Circular Queue — Queue Mastery 9618

Why Circular Queues?

Linear Queue Problem

—

D

E

F

3 wasted slots. Rear at index 5 (max). Reports "FULL" with only 3/6 used!

becomes

Circular Queue Solution

G

·

D

E

F

Rear wraps to index 0. Freed slots reused. G fills the vacated slot.

How a Circular Queue Works

The Key Idea: MOD

Instead of simply incrementing pointers, we use modular arithmetic:

Rear ← (Rear + 1) MOD MaxSize

Front ← (Front + 1) MOD MaxSize

This makes the pointer "wrap around" to index 0 when it passes the end of the array.

Enqueue

Check if the queue is full (size = MaxSize)
Rear ← (Rear + 1) MOD MaxSize
Place item at Queue[Rear]
Increment size counter

Dequeue

Check if the queue is empty (size = 0)
Retrieve item at Queue[Front]
Front ← (Front + 1) MOD MaxSize
Decrement size counter

Detecting Full vs Empty

In a circular queue, front can equal rear when full OR empty. Solutions:

Size counter (simplest — used here)
Keep one slot always empty
Boolean flag

Circular Visualisation

The array is logically arranged in a circle. Pointers wrap using MOD.

Trace Example

Click a step above to trace through circular queue operations.

Interactive Circular Queue Simulator

Observe how the rear pointer wraps around when it reaches the end of the array.

Array size:

Front: 0 Rear: -1 Size: 0

Circular queue initialised. Front = 0, Rear = -1, Size = 0.

Circular Queue — Pseudocode (9618 Style)

PROCEDURE Enqueue(Queue, Front, Rear, Size, MaxSize, Item)
    IF Size >= MaxSize THEN
        OUTPUT "Queue is full"
    ELSE
        Rear ← (Rear + 1) MOD MaxSize
        Queue[Rear] ← Item
        Size ← Size + 1
    ENDIF
ENDPROCEDURE

FUNCTION Dequeue(Queue, Front, Rear, Size)
    IF Size = 0 THEN
        OUTPUT "Queue is empty"
        RETURN ""
    ELSE
        Item ← Queue[Front]
        Front ← (Front + 1) MOD MaxSize
        Size ← Size - 1
        RETURN Item
    ENDIF
ENDFUNCTION

FUNCTION IsEmpty(Size)
    RETURN Size = 0
ENDFUNCTION

FUNCTION IsFull(Size, MaxSize)
    RETURN Size >= MaxSize
ENDFUNCTION

Linear vs Circular — Comparison

Feature	Linear Queue	Circular Queue
Space efficiency	Wasted space after dequeues	Reuses freed space
Pointer movement	Front++ and Rear++	(ptr+1) MOD MaxSize
Full detection	Rear = MaxSize - 1	Size = MaxSize
Empty detection	Front > Rear	Size = 0
Complexity	Simpler to implement	Slightly more complex
Best for	Simple, short-lived queues	Long-running systems