Understanding how rolling hash works with modulus in Rabin Karp algorithm

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.

Answer by @dejvuth is right - i would add this specifically when doing rabin-karp is that sometimes you may end up with a -ve modulus value - in that case it is better to take the +ve equivalent of that modulus value - so that checking if the same modulus was seen before is easier.

For example: with this pattern "abcdabc" - and hash function: hash(i) = (49*S[i]+7*S[i+1]+1*S[i+2])%1123

Results in:

"abc" -> 1046
"bcd" -> 1103
"cda" -> 33
"dab" -> 62
"abc" -> -77

second occurence of "abc" results is -77 that is modulo equivalent of 1046 since (-77 + 1123 = 1046)

PS: i don't have enough "reputation" at this time to add this as a comment..