一段时间以来，我使用了Levenshtein distance的Apache Commons lang StringUtils实现。 它实现了一些众所周知的技巧，通过仅挂接到两个数组而不是为备忘录表分配巨大的nxm表来使用较少的内存。 它还仅检查宽度为2 * k +1的“条带”，其中k为最大编辑次数。

在levenshtein的大多数实际用法中，您只关心一个字符串是否在另一个字符串的少量编辑（1、2、3）之内。 这避免了使levenstein变得“昂贵”的大部分n * m计算。 我们发现，在ak <= 3时，具有这些技巧的levenshtein的速度比Jaro-Winkler distance快，后者是一种近似编辑距离计算，被创建为更快的近似值（这有很多原因）。

不幸的是，Apache Commons Lang实现仅计算Levenshtein，而不计算可能更有用的Damerau-Levenshtein距离 。 Levenshtein定义了编辑操作的插入，删除和替换。 Damerau变体将* transposition *添加到列表中，这对于我使用编辑距离的大多数位置都非常有用。 不幸的是，DL距离不是真正的度量标准，因为它不考虑三角形不等式，但是许多应用程序不受此影响。 从该维基百科页面可以看到，“最佳字符串对齐”和DL距离之间经常会混淆。 实际上，OSA是一种更简单的算法，并且需要较少的簿记，因此运行时间可能略微更快。

我找不到任何使用我在Apache Commons Lang中看到的内存技巧和“条带化”技巧的OSA或DL实现。 因此，我使用这些技巧实现了自己的OSA。 在某些时候，我还将使用这些技巧来实现DL，并查看性能差异是什么：

这是Java中的OSA。 它是公共领域； 随意使用。 单元测试如下。 唯一的依赖关系是Guava-，但它只是前提条件类和文档注释，因此如果您愿意，可以轻松删除该依赖关系：

package com.github.steveash.util;import static com.google.common.base.Preconditions.checkArgument;
import static com.google.common.base.Preconditions.checkNotNull;
import static com.google.common.primitives.Shorts.checkedCast;
import static java.lang.Math.abs;
import static java.lang.Math.max;import java.util.Arrays;import com.google.common.annotations.VisibleForTesting;/*** Implementation of the OSA which is similar to the Damerau-Levenshtein in that it allows for transpositions to* count as a single edit distance, but is not a true metric and can over-estimate the cost because it disallows* substrings to edited more than once.  See wikipedia for more discussion on OSA vs DL* <p/>* See Algorithms on Strings, Trees and Sequences by Dan Gusfield for more information.* <p/>* This also has a set of local buffer implementations to avoid allocating new buffers each time, which might be* a premature optimization* <p/>* @author Steve Ash*/
public class OptimalStringAlignment {private static final int threadLocalBufferSize = 64;private static final ThreadLocal<short[]> costLocal = new ThreadLocal<short[]>() {@Overrideprotected short[] initialValue() {return new short[threadLocalBufferSize];}};private static final ThreadLocal<short[]> back1Local = new ThreadLocal<short[]>() {@Overrideprotected short[] initialValue() {return new short[threadLocalBufferSize];}};private static final ThreadLocal<short[]> back2Local = new ThreadLocal<short[]>() {@Overrideprotected short[] initialValue() {return new short[threadLocalBufferSize];}};public static int editDistance(CharSequence s, CharSequence t, int threshold) {checkNotNull(s, "cannot measure null strings");checkNotNull(t, "cannot measure null strings");checkArgument(threshold >= 0, "Threshold must not be negative");checkArgument(s.length() < Short.MAX_VALUE, "Cannot take edit distance of strings longer than 32k chars");checkArgument(t.length() < Short.MAX_VALUE, "Cannot take edit distance of strings longer than 32k chars");if (s.length() + 1 > threadLocalBufferSize || t.length() + 1 > threadLocalBufferSize)return editDistanceWithNewBuffers(s, t, checkedCast(threshold));short[] cost = costLocal.get();short[] back1 = back1Local.get();short[] back2 = back2Local.get();return editDistanceWithBuffers(s, t, checkedCast(threshold), back2, back1, cost);}@VisibleForTestingstatic int editDistanceWithNewBuffers(CharSequence s, CharSequence t, short threshold) {int slen = s.length();short[] back1 = new short[slen + 1];    // "up 1" row in tableshort[] back2 = new short[slen + 1];    // "up 2" row in tableshort[] cost = new short[slen + 1];     // "current cost"return editDistanceWithBuffers(s, t, threshold, back2, back1, cost);}private static int editDistanceWithBuffers(CharSequence s, CharSequence t, short threshold,short[] back2, short[] back1, short[] cost) {short slen = (short) s.length();short tlen = (short) t.length();// if one string is empty, the edit distance is necessarily the length of the otherif (slen == 0) {return tlen <= threshold ? tlen : -1;} else if (tlen == 0) {return slen <= threshold ? slen : -1;}// if lengths are different > k, then can't be within edit distanceif (abs(slen - tlen) > threshold)return -1;if (slen > tlen) {// swap the two strings to consume less memoryCharSequence tmp = s;s = t;t = tmp;slen = tlen;tlen = (short) t.length();}initMemoiseTables(threshold, back2, back1, cost, slen);for (short j = 1; j <= tlen; j++) {cost[0] = j; // j is the cost of inserting this many characters// stripe boundsint min = max(1, j - threshold);int max = min(slen, (short) (j + threshold));// at this iteration the left most entry is "too much" so reset itif (min > 1) {cost[min - 1] = Short.MAX_VALUE;}iterateOverStripe(s, t, j, cost, back1, back2, min, max);// swap our cost arrays to move on to the next "row"short[] tempCost = back2;back2 = back1;back1 = cost;cost = tempCost;}// after exit, the current cost is in back1// if back1[slen] > k then we exceeded, so return -1if (back1[slen] > threshold) {return -1;}return back1[slen];}private static void iterateOverStripe(CharSequence s, CharSequence t, short j,short[] cost, short[] back1, short[] back2, int min, int max) {// iterates over the stripefor (int i = min; i <= max; i++) {if (s.charAt(i - 1) == t.charAt(j - 1)) {cost[i] = back1[i - 1];} else {cost[i] = (short) (1 + min(cost[i - 1], back1[i], back1[i - 1]));}if (i >= 2 && j >= 2) {// possible transposition to check forif ((s.charAt(i - 2) == t.charAt(j - 1)) &&s.charAt(i - 1) == t.charAt(j - 2)) {cost[i] = min(cost[i], (short) (back2[i - 2] + 1));}}}}private static void initMemoiseTables(short threshold, short[] back2, short[] back1, short[] cost, short slen) {// initial "starting" values for inserting all the lettersshort boundary = (short) (min(slen, threshold) + 1);for (short i = 0; i < boundary; i++) {back1[i] = i;back2[i] = i;}// need to make sure that we don't read a default value when looking "up"Arrays.fill(back1, boundary, slen + 1, Short.MAX_VALUE);Arrays.fill(back2, boundary, slen + 1, Short.MAX_VALUE);Arrays.fill(cost, 0, slen + 1, Short.MAX_VALUE);}private static short min(short a, short b) {return (a <= b ? a : b);}private static short min(short a, short b, short c) {return min(a, min(b, c));}
}

import org.junit.Testimport static com.github.steveash.util.OptimalStringAlignment.editDistance/*** @author Steve Ash*/
class OptimalStringAlignmentTest {@Testpublic void shouldBeZeroForEqualStrings() throws Exception {assert 0 == editDistance("steve", "steve", 1)assert 0 == editDistance("steve", "steve", 0)assert 0 == editDistance("steve", "steve", 2)assert 0 == editDistance("steve", "steve", 100)assert 0 == editDistance("s", "s", 1)assert 0 == editDistance("s", "s", 0)assert 0 == editDistance("s", "s", 2)assert 0 == editDistance("s", "s", 100)assert 0 == editDistance("", "", 0)assert 0 == editDistance("", "", 1)assert 0 == editDistance("", "", 100)}@Testpublic void shouldBeOneForSingleOperation() throws Exception {def a = "steve";for (int i = 0; i < 5; i++) {assertOneOp(new StringBuilder(a).insert(i, 'f'), a)assertOneOp(new StringBuilder(a).deleteCharAt(i), a)def sb = new StringBuilder(a)sb.setCharAt(i, 'x' as char);assertOneOp(sb, a)if (i > 1) {sb = new StringBuilder(a)char t = sb.charAt(i - 1)sb.setCharAt(i - 1, sb.charAt(i))sb.setCharAt(i, t)println "comparing " + sb.toString() + " -> " + aassertOneOp(sb, a)}}}@Testpublic void shouldCountTransposeAsOne() throws Exception {assert 3 == editDistance("xxsteve", "steev", 4)assert 3 == editDistance("xxsteve", "steev", 3)assert 3 == editDistance("steev", "xxsteve", 4)assert 3 == editDistance("steev", "xxsteve", 3)assert -1 == editDistance("steev", "xxsteve", 2)assert 4 == editDistance("xxtseve", "steev", 4)assert 5 == editDistance("xxtsevezx", "steevxz", 5)assert 6 == editDistance("xxtsevezx", "steevxzpp", 6)assert 7 == editDistance("xxtsfevezx", "steevxzpp", 7)assert 4 == editDistance("xxtsf", "st", 7)assert 4 == editDistance("evezx", "eevxzpp", 7)assert 7 == editDistance("xxtsfevezx", "steevxzpp", 7)}@Testpublic void shouldCountLeadingCharacterTranspositionsAsOne() throws Exception {assert 1 == editDistance("rosa", "orsa", 2)}private void assertOneOp(CharSequence a, CharSequence b) {assert 1 == editDistance(a, b, 1)assert 1 == editDistance(b, a, 1)assert 1 == editDistance(a, b, 2)assert 1 == editDistance(b, a, 2)}@Testpublic void shouldShortCutWhenSpecialCase() throws Exception {assert 1 == editDistance("s", "", 1)assert 1 == editDistance("", "s", 1)assert -1 == editDistance("s", "", 0)assert -1 == editDistance("", "s", 0)assert -1 == editDistance("st", "", 1)assert -1 == editDistance("", "st", 1)assert -1 == editDistance("steve", "ste", 0)assert -1 == editDistance("ste", "steve", 0)assert -1 == editDistance("stev", "steve", 0)assert -1 == editDistance("ste", "steve", 1)assert -1 == editDistance("steve", "ste", 1)assert 1 == editDistance("steve", "stev", 1)assert 1 == editDistance("stev", "steve", 1)}
}

翻译自: https://www.javacodegeeks.com/2013/11/java-implementation-of-optimal-string-alignment.html