/*The operator $%$ is used to compute the remainder $a%b$ of
dividing an integer $a$ modulo (by) a non-zero integer $b$.

you might have seen early in school things like 
"17 divided by 5 is 3 remainder 2", perhaps written "3 r 2".

the remainder 2 is what "17 mod 5" or $17%5$ computes.

examples:

17 divided by 5         3 remainder 2           17/5 is 3, 17%5 is 2
15 divided by 5         3 remainder 0           15/5 is 3, 15%5 is 0
 0 divided by 5         0 remainder 0            0/5 is 0,  0%5 is 0
 3 divided by 5         0 remainder 3            3/5 is 0,  3%5 is 3

*/

public class modop {
    public static void main(String[] args) {

	int a,b,rem;

	System.out.println("Calculating Remainder: a%b");
	
	//Try some values
	a=17;b=5;
	System.out.println(a+" mod "+ b+ " is "  + a%b);

	a=0;b=3;
	System.out.println(a+" mod "+ b+ " is "  + a%b);
 	
// What happens with negative numbers?

// Try negative numbers
        a=17;b=-3;
        System.out.println(a+" mod "+ b+ " is "  + a%b);

	a=-17;b=3;
	System.out.println(a+" mod "+ b+ " is "  + a%b);


// Observe that the remainder always takes the sign of the numerator

/* Before we answer,
recall that this course is primarily an
introduction to programming, not an introduction to java.

thus, let us consider a more generally useful question --

what MAY happen in TYPICAL programming languages?


answer 1: if the remainder is 0, there is nothing unexpected:

-15 divided by 5        -3 remainder 0          -15/5 is -3, -15%5 is 0


answer 2: if the remainder is non-zero, it could be EITHER
positive or negative -- you should write code that works in
either case:

-17 divided by 5

         is either      -3 remainder -2   -17/5 is -3 and -17%5 is -2
                or      -4 remainder 3    -17/5 is -4 and -17/5 is  3

usually, we want a non-negative remainder, so code like this is
what we use:
*/

// To obtain a non-negative remainder of a modulo b
	rem = a % b;
        if (rem < 0)
        rem = rem + b;
	System.out.println(a+" mod "+ b+ " is "  + rem);
   
    } //method main
} //class modop