To overcome the problem of False Overflow and efficiently reuse memory, we treat the array as a continuous loop.

  • The Circular Queue, or Ring Buffer, achieves this by using the Modulo Operator (%) to wrap indices back to the start of the array.
  • This mechanism ensures that memory at the beginning of the array, freed by deQueue operations, becomes immediately usable for new enQueue operations.
  • Index Calculation: Both the front and rear pointers advance using the same formula, ensuring they always point to a valid index within the array's bounds.
  • Efficiency: The Circular Queue preserves the desired O(1) time complexity for both enQueue and deQueue operations, efficiently utilizing the fixed memory.
  • The Core Index Wrapping Formula:
    New Index = (Current Index + 1) % MAX_SIZE
  • Example: If MAX_SIZE is 5, and the rear pointer is at index 4, the next index is calculated as: $ (4 + 1) \pmod 5 = 5 \pmod 5 = 0 $. The pointer wraps from 4 to 0.

Key Takeaway

The modulo operator is the key to the Circular Queue. It mathematically transforms a linear array into a circular one, allowing for constant-time operations and maximum space utilization without needing to shift elements.