| // 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 |
| |
| // 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 |
| } |
| |
| // 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. |
| |
| // 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, 0; !(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 |
| } |