1 // Copyright 2017, The Go Authors. All rights reserved.
2 // Use of this source code is governed by a BSD-style
3 // license that can be found in the LICENSE.md file.
5 // Package diff implements an algorithm for producing edit-scripts.
6 // The edit-script is a sequence of operations needed to transform one list
7 // of symbols into another (or vice-versa). The edits allowed are insertions,
8 // deletions, and modifications. The summation of all edits is called the
9 // Levenshtein distance as this problem is well-known in computer science.
11 // This package prioritizes performance over accuracy. That is, the run time
12 // is more important than obtaining a minimal Levenshtein distance.
19 "github.com/google/go-cmp/cmp/internal/flags"
22 // EditType represents a single operation within an edit-script.
26 // Identity indicates that a symbol pair is identical in both list X and Y.
27 Identity EditType = iota
28 // UniqueX indicates that a symbol only exists in X and not Y.
30 // UniqueY indicates that a symbol only exists in Y and not X.
32 // Modified indicates that a symbol pair is a modification of each other.
36 // EditScript represents the series of differences between two lists.
37 type EditScript []EditType
39 // String returns a human-readable string representing the edit-script where
40 // Identity, UniqueX, UniqueY, and Modified are represented by the
41 // '.', 'X', 'Y', and 'M' characters, respectively.
42 func (es EditScript) String() string {
43 b := make([]byte, len(es))
44 for i, e := range es {
55 panic("invalid edit-type")
61 // stats returns a histogram of the number of each type of edit operation.
62 func (es EditScript) stats() (s struct{ NI, NX, NY, NM int }) {
63 for _, e := range es {
74 panic("invalid edit-type")
80 // Dist is the Levenshtein distance and is guaranteed to be 0 if and only if
81 // lists X and Y are equal.
82 func (es EditScript) Dist() int { return len(es) - es.stats().NI }
84 // LenX is the length of the X list.
85 func (es EditScript) LenX() int { return len(es) - es.stats().NY }
87 // LenY is the length of the Y list.
88 func (es EditScript) LenY() int { return len(es) - es.stats().NX }
90 // EqualFunc reports whether the symbols at indexes ix and iy are equal.
91 // When called by Difference, the index is guaranteed to be within nx and ny.
92 type EqualFunc func(ix int, iy int) Result
94 // Result is the result of comparison.
95 // NumSame is the number of sub-elements that are equal.
96 // NumDiff is the number of sub-elements that are not equal.
97 type Result struct{ NumSame, NumDiff int }
99 // BoolResult returns a Result that is either Equal or not Equal.
100 func BoolResult(b bool) Result {
102 return Result{NumSame: 1} // Equal, Similar
104 return Result{NumDiff: 2} // Not Equal, not Similar
108 // Equal indicates whether the symbols are equal. Two symbols are equal
109 // if and only if NumDiff == 0. If Equal, then they are also Similar.
110 func (r Result) Equal() bool { return r.NumDiff == 0 }
112 // Similar indicates whether two symbols are similar and may be represented
113 // by using the Modified type. As a special case, we consider binary comparisons
114 // (i.e., those that return Result{1, 0} or Result{0, 1}) to be similar.
116 // The exact ratio of NumSame to NumDiff to determine similarity may change.
117 func (r Result) Similar() bool {
118 // Use NumSame+1 to offset NumSame so that binary comparisons are similar.
119 return r.NumSame+1 >= r.NumDiff
122 var randInt = rand.New(rand.NewSource(time.Now().Unix())).Intn(2)
124 // Difference reports whether two lists of lengths nx and ny are equal
125 // given the definition of equality provided as f.
127 // This function returns an edit-script, which is a sequence of operations
128 // needed to convert one list into the other. The following invariants for
129 // the edit-script are maintained:
130 // • eq == (es.Dist()==0)
134 // This algorithm is not guaranteed to be an optimal solution (i.e., one that
135 // produces an edit-script with a minimal Levenshtein distance). This algorithm
136 // favors performance over optimality. The exact output is not guaranteed to
137 // be stable and may change over time.
138 func Difference(nx, ny int, f EqualFunc) (es EditScript) {
139 // This algorithm is based on traversing what is known as an "edit-graph".
140 // See Figure 1 from "An O(ND) Difference Algorithm and Its Variations"
141 // by Eugene W. Myers. Since D can be as large as N itself, this is
142 // effectively O(N^2). Unlike the algorithm from that paper, we are not
143 // interested in the optimal path, but at least some "decent" path.
145 // For example, let X and Y be lists of symbols:
146 // X = [A B C A B B A]
149 // The edit-graph can be drawn as the following:
152 // C │_|_|\|_|_|_|_│ 0
153 // B │_|\|_|_|\|\|_│ 1
154 // A │\|_|_|\|_|_|\│ 2
155 // B │_|\|_|_|\|\|_│ 3
156 // A │\|_|_|\|_|_|\│ 4
157 // C │ | |\| | | | │ 5
161 // List X is written along the horizontal axis, while list Y is written
162 // along the vertical axis. At any point on this grid, if the symbol in
163 // list X matches the corresponding symbol in list Y, then a '\' is drawn.
164 // The goal of any minimal edit-script algorithm is to find a path from the
165 // top-left corner to the bottom-right corner, while traveling through the
166 // fewest horizontal or vertical edges.
167 // A horizontal edge is equivalent to inserting a symbol from list X.
168 // A vertical edge is equivalent to inserting a symbol from list Y.
169 // A diagonal edge is equivalent to a matching symbol between both X and Y.
171 // To ensure flexibility in changing the algorithm in the future,
172 // introduce some degree of deliberate instability.
173 // This is achieved by fiddling the zigzag iterator to start searching
174 // the graph starting from the bottom-right versus than the top-left.
175 // The result may differ depending on the starting search location,
176 // but still produces a valid edit script.
177 zigzagInit := randInt // either 0 or 1
178 if flags.Deterministic {
183 // • 0 ≤ fwdPath.X ≤ (fwdFrontier.X, revFrontier.X) ≤ revPath.X ≤ nx
184 // • 0 ≤ fwdPath.Y ≤ (fwdFrontier.Y, revFrontier.Y) ≤ revPath.Y ≤ ny
187 // • fwdFrontier.X < revFrontier.X
188 // • fwdFrontier.Y < revFrontier.Y
189 // Unless, it is time for the algorithm to terminate.
190 fwdPath := path{+1, point{0, 0}, make(EditScript, 0, (nx+ny)/2)}
191 revPath := path{-1, point{nx, ny}, make(EditScript, 0)}
192 fwdFrontier := fwdPath.point // Forward search frontier
193 revFrontier := revPath.point // Reverse search frontier
195 // Search budget bounds the cost of searching for better paths.
196 // The longest sequence of non-matching symbols that can be tolerated is
197 // approximately the square-root of the search budget.
198 searchBudget := 4 * (nx + ny) // O(n)
200 // The algorithm below is a greedy, meet-in-the-middle algorithm for
201 // computing sub-optimal edit-scripts between two lists.
203 // The algorithm is approximately as follows:
204 // • Searching for differences switches back-and-forth between
205 // a search that starts at the beginning (the top-left corner), and
206 // a search that starts at the end (the bottom-right corner). The goal of
207 // the search is connect with the search from the opposite corner.
208 // • As we search, we build a path in a greedy manner, where the first
209 // match seen is added to the path (this is sub-optimal, but provides a
210 // decent result in practice). When matches are found, we try the next pair
211 // of symbols in the lists and follow all matches as far as possible.
212 // • When searching for matches, we search along a diagonal going through
213 // through the "frontier" point. If no matches are found, we advance the
214 // frontier towards the opposite corner.
215 // • This algorithm terminates when either the X coordinates or the
216 // Y coordinates of the forward and reverse frontier points ever intersect.
218 // This algorithm is correct even if searching only in the forward direction
219 // or in the reverse direction. We do both because it is commonly observed
220 // that two lists commonly differ because elements were added to the front
221 // or end of the other list.
223 // Running the tests with the "cmp_debug" build tag prints a visualization
224 // of the algorithm running in real-time. This is educational for
225 // understanding how the algorithm works. See debug_enable.go.
226 f = debug.Begin(nx, ny, f, &fwdPath.es, &revPath.es)
228 // Forward search from the beginning.
229 if fwdFrontier.X >= revFrontier.X || fwdFrontier.Y >= revFrontier.Y || searchBudget == 0 {
232 for stop1, stop2, i := false, false, zigzagInit; !(stop1 && stop2) && searchBudget > 0; i++ {
233 // Search in a diagonal pattern for a match.
235 p := point{fwdFrontier.X + z, fwdFrontier.Y - z}
237 case p.X >= revPath.X || p.Y < fwdPath.Y:
238 stop1 = true // Hit top-right corner
239 case p.Y >= revPath.Y || p.X < fwdPath.X:
240 stop2 = true // Hit bottom-left corner
241 case f(p.X, p.Y).Equal():
242 // Match found, so connect the path to this point.
243 fwdPath.connect(p, f)
244 fwdPath.append(Identity)
245 // Follow sequence of matches as far as possible.
246 for fwdPath.X < revPath.X && fwdPath.Y < revPath.Y {
247 if !f(fwdPath.X, fwdPath.Y).Equal() {
250 fwdPath.append(Identity)
252 fwdFrontier = fwdPath.point
253 stop1, stop2 = true, true
255 searchBudget-- // Match not found
259 // Advance the frontier towards reverse point.
260 if revPath.X-fwdFrontier.X >= revPath.Y-fwdFrontier.Y {
266 // Reverse search from the end.
267 if fwdFrontier.X >= revFrontier.X || fwdFrontier.Y >= revFrontier.Y || searchBudget == 0 {
270 for stop1, stop2, i := false, false, 0; !(stop1 && stop2) && searchBudget > 0; i++ {
271 // Search in a diagonal pattern for a match.
273 p := point{revFrontier.X - z, revFrontier.Y + z}
275 case fwdPath.X >= p.X || revPath.Y < p.Y:
276 stop1 = true // Hit bottom-left corner
277 case fwdPath.Y >= p.Y || revPath.X < p.X:
278 stop2 = true // Hit top-right corner
279 case f(p.X-1, p.Y-1).Equal():
280 // Match found, so connect the path to this point.
281 revPath.connect(p, f)
282 revPath.append(Identity)
283 // Follow sequence of matches as far as possible.
284 for fwdPath.X < revPath.X && fwdPath.Y < revPath.Y {
285 if !f(revPath.X-1, revPath.Y-1).Equal() {
288 revPath.append(Identity)
290 revFrontier = revPath.point
291 stop1, stop2 = true, true
293 searchBudget-- // Match not found
297 // Advance the frontier towards forward point.
298 if revFrontier.X-fwdPath.X >= revFrontier.Y-fwdPath.Y {
305 // Join the forward and reverse paths and then append the reverse path.
306 fwdPath.connect(revPath.point, f)
307 for i := len(revPath.es) - 1; i >= 0; i-- {
309 revPath.es = revPath.es[:i]
317 dir int // +1 if forward, -1 if reverse
318 point // Leading point of the EditScript path
322 // connect appends any necessary Identity, Modified, UniqueX, or UniqueY types
323 // to the edit-script to connect p.point to dst.
324 func (p *path) connect(dst point, f EqualFunc) {
326 // Connect in forward direction.
327 for dst.X > p.X && dst.Y > p.Y {
328 switch r := f(p.X, p.Y); {
333 case dst.X-p.X >= dst.Y-p.Y:
346 // Connect in reverse direction.
347 for p.X > dst.X && p.Y > dst.Y {
348 switch r := f(p.X-1, p.Y-1); {
353 case p.Y-dst.Y >= p.X-dst.X:
368 func (p *path) append(t EditType) {
369 p.es = append(p.es, t)
371 case Identity, Modified:
381 type point struct{ X, Y int }
383 func (p *point) add(dx, dy int) { p.X += dx; p.Y += dy }
385 // zigzag maps a consecutive sequence of integers to a zig-zag sequence.
386 // [0 1 2 3 4 5 ...] => [0 -1 +1 -2 +2 ...]
387 func zigzag(x int) int {