Data Structure and Algorithms - Queue

Queue is an abstract data structure, somewhat similar to Stacks. Unlike stacks, a queue is open at both its ends. One end is always used to insert data (enqueue) and the other is used to remove data (dequeue). Queue follows First-In-First-Out methodology, i.e., the data item stored first will be accessed first.

A real-world example of queue can be a single-lane one-way road, where the vehicle enters first, exits first. More real-world examples can be seen as queues at the ticket windows and bus-stops.

Queue Representation

As we now understand that in queue, we access both ends for different reasons. The following diagram given below tries to explain queue representation as data structure −
As in stacks, a queue can also be implemented using Arrays, Linked-lists, Pointers and Structures. For the sake of simplicity, we shall implement queues using one-dimensional array.

Basic Operations

Queue operations may involve initializing or defining the queue, utilizing it, and then completely erasing it from the memory. Here we shall try to understand the basic operations associated with queues −

• enqueue() − add (store) an item to the queue.
• dequeue() − remove (access) an item from the queue.

Few more functions are required to make the above-mentioned queue operation efficient. These are −

• peek() − Gets the element at the front of the queue without removing it.
• isfull() − Checks if the queue is full.
• isempty() − Checks if the queue is empty.

In queue, we always dequeue (or access) data, pointed by front pointer and while enqueing (or storing) data in the queue we take help of rear pointer.
Let's first learn about supportive functions of a queue −

peek()

This function helps to see the data at the front of the queue. The algorithm of peek() function is as follows −
Algorithm

begin procedure peek

   return queue[front]
   
end procedure

Implementation of peek() function in C programming language −
Example

int peek() {
   return queue[front];
}

isfull()

As we are using single dimension array to implement queue, we just check for the rear pointer to reach at MAXSIZE to determine that the queue is full. In case we maintain the queue in a circular linked-list, the algorithm will differ. Algorithm of isfull() function −
Algorithm

begin procedure isfull

   if rear equals to MAXSIZE
      return true
   else
      return false
   endif
   
end procedure

Implementation of isfull() function in C programming language −
Example

bool isfull() {
   if(rear == MAXSIZE - 1)
      return true;
   else
      return false;
}

isempty()

Algorithm of isempty() function −
Algorithm

begin procedure isempty

   if front is less than MIN  OR front is greater than rear
      return true
   else
      return false
   endif
   
end procedure

If the value of front is less than MIN or 0, it tells that the queue is not yet initialized, hence empty.
Here's the C programming code −
Example

bool isempty() {
   if(front < 0 || front > rear) 
      return true;
   else
      return false;
}

Enqueue Operation

Queues maintain two data pointers, front and rear. Therefore, its operations are comparatively difficult to implement than that of stacks.
The following steps should be taken to enqueue (insert) data into a queue −

• Step 1 − Check if the queue is full.
• Step 2 − If the queue is full, produce overflow error and exit.
• Step 3 − If the queue is not full, increment rear pointer to point the next empty space.
• Step 4 − Add data element to the queue location, where the rear is pointing.
• Step 5 − return success.

Sometimes, we also check to see if a queue is initialized or not, to handle any unforeseen situations.
Algorithm for enqueue operation

procedure enqueue(data)      
   if queue is full
      return overflow
   endif
   
   rear ← rear + 1
   
   queue[rear] ← data
   
   return true
   
end procedure

Implementation of enqueue() in C programming language −
Example

int enqueue(int data)      
   if(isfull())
      return 0;
   
   rear = rear + 1;
   queue[rear] = data;
   
   return 1;
end procedure

Dequeue Operation

Accessing data from the queue is a process of two tasks − access the data where front is pointing and remove the data after access. The following steps are taken to perform dequeue operation −

• Step 1 − Check if the queue is empty.
• Step 2 − If the queue is empty, produce underflow error and exit.
• Step 3 − If the queue is not empty, access the data where front is pointing.
• Step 4 − Increment front pointer to point to the next available data element.
• Step 5 − Return success.

Algorithm for dequeue operation

procedure dequeue
   if queue is empty
      return underflow
   end if

   data = queue[front]
   front ← front + 1
   
   return true
end procedure

Implementation of dequeue() in C programming language −
Example

int dequeue() {

   if(isempty())
      return 0;

   int data = queue[front];
   front = front + 1;

   return data;
}

For a complete Queue program in C programming language, please click here.