jigsaw7's blog

Strings Problem
By jigsaw7, history, 5 years ago, In English

Given 2 strings S1 and S2 consisting of English letters.
For each index i in S1, it is required to find the largest index j >= i such that S1[i..j] is a substring of S2.

For example,
S1 = "acdsuaf"
S2 = "cadsua"
ans = [1, 2, 6, 6, 6, 6, -1].

How to approach this problem in linear time?

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Comments Comments (6)
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5 years ago, # |
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Is there a problem link

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5 years ago, # |
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i think u can refer geeks for geeks their is a article on it

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5 years ago, # |
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This isn’t the linear time algorithm but binary searching on j will work in O(n log n) which should normally be fast enough for most purposes

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    5 years ago, # ^ |
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    Please explain how to check that S1[i..j] is a substring of S2 in O(1)?

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5 years ago, # |
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Let $$$ S=S_1+ | +S_2 $$$.

Using Suffix Array, construct the LCP array of string $$$S$$$. For each suffix of $$$S_1$$$, find the maximum LCP with the nearest suffixes of $$$S_2$$$ using binary search on the already constructed LCP array of string $$$S$$$.

Complexity: $$$O(n log n)$$$.

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