The linear array queue implementation, where the `front` and `rear` pointers only move forward, quickly leads to the condition we call False Overflow. This happens because the `rear` index eventually hits the array boundary (`MAX_SIZE`), preventing further insertion, even if elements have been removed from the `front`.

  • This linear movement results in irrecoverable wasted memory at the beginning of the array.
  • The queue logically runs out of space when `rear` reaches `MAX_SIZE` (in our `Example_Array_Capacity` of 5, this means `rear = 5`).
  • Any space freed by `deQueue` operations at indices less than the current `front` pointer is permanently unusable for subsequent `enQueue` operations.
  • This defeats the purpose of using a fixed-size array, as the effective capacity rapidly shrinks, leading to premature failure and forcing developers into slow $O(n)$ workarounds (like shifting all existing elements back to index 0).
  • The solution must allow the pointers to utilize the space *behind* the current `front` pointer once they reach the end—a concept known as index wrapping.

Defining False Overflow

The queue's logical capacity check (`rear == MAX_SIZE`) returns true, causing an overflow error, even though the array has empty physical slots available for use. This violates the efficiency expected of an $O(1)$ data structure.