Deque

Terminology

• Head - the first node/located in the front of the deque.
• Tail - the last node/located at the back of the deque.

Definition

Deque (Double-ended Queue) is a linear data structure that is similar with the Doubly Linked List data structure as well as a variation of the Queue. One thing that differentiates a Deque with a Queue is the way how a data is added or removed. Unlike Queues, that can only add a data at the back and remove the data in the front of the queue, Deques can add/remove data at the back or in the front.

Basic Operation

• isEmpty - to check whether a Deque is empty or not.
• pushFront - to add a new data at the front.
• pushBack - to add new data at the back.
• front - to get the data located at the front.
• back - to get the data located at the back.
• popFront - to remove the data located at the front.
• popBack - to remove a data located at the back.

The Time Complexity for the above operations are constant O(1).

Deque's Use Cases

Deques are commonly used to solve problems with a Sliding Window characteristic. On such problems, we need to remove both data located at the front and at the back. An example of a Sliding Window problem is to search the maximum value within a subarray with a certain size.

ADT Implementation: Deque

A complete implementation of Deque can be accessed here.

As mentioned earlier, Deques can be implemented by modifying the Doubly Linked List data structure where two pointers, tail/rear is used to refer to the node located at the back and head/front to refer to the node located at the front.

• Node Representation

  Nodes within a Deque can be represented by a struct named DListNode that stores an int and a referenced to the next and previous nodes.

  typedef struct dnode_t {
      int data;
      struct dnode_t      \
          *next,
          *prev;
  } DListNode;
  

• Deque Structure

  Deques have two pointers within their structures, that is head and tail.

  typedef struct deque_t {
      DListNode           \
          *_head, 
          *_tail;
      unsigned _size;
  } Deque;
  

• isEmpty

  To check whether a Deque is empty or not, check whether both the head and tail are pointing to NULL or not.

  bool deq_isEmpty(Deque *deque) {
      return (deque->_head == NULL && \
              deque->_tail == NULL);
  }
  

• pushFront

  to do a pushFront, do the following steps:
  • make a new node
  • if the Deque is empty, make that new node as the head and the tail.
  • if it is not, make the next of the new node points to the current head and the prev of the current head to the new node.
  • make the head points to the new node.

  void deq_pushFront(Deque *deque, int value)
  {
      DListNode *newNode = __dlist_createNode(value);
      if (newNode) {
          deque->_size++;
          if (deq_isEmpty(deque)) {
              deque->_head = newNode;
              deque->_tail = newNode;
              return;
          }
  
          newNode->next = deque->_head;
          deque->_head->prev = newNode;
          deque->_head = newNode;
      }
  }
  

• pushBack

  Follow the following steps to do a pushBack.
  • make a new node.
  • if the Deque is empty, make the new node as both the head and the tail.
  • if it is not empty, make the prev of the new node to point at the current tail node, and the next of the current tail to point at the new node.
  • make the tail node to point at the new node.

  void deq_pushBack(Deque *deque, int value)
  {
      DListNode *newNode = __dlist_createNode(value);
      if (newNode) {
          deque->_size++;
          if (deq_isEmpty(deque)) {
              deque->_head = newNode;
              deque->_tail = newNode;
              return;
          }
  
          deque->_tail->next = newNode;
          newNode->prev = deque->_tail;
          deque->_tail = newNode;
      }
  }
  

• front

  int deq_front(Deque *deque) {
      if (!deq_isEmpty(deque)) {
          return (deque->_head->data);
      }
      return 0;
  }
  

• rear

  int deq_back(Deque *deque) {
      if (!deq_isEmpty(deque)) {
          return (deque->_tail->data);
      }
      return 0;
  }
  

• popFront

  To do a popFront, follow these steps:
  • store the current head node within a temporary variable
  • make the 'head' to refer to the next of the current 'head'
  • remove the node within the temporary variable
  • if the head is empty, the the tail should be too.

  void deq_popFront(Deque *deque)
  {
      if (!deq_isEmpty(deque)) {
          DListNode *temp = deque->_head;
          if (deque->_head == deque->_tail) {
              deque->_head = NULL;
              deque->_tail = NULL;
              free(temp);
          }
          else {
              deque->_head = deque->_head->next;
              deque->_head->prev = NULL;
              free(temp);
          }
          deque->_size--;
      }
  }
  

• popBack

  To do a popBack, follow these steps:
  • store the current tail within a temporary variable.
  • make the tail to refer to the prev of the current tail.
  • remove the node within the temporary variable
  • if the tail is empty, then the head should be too.

  void deq_popBack(Deque *deque)
  {
      if (!deq_isEmpty(deque)) {
          DListNode *temp;
          if (deque->_head == deque->_tail) {
              temp = deque->_head;
              deque->_head = NULL;
              deque->_tail = NULL;
              free(temp);
          }
          else {
              temp = deque->_tail;
              deque->_tail = deque->_tail->prev;
              deque->_tail->next = NULL;
              free(temp);
          }
          deque->_size--;
      }
  }