我刚刚实现了最佳匹配文件搜索算法来查找与字典中的字符串最接近的匹配。对我的代码进行分析后，我发现绝大多数时间都花在计算查询与可能结果之间的距离上。我目前正在实现使用二维数组计算编辑距离的算法，这使得实现成为 O(n^2) 操作。我希望有人能建议一种更快的方法来完成同样的事情。
这是我的实现：
public int calculate(String root, String query)
{
int arr[][] = new int[root.length() + 2][query.length() + 2];
for (int i = 2; i < root.length() + 2; i++)
{
arr[i][0] = (int) root.charAt(i - 2);
arr[i][1] = (i - 1);
}
for (int i = 2; i < query.length() + 2; i++)
{
arr[0][i] = (int) query.charAt(i - 2);
arr[1][i] = (i - 1);
}
for (int i = 2; i < root.length() + 2; i++)
{
for (int j = 2; j < query.length() + 2; j++)
{
int diff = 0;
if (arr[0][j] != arr[i][0])
{
diff = 1;
}
arr[i][j] = min((arr[i - 1][j] + 1), (arr[i][j - 1] + 1), (arr[i - 1][j - 1] + diff));
}
}
return arr[root.length() + 1][query.length() + 1];
}
public int min(int n1, int n2, int n3)
{
return (int) Math.min(n1, Math.min(n2, n3));
}
Levenshtein 距离上的 wikipedia 条目对优化计算提供了有用的建议——在您的情况下最适用的建议是，如果您可以在感兴趣的最大距离上设置一个界限
kO(n times k)O(n squared)> k由于您正在寻找最接近的匹配，因此您可以逐渐减少
k我相信，如果您需要获得大幅更好的性能，您可能必须接受一些强有力的妥协来计算更近似的距离（因此获得“相当好的匹配”而不一定是最佳匹配）。
根据此博客上的评论，加速 Levenshtein，您可以使用 VP 树并实现 O(nlogn)。 同一篇博客上的另一条评论指出了 VP-Trees 和 Levenshtein 的 python 实现。 请告诉我们这是否有效。
post上找到的编辑距离VBA函数以使用一维数组。 它的执行速度要快得多。
'Calculate the Levenshtein Distance between two strings (the number of insertions,
'deletions, and substitutions needed to transform the first string into the second)
Public Function LevenshteinDistance2(ByRef s1 As String, ByRef s2 As String) As Long
Dim L1 As Long, L2 As Long, D() As Long, LD As Long 'Length of input strings and distance matrix
Dim i As Long, j As Long, ss2 As Long, ssL As Long, cost As Long 'loop counters, loop step, loop start, and cost of substitution for current letter
Dim cI As Long, cD As Long, cS As Long 'cost of next Insertion, Deletion and Substitution
Dim L1p1 As Long, L1p2 As Long 'Length of S1 + 1, Length of S1 + 2
L1 = Len(s1): L2 = Len(s2)
L1p1 = L1 + 1
L1p2 = L1 + 2
LD = (((L1 + 1) * (L2 + 1))) - 1
ReDim D(0 To LD)
ss2 = L1 + 1
For i = 0 To L1 Step 1: D(i) = i: Next i 'setup array positions 0,1,2,3,4,...
For j = 0 To LD Step ss2: D(j) = j / ss2: Next j 'setup array positions 0,1,2,3,4,...
For j = 1 To L2
ssL = (L1 + 1) * j
For i = (ssL + 1) To (ssL + L1)
If Mid$(s1, i Mod ssL, 1) <> Mid$(s2, j, 1) Then cost = 1 Else cost = 0
cI = D(i - 1) + 1
cD = D(i - L1p1) + 1
cS = D(i - L1p2) + cost
If cI <= cD Then 'Insertion or Substitution
If cI <= cS Then D(i) = cI Else D(i) = cS
Else 'Deletion or Substitution
If cD <= cS Then D(i) = cD Else D(i) = cS
End If
Next i
Next j
LevenshteinDistance2 = D(LD)
End Function
我已经使用长度为 11,304 的字符串“s1”和长度为 5,665 的字符串“s2”测试了此函数（> 6400 万个字符比较）。 使用上述单维版本的函数，在我的机器上执行时间约为 24 秒。 我在上面的链接中引用的原始二维函数对于相同的字符串需要约 37 秒。 我进一步优化了单维函数，如下所示，对于相同的字符串，它需要 ~10 秒。
'Calculate the Levenshtein Distance between two strings (the number of insertions,
'deletions, and substitutions needed to transform the first string into the second)
Public Function LevenshteinDistance(ByRef s1 As String, ByRef s2 As String) As Long
Dim L1 As Long, L2 As Long, D() As Long, LD As Long 'Length of input strings and distance matrix
Dim i As Long, j As Long, ss2 As Long 'loop counters, loop step
Dim ssL As Long, cost As Long 'loop start, and cost of substitution for current letter
Dim cI As Long, cD As Long, cS As Long 'cost of next Insertion, Deletion and Substitution
Dim L1p1 As Long, L1p2 As Long 'Length of S1 + 1, Length of S1 + 2
Dim sss1() As String, sss2() As String 'Character arrays for string S1 & S2
L1 = Len(s1): L2 = Len(s2)
L1p1 = L1 + 1
L1p2 = L1 + 2
LD = (((L1 + 1) * (L2 + 1))) - 1
ReDim D(0 To LD)
ss2 = L1 + 1
For i = 0 To L1 Step 1: D(i) = i: Next i 'setup array positions 0,1,2,3,4,...
For j = 0 To LD Step ss2: D(j) = j / ss2: Next j 'setup array positions 0,1,2,3,4,...
ReDim sss1(1 To L1) 'Size character array S1
ReDim sss2(1 To L2) 'Size character array S2
For i = 1 To L1 Step 1: sss1(i) = Mid$(s1, i, 1): Next i 'Fill S1 character array
For i = 1 To L2 Step 1: sss2(i) = Mid$(s2, i, 1): Next i 'Fill S2 character array
For j = 1 To L2
ssL = (L1 + 1) * j
For i = (ssL + 1) To (ssL + L1)
If sss1(i Mod ssL) <> sss2(j) Then cost = 1 Else cost = 0
cI = D(i - 1) + 1
cD = D(i - L1p1) + 1
cS = D(i - L1p2) + cost
If cI <= cD Then 'Insertion or Substitution
If cI <= cS Then D(i) = cI Else D(i) = cS
Else 'Deletion or Substitution
If cD <= cS Then D(i) = cD Else D(i) = cS
End If
Next i
Next j
LevenshteinDistance = D(LD)
End Function
讨论了您的算法和各种改进。然而，至少在一般情况下，O(n^2) 是你能得到的最好结果。 但是，如果您可以限制您的问题，则可以进行一些改进（例如，如果您只对小于
d的距离感兴趣，则复杂性为 O(dn) - 这可能是有意义的，因为距离很近的匹配字符串长度可能不是很有趣）。看看您是否可以利用您问题的具体情况...
// The code below is based on code from the Apache Commons lang project.
/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with this
* work for additional information regarding copyright ownership. The ASF
* licenses this file to You under the Apache License, Version 2.0 (the
* "License"); you may not use this file except in compliance with the
* License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
* License for the specific language governing permissions and limitations
* under the License.
*/
/**
* assert(levenshtein("algorithm", "altruistic")==6)
* assert(levenshtein("1638452297", "444488444")==9)
* assert(levenshtein("", "") == 0)
* assert(levenshtein("", "a") == 1)
* assert(levenshtein("aaapppp", "") == 7)
* assert(levenshtein("frog", "fog") == 1)
* assert(levenshtein("fly", "ant") == 3)
* assert(levenshtein("elephant", "hippo") == 7)
* assert(levenshtein("hippo", "elephant") == 7)
* assert(levenshtein("hippo", "zzzzzzzz") == 8)
* assert(levenshtein("hello", "hallo") == 1)
*
*/
def levenshtein(s: CharSequence, t: CharSequence, max: Int = Int.MaxValue) = {
import scala.annotation.tailrec
def impl(s: CharSequence, t: CharSequence, n: Int, m: Int) = {
// Inside impl n <= m!
val p = new Array[Int](n + 1) // 'previous' cost array, horizontally
val d = new Array[Int](n + 1) // cost array, horizontally
@tailrec def fillP(i: Int) {
p(i) = i
if (i < n) fillP(i + 1)
}
fillP(0)
@tailrec def eachJ(j: Int, t_j: Char, d: Array[Int], p: Array[Int]): Int = {
d(0) = j
@tailrec def eachI(i: Int) {
val a = d(i - 1) + 1
val b = p(i) + 1
d(i) = if (a < b) a else {
val c = if (s.charAt(i - 1) == t_j) p(i - 1) else p(i - 1) + 1
if (b < c) b else c
}
if (i < n)
eachI(i + 1)
}
eachI(1)
if (j < m)
eachJ(j + 1, t.charAt(j), p, d)
else
d(n)
}
eachJ(1, t.charAt(0), d, p)
}
val n = s.length
val m = t.length
if (n == 0) m else if (m == 0) n else {
if (n > m) impl(t, s, m, n) else impl(s, t, n, m)
}
}