Data Structures and Algorithms in Java[1].pdf - Fulvio Frisone

Using the Modulo Operator to Implement a Circular
Array
Implementing this circular view of Q is actually pretty easy. Each time we
increment f or r, we compute this increment as "(f + 1) mod N" or "(r + 1) mod
N," respectively.
Recall that operator "mod" is the modulo operator, which is computed by taking
the remainder after an integral division. For example, 14 divided by 4 is 3 with
remainder 2, so 14 mod 4 = 2. Specifically, given integers x and y such that x ≥ 0
and y > 0, we have x mod y = x − x/yy. That is, if r = x mod y, then there is a
nonnegative integer q, such that x = qy + r. Java uses "%" to denote the modulo
operator. By using the modulo operator, we can view Q as a circular array and
implement each queue method in a constant amount of time (that is, O(1) time).
We describe how to use this approach to implement a queue in Code Fragment
5.14.
Code Fragment 5.14: Implementation of a queue
using a circular array. The implementation uses the
modulo operator to "wrap" indices around the end of
the array and it also includes two instance variables, f
and r, which index the front of the queue and first
empty cell after the rear of the queue respectively.
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