一个用Java实现的双向队列，可以分别在头尾插入和删除节点

分析，双向队列的内部实现是一个双向链表，可以分别从头尾插入和删除节点。

通常使用一个first指向头 last指向尾。然后分别维护各种next和prev指针。通常情况要考虑边界条件，即当队列本身为空的时候插入新节点如何维护first和last的指向

删除节点的时候，若队列变为空又应该如何维护first和last指针。非常繁琐而且容易写错，不过使用的空间最少，代码如下

import java.util.Iterator;
import java.util.NoSuchElementException;
import edu.princeton.cs.algs4.StdOut;

public class Deque implements Iterable {
    private int n;
    private Node first;
    private Node last;

    private class Node {
        private Item item;
        private Node next;
        private Node prev;
    }
    public Deque() {
        n = 0;
        first = null;
        last = null;
    }

    public boolean isEmpty() {
        return first == null;
    }

    public int size() {
        return n;
    }

    public void addFirst(Item item) {
        if (item == null)
            throw new NullPointerException("can't add null element!");
        Node oldfirst = first;
        first = new Node();
        first.item = item;
        first.prev = null;
        // it is and empty queue..
        if (oldfirst == null) {
            last = first;
            first.next = null;
        }
        else {
            first.next = oldfirst;
            oldfirst.prev = first;
        }
        n++;
    }

    public void addLast(Item item) {
        if (item == null)
            throw new NullPointerException("can't add null element!");
        Node oldlast = last;
        last = new Node();
        last.item = item;
        last.next = null;
        if (oldlast == null) {
            first = last;
            last.prev = null;
        } else {
            last.prev = oldlast;
            oldlast.next = last;
        }
        n++;
    }

    public Item removeFirst() {
        if (isEmpty())
            throw new NoSuchElementException(
                    "Can't remove from empty deque");
        Item item = first.item;
        first = first.next;
        n--;
        if (n == 0)
            last = null;
        else
            first.prev = null;
        return item;
    }

    public Item removeLast() {
        if (isEmpty())
            throw new NoSuchElementException(
                    "Stack underflow");
        Item item = last.item;
        last = last.prev;
        n--;
        if (n == 0)
            first = null;
        else
            last.next = null;
        return item;
    }
    public Iterator iterator() {
        return new DequeIterator();
    }


    private class DequeIterator implements Iterator {
        private Node current = first;
        public boolean hasNext() {
            return current != null;
        }

        public void remove() {
            throw new UnsupportedOperationException(
                    "remove is not supported!");
        }

        public Item next() {
            if (!hasNext())
                throw new NoSuchElementException();
            Item item = current.item;
            current = current.next;
            return item;
        }
    }

    public static void main(String[] args) {
        Deque dq = new Deque();
        dq.addFirst("A");
        dq.addFirst("B");
        dq.addFirst("C");
        dq.addLast("Q");
        dq.addLast("E");
        dq.addLast("D");
        for (String s : dq) {
            StdOut.println(s);
        }
        StdOut.println("Remove first" + dq.removeFirst());
        StdOut.println("Remove last" + dq.removeLast());
        for (String s : dq) {
            StdOut.println(s);
        }
    }
}

另一种方法是引入一个哨兵节点nil， 初始化时nil的prev和next分别指向自身。用于判断队列是否为空

加入新元素以后只需要操作新增节点，nil 和 nil的下一个节点。不需要考虑边界情况（因为没有nullpointer）

该方法仅多使用了一个节点的空间，但是代码看起来更加简洁如下

import java.util.Iterator;
import java.util.NoSuchElementException;
import edu.princeton.cs.algs4.StdOut;
import edu.princeton.cs.algs4.StdRandom;

public class Deque implements Iterable {
    private int n;
    private Node nil;

    private class Node {
        private Item item;
        private Node next;
        private Node prev;
    }
    public Deque() {
        n = 0;
        nil = new Node();
        nil.next = nil;
        nil.prev = nil;
    }

    public boolean isEmpty() {
        return nil.next == nil;
    }

    public int size() {
        return n;
    }

    public void addFirst(Item item) {
        if (item == null)
            throw new NullPointerException("can't add null element!");
        Node first = new Node();
        first.item = item;
        first.prev = nil;
        first.next = nil.next;
        nil.next.prev = first;
        nil.next = first;
        
        n++;
    }

    public void addLast(Item item) {
        if (item == null)
            throw new NullPointerException("can't add null element!");
        Node last = new Node();
        last.item = item;
        last.next = nil;
        last.prev = nil.prev;
        nil.prev.next = last;
        nil.prev = last;

        n++;
    }

    public Item removeFirst() {
        if (isEmpty())
            throw new NoSuchElementException(
                    "Can't remove from empty deque");
        Node del = nil.next;
        Item item = del.item;
        del.next.prev = nil;
        nil.next = del.next;
        n--;
        return item;
    }

    public Item removeLast() {
        if (isEmpty())
            throw new NoSuchElementException(
                    "Stack underflow");
        Node del = nil.prev;
        Item item = del.item;
        del.prev.next = nil;
        nil.prev = del.prev;
        n--;
        return item;
    }
    public Iterator iterator() {
        return new DequeIterator();
    }


    private class DequeIterator implements Iterator {
        private Node current = nil.next;
        public boolean hasNext() {
            return current != nil;
        }

        public void remove() {
            throw new UnsupportedOperationException(
                    "remove is not supported!");
        }

        public Item next() {
            if (!hasNext())
                throw new NoSuchElementException();
            Item item = current.item;
            current = current.next;
            return item;
        }
    }

    public static void main(String[] args) {
        Deque dq = new Deque();
        for (int i = 0; i < 10; i++) {
            int r = StdRandom.uniform(1, 65535);
            StdOut.println("Random add and remove node for " + r);
            for (int j = 0; j < r; j++) {
               if (StdRandom.uniform() > 0.5)
                   dq.addFirst(StdRandom.uniform(0, 10));
               else
                   dq.addLast(StdRandom.uniform(0, 10));
            }
            for (int n : dq)
                StdOut.println(n); 

            for (int j = 0; j < r; j++) {
                if (StdRandom.uniform() > 0.5)
                    dq.removeFirst();
                else
                    dq.removeLast();
            }
        }
        StdOut.println("Done!");
    }

}