Update string-algorithms.md

Author: ankitpriyarup

string-algorithms.md

@@ -390,7 +390,7 @@ vector<vector<int>> group_identical_strings(vector<string> const& s)
 
 ![](.gitbook/assets/image%20%2863%29%20%281%29.png)
 
-### Number of different substrings in a string \(N^2 log N\)
+### Number of different substrings or Number of unique substring in a string \(N^2 log N\)
 
 ```cpp
 int count_unique_substrings(string const& s)
@@ -421,6 +421,7 @@ int count_unique_substrings(string const& s)
  }
  return cnt;
 }
+// There's a better way using LCP & Suffix Array below.
 ```
 
 ## Rolling Hashes and Bloom Filters
@@ -629,8 +630,24 @@ vector<int> constructLCP(string const& s, vector<int> const& p) // string s
 }
 ```
 
-### Count number of different substrings
+### Count number of different substrings or unique substrings
 ```c++
+/*
+Calculate suffix array and LCP array first.
+Example: "ABABBAB"
+SA String LCP
+5 AB 0
+0 ABABBAB 2
+2 ABBAB 2
+6 B 0
+4 BAB 1
+1 BABBAB 3
+3 BBAB 1
+
+A substring is a prefix of a suffix. So problem now is calculate unique prefixes across suffixes.
+For n chars it will be n*(n+1)/2
+There will be LCP[i] duplicates at every suffix level
+*/
 intnumberOfDiffSubstrings(vector<int> &lcp, string &s)
 {
  int n = s.size();