithm to terminate.
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fwdPath := path{+1, point{0, 0}, make(EditScript, 0, (nx+ny)/2)}
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revPath := path{-1, point{nx, ny}, make(EditScript, 0)}
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fwdFrontier := fwdPath.point // Forward search frontier
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revFrontier := revPath.point // Reverse search frontier
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// Search budget bounds the cost of searching for better paths.
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// The longest sequence of non-matching symbols that can be tolerated is
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// approximately the square-root of the search budget.
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searchBudget := 4 * (nx + ny) // O(n)
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// The algorithm below is a greedy, meet-in-the-middle algorithm for
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// computing sub-optimal edit-scripts between two lists.
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//
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// The algorithm is approximately as follows:
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// • Searching for differences switches back-and-forth between
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// a search that starts at the beginning (the top-left corner), and
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// a search that starts at the end (the bottom-right corner). The goal of
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// the search is connect with the search from the opposite corner.
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// • As we search, we build a path in a greedy manner, where the first
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// match seen is added to the path (this is sub-optimal, but provides a
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// decent result in practice). When matches are found, we try the next pair
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// of symbols in the lists and follow all matches as far as possible.
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// • When searching for matches, we search along a diagonal going through
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// through the "frontier" point. If no matches are found, we advance the
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// frontier towards the opposite corner.
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// • This algorithm terminates when either the X coordinates or the
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// Y coordinates of the forward and reverse frontier points ever intersect.
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//
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// This algorithm is correct even if searching only in the forward direction
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// or in the reverse direction. We do both because it is commonly observed
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// that two lists commonly differ because elements were added to the front
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// or end of the other list.
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//
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// Running the tests with the "cmp_debug" build tag prints a visualization
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// of the algorithm running in real-time. This is educational for
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// understanding how the algorithm works. See debug_enable.go.
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f = debug.Begin(nx, ny, f, &fwdPath.es, &revPath.es)
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for {
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// Forward search from the beginning.
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if fwdFrontier.X >= revFrontier.X || fwdFrontier.Y >= revFrontier.Y || searchBudget == 0 {
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break
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}
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for stop1, stop2, i := false, false, 0; !(stop1 && stop2) && searchBudget > 0; i++ {
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// Search in a diagonal pattern for a match.
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z := zigzag(i)
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p := point{fwdFrontier.X + z, fwdFrontier.Y - z}
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switch {
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case p.X >= revPath.X || p.Y < fwdPath.Y:
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stop1 = true // Hit top-right corner
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case p.Y >= revPath.Y || p.X < fwdPath.X:
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stop2 = true // Hit bottom-left corner
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case f(p.X, p.Y).Equal():
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// Match found, so connect the path to this point.
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fwdPath.connect(p, f)
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fwdPath.append(Identity)
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// Follow sequence of matches as far as possible.
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for fwdPath.X < revPath.X && fwdPath.Y < revPath.Y {
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if !f(fwdPath.X, fwdPath.Y).Equal() {
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break
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}
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fwdPath.append(Identity)
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}
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fwdFrontier = fwdPath.point
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stop1, stop2 = true, true
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default:
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searchBudget-- // Match not found
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}
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debug.Update()
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}
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// Advance the frontier towards reverse point.
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if revPath.X-fwdFrontier.X >= revPath.Y-fwdFrontier.Y {
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fwdFrontier.X++
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} else {
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fwdFrontier.Y++
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}
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// Reverse search from the end.
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if fwdFrontier.X >= revFrontier.X || fwdFrontier.Y >= revFrontier.Y || searchBudget == 0 {
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break
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}
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for stop1, stop2, i := false, false, 0; !(stop1 && stop2) && searchBudget > 0; i++ {
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// Search in a diagonal pattern for a match.
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z := zigzag(i)
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p := point{revFrontier.X - z, revFrontier.Y + z}
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switch {
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case fwdPath.X >= p.X || revPath.Y < p.Y:
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stop1 = true // Hit bottom-left corner
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case fwdPath.Y >= p.Y || revPath.X < p.X:
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stop2 = true // Hit top-right corner
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case f(p.X-1, p.Y-1).Equal():
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// Match found, so connect the path to this point.
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revPath.connect(p, f)
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revPath.append(Identity)
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// Follow sequence of matches as far as possible.
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for fwdPath.X < revPath.X && fwdPath.Y < revPath.Y {
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if !f(revPath.X-1, revPath.Y-1).Equal() {
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break
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}
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revPath.append(Identity)
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}
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revFrontier = revPath.point
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stop1, stop2 = true, true
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default:
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searchBudget-- // Match not found
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}
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debug.Update()
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}
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// Advance the frontier towards forward point.
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if revFrontier.X-fwdPath.X >= revFrontier.Y-fwdPath.Y {
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revFrontier.X--
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} else {
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revFrontier.Y--
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}
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}
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// Join the forward and reverse paths and then append the reverse path.
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fwdPath.connect(revPath.point, f)
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for i := len(revPath.es) - 1; i >= 0; i-- {
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t := revPath.es[i]
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revPath.es = revPath.es[:i]
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fwdPath.append(t)
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}
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debug.Finish()
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return fwdPath.es
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}
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type path struct {
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dir int // +1 if forward, -1 if reverse
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point // Leading point of the EditScript path
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es EditScript
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}
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// connect appends any necessary Identity, Modified, UniqueX, or UniqueY types
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// to the edit-script to connect p.point to dst.
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func (p *path) connect(dst point, f EqualFunc) {
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if p.dir > 0 {
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// Connect in forward direction.
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for dst.X > p.X && dst.Y > p.Y {
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switch r := f(p.X, p.Y); {
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case r.Equal():
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p.append(Identity)
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case r.Similar():
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p.append(Modified)
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case dst.X-p.X >= dst.Y-p.Y:
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p.append(UniqueX)
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default:
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p.append(UniqueY)
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}
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}
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for dst.X > p.X {
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p.append(UniqueX)
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}
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for dst.Y > p.Y {
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p.append(UniqueY)
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}
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} else {
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// Connect in reverse direction.
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for p.X > dst.X && p.Y > dst.Y {
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switch r := f(p.X-1, p.Y-1); {
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case r.Equal():
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p.append(Identity)
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case r.Similar():
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p.append(Modified)
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case p.Y-dst.Y >= p.X-dst.X:
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p.append(UniqueY)
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default:
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p.append(UniqueX)
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}
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}
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for p.X > dst.X {
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p.append(UniqueX)
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}
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for p.Y > dst.Y {
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p.append(UniqueY)
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}
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}
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}
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func (p *path) append(t EditType) {
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p.es = append(p.es, t)
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switch t {
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case Identity, Modified:
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p.add(p.dir, p.dir)
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||
|
|
case UniqueX:
|
||
|
|
p.add(p.dir, 0)
|
||
|
|
case UniqueY:
|
||
|
|
p.add(0, p.dir)
|
||
|
|
}
|
||
|
|
debug.Update()
|
||
|
|
}
|
||
|
|
|
||
|
|
type point struct{ X, Y int }
|
||
|
|
|
||
|
|
func (p *point) add(dx, dy int) { p.X += dx; p.Y += dy }
|
||
|
|
|
||
|
|
// zigzag maps a consecutive sequence of integers to a zig-zag sequence.
|
||
|
|
// [0 1 2 3 4 5 ...] => [0 -1 +1 -2 +2 ...]
|
||
|
|
func zigzag(x int) int {
|
||
|
|
if x&1 != 0 {
|
||
|
|
x = ^x
|
||
|
|
}
|
||
|
|
return x >> 1
|
||
|
|
}
|