I am reading Algorithms 4th edition by Robert Sedgewick and am stumped at a particular problem. On page 460 of the book the author is describing a technique to hash strings and use prime numbers for modular hashing. Starting from the fourth line:

 If R is greater than any character value, this computation would
 be equivalent to treating the String as an N-digit base-R integer, 
 computing the remainder that results when dividing that number by M.

Where the algorithm being used to hash a N-character long String is:

int hash = 0;
for (int i = 0; i < s.length(); i++)
   hash = (R * hash + s.charAt(i)) % M;

How does the above algorithm result in a base-R integer?

Here M and R are integers (random) and s is the string of length N.

I am assuming that by the 'above computation' the author means the computation within the parentheses => R*hash + s.charAt(i)


1 Answer 1


The iteration results in :

(R^2*C + R^1*B + R^0*A + some constant)mod(M) for the string ABC, the value inside the brackets is a base 16 representation of CBA plus some constant value.


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