LCS(Longest Common Subsequence)算法

LCS：最长公共子序列。

例：A{a,d,h,e,g,s,l} B{y,a,r,e,s,d}

LCS< A,B >={a,e,s}

思路：设A{a1,a2,…,an} B{b1,b2,…,bm}

若an==bm;则LCS< A,B >=LCS< A(n-1),B(m-1) >+an/bm

若an!=bm;则LCS< A,B >=LCS< A(n-1),B >或LCS< A,B >=LCS< A,B(m-1) >,即LCS< A,B >=max{LCS< A(n-1),B >，LCS< A,B(m-1) >}





Java实现

public class LCS {
private final static String[] empty = new String[0];

/**
* @return 最长公共字符串(可能有多个长度相同的)
*/
public static String[] lcs(String s1, String s2, boolean noRepeat) {
//排除常用情况
if (s1 == null || s1.length() == 0 || s2 == null || s2.length() == 0) {
return empty;
}
int len1 = s1.length();
int len2 = s2.length();
if (len1==len2&&s1.equals(s2)) {
return new String[] { s1 };
}
if (len1 > len2 && s1.indexOf(s2) != -1) {
return new String[] { s2 };
}
if (len2 > len1 && s2.indexOf(s1) != -1) {
return new String[] { s1 };
}
//构造对比矩阵
char[] chs1 = s1.toCharArray();
char[] chs2 = s2.toCharArray();
boolean[][] as = new boolean[len1][len2];
for (int i = 0; i < len1; i++) {
char ch1 = chs1[i];
for (int j = 0; j < len2; j++) {
char ch2 = chs2[j];
as[i][j] = ch1 == ch2;
}
}
// 收集正向\对角线
int max = 0;
Collection<String> buf = noRepeat ? (new HashSet<String>())
: (new ArrayList<String>());
for (int i = 0; i < len1; i++) {
for (int j = 0; j < len2; j++) {
int len = lcsLength(i, j, len1, len2, as);
if (len > 0 && len >= max) {
max = len;
buf.add(s1.substring(i, i + len));
}
}
}
// 取最长对角线(最长匹配字符)
List<String> ret = new ArrayList<String>();
for (String s : buf) {
if (s.length() == max) {
ret.add(s);
}
}
return ret.toArray(empty);
}

/**
* 递归计算长度(对角线)
*/
private static int lcsLength(int i, int j, int len1, int len2,
boolean[][] as) {
if (as[i][j]) {
int c = 1;
i++;
j++;
if (i < len1 && j < len2) {
c += lcsLength(i, j, len1, len2, as);
}
return c;
}
return 0;
}

public static void main(String[] args) {
{
String s1 = "12345";
String s2 = "12456";
// 输出[45,12]
System.out.println(Arrays.asList(lcs(s1, s2, true)));
}
{
String s1 = "123456";
String s2 = "1205678";
// 输出[56,12]
System.out.println(Arrays.asList(lcs(s1, s2, true)));
}
}
}