java modulo operator

The % in Java is modulo. The integers are partitioned by a modulo operation into multiple "classes".

Java has slightly different behavior when working through modulo operations in negatives. True and expected behaviors are listed below.

Example:

// Integers by modulo 2

// Divides the integers into 2 `classes`
// these are "divisible evenly by 2" and "not divisibile evenly by 2"
// also known as even or odd

{..., 1, 3, 5, ...}, {..., 2, 4, 6, ...}

• Doing a modulo by 3 would give 3 classes, etc.

The integers modulo n gives us n different classes of numbers, based on the remainder.

Expected behavior

Typically when working with remainders we want the smallest non-negative member of the class. This gives a unique number to think of when thinking of modulo operations.

Example of modulo expected behavior:

// taking 9 % 5
9 % 5 = 4

// using a negative, -9 % 5
-9 % 5 = 1
-10 = 5 * (-2) + 1 // this is the smallest non-negative remainder

True behavior

When working with Java we get the signed remainder closest to 0

Java's % operator returns the closest remainder to 0.

Example above with true behavior:

// taking 9 % 5
9 % 5 = 4

// using a negative, -9 % 5
-9 % 5 = -4 // -9 is negative, -4 is the closest to 0 of the negative remainders

• When implementing a Deque we want a helper method to handle a negative number case