计算后缀数组的LCP(Longest Common Prefix)

转载自：/article/7610616.html特此感谢作者，仅作笔记使用

所谓LCP(Longest Common Prefix)是指后缀数组中相邻两个后缀的最长公共前缀的长度。在后缀数组的应用中，LCP是很重要的信息。

设后缀数组为SA, 用LCP(i)定义为第SA[i]个后缀和第SA[i-1]个后缀之间的最长公共前缀长度。由于输入文本T的第p个后缀和第p-1个后缀之间存在如下关系：LCP(p) >= LCP(p-1) - 1，因此如果已知第p-1个后缀的LCP(p-1)，那么在计算第p个后缀的LCP(p)时，可以直接跳过第p个后缀的前LCP(p-1)-1个字符，然后在下一个字符位置开始与后缀数组中与p相邻的前一个后缀（设它为文本T的第q个后缀，即q=SA[Rank[p]-2]）依次按照LCP的定义计算出LCP(p)的值。按照该算法计算出的LCP数组的复杂度为O(n)。

实现：

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/**

*

* Derive LCP(Longest Common Prefix) from Suffix Array in O(n)

*

*

* Copyright (c) 2011 ljs (http://blog.csdn.net/ljsspace/)

* Licensed under GPL (http://www.opensource.org/licenses/gpl-license.php)

*

* @author ljs

* 2011-07-20

*

*/

public class LCP {

//rank[p]'s index starts with 1 (not 0)

public int[] solve(String text,int[] sa,int[] rank){

if(text == null)return null;

int len = text.length();

if(len == 0) return null;

int[] lcpz = new int[len];

//base case: p=0

//caculate LCP of suffix[0]

int lcp = 0;

int r = rank[0]-1;

if(r>0){

int q=sa[r-1];

//caculate LCP by definition

for(int i=0,j=q;i<len && j<len;i++,j++){

if(text.charAt(i) != text.charAt(j)){

lcp=i;

break;

}

}

}

lcpz[0] = lcp;

//other cases: p>=1

//ignore p == sa[0] because LCP=0 for suffix[p] where rank[p]=0

for(int p=1;p<len && p != sa[0];p++){

int h = lcpz[p-1];

int q=sa[rank[p]-2];

lcp = 0;

if(h>1){ //for h<=1, caculate LCP by definition (i.e. start with lcp=0)

//jump h-1 chars for suffix[p] and suffix[q]

lcp = h-1;

}

for(int i=p+lcp,j=q+lcp,k=0;i<len && j<len;i++,j++,k++){

if(text.charAt(i) != text.charAt(j)){

lcp+=k;

break;

}

}

lcpz[p] = lcp;

}

//caculate LCP

int[] LCP = new int[len];

for(int i=0;i<len;i++){

LCP[i] = lcpz[sa[i]];

}

return LCP;

}

public static void main(String[] args) {

String text = "mississippi#";

LCP solver = new LCP();

int[] LCP = solver.solve(text,

new int[]{11,10,7,4,1,0,9,8,6,3,5,2},

new int[]{6,5,12,10,4,11,9,3,8,7,2,1});

System.out.format("LCP array for text: %s%n",text);

for(int i=0;i<LCP.length;i++){

System.out.format(" %d",LCP[i]);

}

}

}

测试：

LCP array for text: mississippi#

0 0 1 1 4 0 0 1 0 2 1 3