I am having trouble understanding how the rolling hash algorithm works after the hash has been reduced to modulus value by dividing by a prime number.
Consider the sequence of 5 digits in the number 123456.
The first chunk is 12345. I store the value, in the next window, 6 comes in and 1 goes out.
So the new hash will be (12345-1*10^4)*10 + 6 = 23456. This is fairly intuitive.
As obvious, these numbers are large, so we need a modulus function to keep them small. Suppose I take 101 as the prime number for this purpose.
So 12345 will reduce to 23. How then, from this, will I derive the rolling hash for the next window, 23456?
You calculate it the same way you calculate 23456, but always with modulo 101.
(((23 - (10^4 mod 101))*10) mod 101 + 6) mod 101 = 24.
which is the value you want because 23456 mod 101 = 24.