计算后缀数组的LCP(Longest Common Prefix)

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：

 

/**
 * 
 * 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