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To find the number of occurrences of a given string P ( length m ) in a text T ( length N )

We must use binary search against the suffix array of T.

The issue with using standard binary search ( without the LCP information ) is that in each of the O(log N) comparisons you need to make, you compare P to the current entry of the suffix array, which means a full string comparison of up to m characters. So the complexity is O(m*log N).

The LCP-LR array helps improve this to O(m+log N). know more

How we precompute LCP-LR array from LCP array?

And How does LCP-LR help in finding the number of occurrences of a pattern?

Please Explain the Algorithm with Example

Thank you

pavaniiitn
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2 Answers2

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// 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]);
}

Reference: https://stackoverflow.com/a/28385677/1428052

Community
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Abhijeet Ashok Muneshwar
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  • We can construct LCP Array using segment tree in O(n) but each operation on segment tree takes O(log n). How can we improve this to O(1) ? Is it possible? – pavaniiitn Sep 16 '16 at 06:05
  • the LCP-LR should precompute all possible results so you won't need to divide it to find what you need – Daniel Dec 10 '16 at 02:35
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    The computation of `mid = (low + high) / 2` will overflow on large arrays. Consider changing it to `mid = low + (high - low) / 2`. – John Källén Oct 10 '17 at 08:45
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Not having enough reps to comment so posting. Is anybody able to create the LCP-LR using @Abhijeet Ashok Muneshwar solution. For ex for text- mississippi the Suffix array-

0 1 2 3 4 5 6 7 8 9 10

10 7 1 4 0 9 8 3 6 2 5

The LCP array will be

0 1 2 3 4 5 6 7 8 9 10

1 1 4 0 0 1 0 2 1 3 0

And LCP-LR will be

0 1 2 3 4 5 6 7 8 9 10

1 1 0 4 0 0 0 0 0 1 3

But the LCP-LR obtained using the code is not same as above. To the method buildLCP_LR i am passing index=0, low=0, high=n

Braj
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