Create Double Linked List.md

Author: EhsanShahbazii

chapter3/Fundamental Data Structures/Summary/Double Linked List.md

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+# Summary
+
+
+## Double Linked List (DLL)
+#### Node class variables:
+```java
+private E element;                   // reference to the element stored at this node
+private Node<E> prev;                // reference to the previous node in the list
+private Node<E> next;                // reference to the subsequent node in the list
+```
+#### DLL class variables:
+```java
+private Node<E> header;              // header sentinel
+private Node<E> trailer;             // trailer sentinel
+private int size = 0;                // number of elements in the list
+```
+### methods:
+  - **size( ):** Returns the number of elements in the list.
+  - **isEmpty( ):** Returns true if the list is empty, and false otherwise.
+  - **first( ):** Returns (but does not remove) the first element in the list.
+  - **last( ):** Returns (but does not remove) the last element in the list.
+  - **addFirst(e):** Adds a new element to the front of the list.
+  - **addLast(e):** Adds a new element to the end of the list.
+  - **removeFirst( ):** Removes and returns the first element of the list.
+  - **removeLast( ):** Removes and returns the last element of the list.
+
+| Operations                 | Access | Search | Insertion | Deletion |
+|----------------------------|--------|--------|-----------|----------|
+| Best case time complexity  | O(1)   | O(1)   | O(1)      | O(1)     |
+| Worst Case time complexity | O(n)   | O(n)   | O(1)      | O(1)     |
+| Average time complexity    | O(n)   | O(n)   | O(1)      | O(1)     |
+
+### special method:
+```java
+/** Removes and returns the last element of the list. */
+public E removeLast( ) {
+  if (isEmpty( )) return null;              // nothing to remove
+  return remove(trailer.getPrev( ));        // last element is before trailer
+}
+
+/** Removes the given node from the list and returns its element. */
+private E remove(Node<E> node) {
+  Node<E> predecessor = node.getPrev( );
+  Node<E> successor = node.getNext( );
+  predecessor.setNext(successor);
+  successor.setPrev(predecessor);
+  size−−;
+  return node.getElement( );
+}
+```