What is the difference between hash()%n and n%hash()

Think of operator modulus % as a way to distribute uniformly a set of numbers through reducingthem over a smaller range. The set of numbers are, of corse, the hashcodes of input keys. The small range is the capacity of the table.

This is a useful technique when you want to assign an index in a small table to store a high number.

The inverse operation sounds quite weird (and useless): Taking in account that the hash codes are high numbers and n is small, n % hash would return always n, so it has no interest at all.

Java choses indexes through hash & (length-1), indeed, which is not aritmetically equivalent to hash % length, but it is an alternative -and cheaper than modulus- formula to reduce and distribute (credits to @Zabuza).

Think of operator modulus % as a way to distribute uniformly a set of numbers through reducingthem over a smaller range. The set of numbers are, of corse, the hashcodes of input keys. The small range is the capacity of the table.

This is a useful technique when you want to assign an index in a small table to store a high number.

The inverse operation sounds quite weird (and useless): Taking in account that the hash codes are high numbers and n is small, n % hash would return always n, so it has no interest at all.

Java choses indexes through hash & (length-1), indeed, which is not aritmetically equivalent to hash % length, but it is an alternative -and cheaper than modulus- formula to reduce and distribute (credits to @Zabuza).