Enqueue and dequeue in circular queue

A queue is a linear data structure in which insertion takes place at one end, the rear, and deletion at the other end, the front. The element inserted first is removed first, so it follows FIFO (First In First Out).

In a circular queue the last position is joined to the first, so the array is treated as a ring and positions freed at the front are reused. Indices wrap around using the modulus operator.

Enqueue and dequeue

Algorithm ENQUEUE(CQ, N, x)      /* front = rear = -1 initially */
1. if (rear + 1) % N == front:
       print "Queue overflow"; return
2. if front == -1:               /* first element */
       front = rear = 0
   else
       rear = (rear + 1) % N
3. CQ[rear] = x

Algorithm DEQUEUE(CQ, N)
1. if front == -1:
       print "Queue underflow"; return
2. x = CQ[front]
3. if front == rear:             /* last element removed */
       front = rear = -1
   else
       front = (front + 1) % N
4. return x

• Full condition: (rear + 1) % N == front
• Empty condition: front == -1

Example (N = 5)

After two dequeues, enqueue(60) and enqueue(70) succeed by wrapping rear to index 0 and 1; a linear queue would have reported overflow.