Count distinct substrings of a string using Rabin Karp algorithm
Given a string, count the number of distinct substrings using Rabin Karp Algorithm.
Input : str = “aba” Output : 5 Explanation : Total number of distinct substring are 5 - "a", "ab", "aba", "b" ,"ba" Input : str = “abcd” Output : 10 Explanation : Total number of distinct substring are 10 - "a", "ab", "abc", "abcd", "b", "bc", "bcd", "c", "cd", "d"
Prerequisite: Rabin-Karp Algorithm for Pattern Searching
Calculate the current hash value of the current character and store
in a dictionary/map to avoid repetition.
To compute the hash (rolling hash) as done in Rabin-Karp algorithm follow:
The hash function suggested by Rabin and Karp calculates an integer value. The integer value for a string is numeric value of a string. For example, if all possible characters are from 1 to 10, the numeric value of “122” will be 122. The number of possible characters is higher than 10 (256 in general) and pattern length can be large. So the numeric values cannot be practically stored as an integer. Therefore, the numeric value is calculated using modular arithmetic to make sure that the hash values can be stored in an integer variable (can fit in memory words). To do rehashing, we need to take off the most significant digit and add the new least significant digit for in hash value. Rehashing is done using the following formula.
hash( txt[s+1 .. s+m] ) = ( d ( hash( txt[s .. s+m-1]) – txt[s]*h ) + txt[s + m] ) mod q
hash( txt[s .. s+m-1] ) : Hash value at shift s.
hash( txt[s+1 .. s+m] ) : Hash value at next shift (or shift s+1)
d: Number of characters in the alphabet
q: A prime number
The idea is similar as we evaluate a mathematical expression. For example, we have a string of “1234” let we compute the value of the substring “12” is 12 and we want to compute the value of the substring “123” this can be calculated as ((12)*10+3)=123, similar logic is applied here.
10 a ab abc abcd b bc bcd c cd d
Time Complexity: O(N2), N is the length of string