finding all distinct substring of a string

Question

hello guys i was given homework problem where it asks me to find all distinct substring of a string. I have implemented a method which will tell you all the substrings of s

Answer 1

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The solution consists of constructing the suffix array and then finding the number of distinct substrings based on the Longest Common Prefixes.

One key observation here is that:

If you look through the prefixes of each suffix of a string, you have covered all substrings of that string.

Let us take an example: BANANA

Suffixes are: 0) BANANA 1) ANANA 2) NANA 3) ANA 4) NA 5) A

It would be a lot easier to go through the prefixes if we sort the above set of suffixes, as we can skip the repeated prefixes easily.

Sorted set of suffixes: 5) A 3) ANA 1) ANANA 0) BANANA 4) NA 2) NANA

From now on,

LCP = Longest Common Prefix of 2 strings.

Initialize

ans = length(first suffix) = length("A") = 1.

Now consider the consecutive pairs of suffixes, i.e, [A, ANA], [ANA, ANANA], [ANANA, BANANA], etc. from the above set of sorted suffixes.

We can see that, LCP("A", "ANA") = "A".

All characters that are not part of the common prefix contribute to a distinct substring. In the above case, they are 'N' and 'A'. So they should be added to ans.

So we have, 1 2 ans += length("ANA") - LCP("A", "ANA") ans = ans + 3 - 1 = ans + 2 = 3

Do the same for the next pair of consecutive suffixes: ["ANA", "ANANA"]

1 2 3 4 LCP("ANA", "ANANA") = "ANA". ans += length("ANANA") - length(LCP) => ans = ans + 5 - 3 => ans = 3 + 2 = 5.

Similarly, we have:

1 2 LCP("ANANA", "BANANA") = 0 ans = ans + length("BANANA") - 0 = 11

1 2 LCP("BANANA", "NA") = 0 ans = ans + length("NA") - 0 = 13

1 2 LCP("NA", "NANA") = 2 ans = ans + length("NANA") - 2 = 15

Hence the number of distinct substrings for the string "BANANA" = 15.