Implementation of string pattern matching using Suffix Array and LCP(-LR)

Question

During the last weeks I tried to figure out how to efficiently find a string pattern within another string.

I found out that for a long time, the most efficient way

Answer 1

The termin that can help you: enchanced suffix array, which is used to describe suffix array with various other arrays in order to replace suffix tree (lcp, child).

These can be some of the examples:

https://code.google.com/p/esaxx/ ESAXX

http://bibiserv.techfak.uni-bielefeld.de/mkesa/ MKESA

The esaxx one seems to be doing what you want, plus, it has example enumSubstring.cpp how to use it.

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If you take a look at the referenced paper, it mentions an useful property (4.2). Since SO does not support math, there is no point to copy it here.

I've done quick implementation, it uses segment tree:

// note that arrSize is O(n)
// int arrSize = 2 * 2 ^ (log(N) + 1) + 1; // start from 1

// LCP = new int[N];
// fill the LCP...
// LCP_LR = new int[arrSize];
// memset(LCP_LR, maxValueOfInteger, arrSize);
// 

// init: buildLCP_LR(1, 1, N);
// LCP_LR[1] == [1..N]
// LCP_LR[2] == [1..N/2]
// LCP_LR[3] == [N/2+1 .. N]

// rangeI = LCP_LR[i]
//   rangeILeft  = LCP_LR[2 * i]
//   rangeIRight = LCP_LR[2 * i + 1]
// ..etc
void buildLCP_LR(int index, int low, int high)
{
    if(low == high)
    {
        LCP_LR[index] = LCP[low];
        return;
    }

    int mid = (low + high) / 2;

    buildLCP_LR(2*index, low, mid);
    buildLCP_LR(2*index+1, mid + 1, high);

    LCP_LR[index] = min(LCP_LR[2*index], LCP_LR[2*index + 1]);
}