Mathematical approach to derive Modulo expression
Below are two expressions to find modulo(n,d) in java, using euclidean division
(d + (n % d)) if (n < 0)
(n%d) if n > 0
My question is,
Am not clear, How to think mathematically before writing above expression, if n<0?
Please help me with mathematical approach, Because i do not want to remember logic!!!
If you want to remember what n % d does, it returns a value in the range (-d, d) congruent mod d to n and matching the sign of n.
If you want to know how to get a positive result (or strictly speaking, a result matching the sign of d instead of n), there's an easier way than the if .
Since (n % d) is in the range (-d, d) , that means (n % d) + n is in the range (0, 2d) , so ((n % d) + n) % d is a value in the range [0, d) , congruent to n.
Thus, ((n % d) + n) % d is what you're looking for.
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