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