5.3: Queues

A queue is a basic data structure that is used throughout programming. You can think of it as a line in a grocery store. The first one in the line is the first one to be served.Just like a queue.

A queue is also called a FIFO (First In First Out) to demonstrate the way it accesses data.

Queue<item-type> Operations

enqueue(new-item:item-type)

Adds an item onto the end of the queue.

front():item-type

Returns the item at the front of the queue.

dequeue()

Removes the item from the front of the queue.

is-empty():Boolean

True if no more items can be dequeued and there is no front item.

is-full():Boolean

True if no more items can be enqueued.

get-size():Integer

Returns the number of elements in the queue.

All operations except get-size() can be performed in \({\displaystyle O(1)}\) time. get-size() runs in at worst \({\displaystyle O(N).}\)

Linked List Implementation

The basic linked list implementation uses a singly-linked list with a tail pointer to keep track of the back of the queue.

type Queue<item_type>
  data list:Singly Linked List<item_type>
  data tail:List Iterator<item_type>

  constructor()
    list := new Singly-Linked-List()
    tail := list.get-begin() # null
  end constructor

When you want to enqueue something, you simply add it to the back of the item pointed to by the tail pointer. So the previous tail is considered next compared to the item being added and the tail pointer points to the new item. If the list was empty, this doesn't work, since the tail iterator doesn't refer to anything

 method enqueue(new_item:item_type)
   if is-empty()
     list.prepend(new_item)
     tail := list.get-begin()
   else
     list.insert_after(new_item, tail)
     tail.move-next()
   end if
 end method

The front item on the queue is just the one referred to by the linked list's head pointer

  method front():item_type
    return list.get-begin().get-value()
  end method

When you want to dequeue something off the list, simply point the head pointer to the previous from head item. The old head item is the one you removed of the list. If the list is now empty, we have to fix the tail iterator.

  method dequeue()
    list.remove-first()
    if is-empty()
      tail := list.get-begin()
    end if
  end method

A check for emptiness is easy. Just check if the list is empty.

  method is-empty():Boolean
    return list.is-empty()
  end method

A check for full is simple. Linked lists are considered to be limitless in size.

  method is-full():Boolean
    return False
  end method

A check for the size is again passed through to the list.

  method get-size():Integer
    return list.get-size()
  end method
end type

Performance Analysis

In a linked list, accessing the first element is an \({\displaystyle O(1)}\) operation because the list contains a pointer directly to it. Therefore, enqueue, front, and dequeue are a quick \({\displaystyle O(1)}\) operations.

The checks for empty/fullness as done here are also \({\displaystyle O(1)}\).

The performance of getSize() depends on the performance of the corresponding operation in the linked list implementation. It could be either \({\displaystyle O(n)}\), or \({\displaystyle O(1)}\), depending on what time/space tradeoff is made. Most of the time, users of a Queue do not use the getSize() operation, and so a bit of space can be saved by not optimizing it.

Related Links

• Queue (Wikipedia)