| 1 | // Copyright 2022 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 file. |
| 4 | |
| 5 | package lcs |
| 6 | |
| 7 | import ( |
| 8 | "log" |
| 9 | "sort" |
| 10 | ) |
| 11 | |
| 12 | // lcs is a longest common sequence |
| 13 | type lcs []diag |
| 14 | |
| 15 | // A diag is a piece of the edit graph where A[X+i] == B[Y+i], for 0<=i<Len. |
| 16 | // All computed diagonals are parts of a longest common subsequence. |
| 17 | type diag struct { |
| 18 | X, Y int |
| 19 | Len int |
| 20 | } |
| 21 | |
| 22 | // sort sorts in place, by lowest X, and if tied, inversely by Len |
| 23 | func (l lcs) sort() lcs { |
| 24 | sort.Slice(l, func(i, j int) bool { |
| 25 | if l[i].X != l[j].X { |
| 26 | return l[i].X < l[j].X |
| 27 | } |
| 28 | return l[i].Len > l[j].Len |
| 29 | }) |
| 30 | return l |
| 31 | } |
| 32 | |
| 33 | // validate that the elements of the lcs do not overlap |
| 34 | // (can only happen when the two-sided algorithm ends early) |
| 35 | // expects the lcs to be sorted |
| 36 | func (l lcs) valid() bool { |
| 37 | for i := 1; i < len(l); i++ { |
| 38 | if l[i-1].X+l[i-1].Len > l[i].X { |
| 39 | return false |
| 40 | } |
| 41 | if l[i-1].Y+l[i-1].Len > l[i].Y { |
| 42 | return false |
| 43 | } |
| 44 | } |
| 45 | return true |
| 46 | } |
| 47 | |
| 48 | // repair overlapping lcs |
| 49 | // only called if two-sided stops early |
| 50 | func (l lcs) fix() lcs { |
| 51 | // from the set of diagonals in l, find a maximal non-conflicting set |
| 52 | // this problem may be NP-complete, but we use a greedy heuristic, |
| 53 | // which is quadratic, but with a better data structure, could be D log D. |
| 54 | // indepedent is not enough: {0,3,1} and {3,0,2} can't both occur in an lcs |
| 55 | // which has to have monotone x and y |
| 56 | if len(l) == 0 { |
| 57 | return nil |
| 58 | } |
| 59 | sort.Slice(l, func(i, j int) bool { return l[i].Len > l[j].Len }) |
| 60 | tmp := make(lcs, 0, len(l)) |
| 61 | tmp = append(tmp, l[0]) |
| 62 | for i := 1; i < len(l); i++ { |
| 63 | var dir direction |
| 64 | nxt := l[i] |
| 65 | for _, in := range tmp { |
| 66 | if dir, nxt = overlap(in, nxt); dir == empty || dir == bad { |
| 67 | break |
| 68 | } |
| 69 | } |
| 70 | if nxt.Len > 0 && dir != bad { |
| 71 | tmp = append(tmp, nxt) |
| 72 | } |
| 73 | } |
| 74 | tmp.sort() |
| 75 | if false && !tmp.valid() { // debug checking |
| 76 | log.Fatalf("here %d", len(tmp)) |
| 77 | } |
| 78 | return tmp |
| 79 | } |
| 80 | |
| 81 | type direction int |
| 82 | |
| 83 | const ( |
| 84 | empty direction = iota // diag is empty (so not in lcs) |
| 85 | leftdown // proposed acceptably to the left and below |
| 86 | rightup // proposed diag is acceptably to the right and above |
| 87 | bad // proposed diag is inconsistent with the lcs so far |
| 88 | ) |
| 89 | |
| 90 | // overlap trims the proposed diag prop so it doesn't overlap with |
| 91 | // the existing diag that has already been added to the lcs. |
| 92 | func overlap(exist, prop diag) (direction, diag) { |
| 93 | if prop.X <= exist.X && exist.X < prop.X+prop.Len { |
| 94 | // remove the end of prop where it overlaps with the X end of exist |
| 95 | delta := prop.X + prop.Len - exist.X |
| 96 | prop.Len -= delta |
| 97 | if prop.Len <= 0 { |
| 98 | return empty, prop |
| 99 | } |
| 100 | } |
| 101 | if exist.X <= prop.X && prop.X < exist.X+exist.Len { |
| 102 | // remove the beginning of prop where overlaps with exist |
| 103 | delta := exist.X + exist.Len - prop.X |
| 104 | prop.Len -= delta |
| 105 | if prop.Len <= 0 { |
| 106 | return empty, prop |
| 107 | } |
| 108 | prop.X += delta |
| 109 | prop.Y += delta |
| 110 | } |
| 111 | if prop.Y <= exist.Y && exist.Y < prop.Y+prop.Len { |
| 112 | // remove the end of prop that overlaps (in Y) with exist |
| 113 | delta := prop.Y + prop.Len - exist.Y |
| 114 | prop.Len -= delta |
| 115 | if prop.Len <= 0 { |
| 116 | return empty, prop |
| 117 | } |
| 118 | } |
| 119 | if exist.Y <= prop.Y && prop.Y < exist.Y+exist.Len { |
| 120 | // remove the beginning of peop that overlaps with exist |
| 121 | delta := exist.Y + exist.Len - prop.Y |
| 122 | prop.Len -= delta |
| 123 | if prop.Len <= 0 { |
| 124 | return empty, prop |
| 125 | } |
| 126 | prop.X += delta // no test reaches this code |
| 127 | prop.Y += delta |
| 128 | } |
| 129 | if prop.X+prop.Len <= exist.X && prop.Y+prop.Len <= exist.Y { |
| 130 | return leftdown, prop |
| 131 | } |
| 132 | if exist.X+exist.Len <= prop.X && exist.Y+exist.Len <= prop.Y { |
| 133 | return rightup, prop |
| 134 | } |
| 135 | // prop can't be in an lcs that contains exist |
| 136 | return bad, prop |
| 137 | } |
| 138 | |
| 139 | // manipulating Diag and lcs |
| 140 | |
| 141 | // prepend a diagonal (x,y)-(x+1,y+1) segment either to an empty lcs |
| 142 | // or to its first Diag. prepend is only called to extend diagonals |
| 143 | // the backward direction. |
| 144 | func (lcs lcs) prepend(x, y int) lcs { |
| 145 | if len(lcs) > 0 { |
| 146 | d := &lcs[0] |
| 147 | if int(d.X) == x+1 && int(d.Y) == y+1 { |
| 148 | // extend the diagonal down and to the left |
| 149 | d.X, d.Y = int(x), int(y) |
| 150 | d.Len++ |
| 151 | return lcs |
| 152 | } |
| 153 | } |
| 154 | |
| 155 | r := diag{X: int(x), Y: int(y), Len: 1} |
| 156 | lcs = append([]diag{r}, lcs...) |
| 157 | return lcs |
| 158 | } |
| 159 | |
| 160 | // append appends a diagonal, or extends the existing one. |
| 161 | // by adding the edge (x,y)-(x+1.y+1). append is only called |
| 162 | // to extend diagonals in the forward direction. |
| 163 | func (lcs lcs) append(x, y int) lcs { |
| 164 | if len(lcs) > 0 { |
| 165 | last := &lcs[len(lcs)-1] |
| 166 | // Expand last element if adjoining. |
| 167 | if last.X+last.Len == x && last.Y+last.Len == y { |
| 168 | last.Len++ |
| 169 | return lcs |
| 170 | } |
| 171 | } |
| 172 | |
| 173 | return append(lcs, diag{X: x, Y: y, Len: 1}) |
| 174 | } |
| 175 | |
| 176 | // enforce constraint on d, k |
| 177 | func ok(d, k int) bool { |
| 178 | return d >= 0 && -d <= k && k <= d |
| 179 | } |
| 180 |
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