The array-based implementations of the ADT queue in this chapter used a circular array. One implementation counted the entries in the queue, while the other left one location in the array unused. We used these strategies to tell when the queue was empty and when it was full. A third strategy is possible. It does not count and does not have an unused location in the circular array. After initializing frontIndex to 0 and backIndex to -1, you do not use modulo arithmetic when you increment these fields. Instead, you use modulo arithmetic when you index the array, but without changing frontIndex and backIndex. Thus, if queue is the array, queue[frontIndex % queue.length] is the front entry, and the entry at the back of the queue is queue[backIndex % queue.length]. Now if backIndex is less than frontIndex, the queue is empty. The number of entries in the queue is backIndex - frontIndex + 1. You can compare this number with the size of the array to see whether the array is full.
Since frontIndex and backIndex can continue to grow, they might become too large to represent. To reduce the chance of this happening, set frontIndex to 0 and backIndex to -1 whenever the implementation detects an empty queue. Note that adding to a full queue invokes ensureCapacity, which sets frontIndex to 0 and backIndex to the index of the entry at the back of the queue. Complete this array-based implementation of the ADT queue.