Is there a problem link

https://cp-algorithms.com/string/string-hashing.html in this tutorial you can learn how to find the number of distinct substrings using hashing.

To solve this you can build a suffix tree of the original string S and count the amount of nodes on the tree. The complexity of this solution is O(N) if you use Ukkonen's algorithm to build the suffix tree.

Problem link: http://acm.timus.ru/problem.aspx?space=1&num=1590

here is the problem link

and here is the solution by me.

I know that there is a solution in O (N log N) with Suffix Array and LCP, but the real question is the maximum value that the F () function could reach in any string of at most 100,000 characters with a 26 letter dictionary.

I think that the more characters the string has, the less possibility there is that the function F () defined for every string of at most 100000 and with a 26-letter dictionary reaches its maximum value but I am not sure of the maximum value of the function F (). Which would suit me very well because I think I solve many problems depending on the maximum value of F ().

I wrote the Suffix Array solution, and generated a few random strings of length 100.000.

The maximal value of the number of substrings is N * (N - 1) / 2 = 5000050000, and all the random strings i generated had around 4999700000 distinct substrings. It's almost 0.99995% of the maximal value we could get.

If we think about it it's quite obvious why: as the string is random, there is virtually no chance that two different substrings of length >= 10 match (the probability of a colision is 1/26^10 = 7e-15 ~= 0). So except for the small substrings of length 1, 2, ... 9 (which are 9 * N = 900000), all the remaining 4999500000 are distinct.

So if your hope was that there are few such distinct substrings, sorry to break it down :(