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5.3   Double-ended queue

In a queue, we can only delete elements from the head or add elements to the tail. As shown in the following diagram, a "double-ended queue (deque)" offers more flexibility, allowing the addition or removal of elements at both the head and the tail.

Operations in double-ended queue

Figure 5-7   Operations in double-ended queue

5.3.1   Common operations in double-ended queue

The common operations in a double-ended queue are listed below, and the names of specific methods depend on the programming language used.

Table 5-3   Efficiency of double-ended queue operations

Method Name Description Time Complexity
pushFirst() Add an element to the head \(O(1)\)
pushLast() Add an element to the tail \(O(1)\)
popFirst() Remove the first element \(O(1)\)
popLast() Remove the last element \(O(1)\)
peekFirst() Access the first element \(O(1)\)
peekLast() Access the last element \(O(1)\)

Similarly, we can directly use the double-ended queue classes implemented in programming languages:

deque.py
from collections import deque

# Initialize the deque
deque: deque[int] = deque()

# Enqueue elements
deque.append(2)      # Add to the tail
deque.append(5)
deque.append(4)
deque.appendleft(3)  # Add to the head
deque.appendleft(1)

# Access elements
front: int = deque[0]  # The first element
rear: int = deque[-1]  # The last element

# Dequeue elements
pop_front: int = deque.popleft()  # The first element dequeued
pop_rear: int = deque.pop()       # The last element dequeued

# Get the length of the deque
size: int = len(deque)

# Check if the deque is empty
is_empty: bool = len(deque) == 0
deque.cpp
/* Initialize the deque */
deque<int> deque;

/* Enqueue elements */
deque.push_back(2);   // Add to the tail
deque.push_back(5);
deque.push_back(4);
deque.push_front(3);  // Add to the head
deque.push_front(1);

/* Access elements */
int front = deque.front(); // The first element
int back = deque.back();   // The last element

/* Dequeue elements */
deque.pop_front();  // The first element dequeued
deque.pop_back();   // The last element dequeued

/* Get the length of the deque */
int size = deque.size();

/* Check if the deque is empty */
bool empty = deque.empty();
deque.java
/* Initialize the deque */
Deque<Integer> deque = new LinkedList<>();

/* Enqueue elements */
deque.offerLast(2);   // Add to the tail
deque.offerLast(5);
deque.offerLast(4);
deque.offerFirst(3);  // Add to the head
deque.offerFirst(1);

/* Access elements */
int peekFirst = deque.peekFirst();  // The first element
int peekLast = deque.peekLast();    // The last element

/* Dequeue elements */
int popFirst = deque.pollFirst();  // The first element dequeued
int popLast = deque.pollLast();    // The last element dequeued

/* Get the length of the deque */
int size = deque.size();

/* Check if the deque is empty */
boolean isEmpty = deque.isEmpty();
deque.cs
/* Initialize the deque */
// In C#, LinkedList is used as a deque
LinkedList<int> deque = new();

/* Enqueue elements */
deque.AddLast(2);   // Add to the tail
deque.AddLast(5);
deque.AddLast(4);
deque.AddFirst(3);  // Add to the head
deque.AddFirst(1);

/* Access elements */
int peekFirst = deque.First.Value;  // The first element
int peekLast = deque.Last.Value;    // The last element

/* Dequeue elements */
deque.RemoveFirst();  // The first element dequeued
deque.RemoveLast();   // The last element dequeued

/* Get the length of the deque */
int size = deque.Count;

/* Check if the deque is empty */
bool isEmpty = deque.Count == 0;
deque_test.go
/* Initialize the deque */
// In Go, use list as a deque
deque := list.New()

/* Enqueue elements */
deque.PushBack(2)      // Add to the tail
deque.PushBack(5)
deque.PushBack(4)
deque.PushFront(3)     // Add to the head
deque.PushFront(1)

/* Access elements */
front := deque.Front() // The first element
rear := deque.Back()   // The last element

/* Dequeue elements */
deque.Remove(front)    // The first element dequeued
deque.Remove(rear)     // The last element dequeued

/* Get the length of the deque */
size := deque.Len()

/* Check if the deque is empty */
isEmpty := deque.Len() == 0
deque.swift
/* Initialize the deque */
// Swift does not have a built-in deque class, so Array can be used as a deque
var deque: [Int] = []

/* Enqueue elements */
deque.append(2) // Add to the tail
deque.append(5)
deque.append(4)
deque.insert(3, at: 0) // Add to the head
deque.insert(1, at: 0)

/* Access elements */
let peekFirst = deque.first! // The first element
let peekLast = deque.last!   // The last element

/* Dequeue elements */
// Using Array, popFirst has a complexity of O(n)
let popFirst = deque.removeFirst() // The first element dequeued
let popLast = deque.removeLast()   // The last element dequeued

/* Get the length of the deque */
let size = deque.count

/* Check if the deque is empty */
let isEmpty = deque.isEmpty
deque.js
/* Initialize the deque */
// JavaScript does not have a built-in deque, so Array is used as a deque
const deque = [];

/* Enqueue elements */
deque.push(2);
deque.push(5);
deque.push(4);
// Note that unshift() has a time complexity of O(n) as it's an array
deque.unshift(3);
deque.unshift(1);

/* Access elements */
const peekFirst = deque[0]; // The first element
const peekLast = deque[deque.length - 1]; // The last element

/* Dequeue elements */
// Note that shift() has a time complexity of O(n) as it's an array
const popFront = deque.shift(); // The first element dequeued
const popBack = deque.pop();    // The last element dequeued

/* Get the length of the deque */
const size = deque.length;

/* Check if the deque is empty */
const isEmpty = size === 0;
deque.ts
/* Initialize the deque */
// TypeScript does not have a built-in deque, so Array is used as a deque
const deque: number[] = [];

/* Enqueue elements */
deque.push(2);
deque.push(5);
deque.push(4);
// Note that unshift() has a time complexity of O(n) as it's an array
deque.unshift(3);
deque.unshift(1);

/* Access elements */
const peekFirst: number = deque[0]; // The first element
const peekLast: number = deque[deque.length - 1]; // The last element

/* Dequeue elements */
// Note that shift() has a time complexity of O(n) as it's an array
const popFront: number = deque.shift() as number; // The first element dequeued
const popBack: number = deque.pop() as number;    // The last element dequeued

/* Get the length of the deque */
const size: number = deque.length;

/* Check if the deque is empty */
const isEmpty: boolean = size === 0;
deque.dart
/* Initialize the deque */
// In Dart, Queue is defined as a deque
Queue<int> deque = Queue<int>();

/* Enqueue elements */
deque.addLast(2);  // Add to the tail
deque.addLast(5);
deque.addLast(4);
deque.addFirst(3); // Add to the head
deque.addFirst(1);

/* Access elements */
int peekFirst = deque.first; // The first element
int peekLast = deque.last;   // The last element

/* Dequeue elements */
int popFirst = deque.removeFirst(); // The first element dequeued
int popLast = deque.removeLast();   // The last element dequeued

/* Get the length of the deque */
int size = deque.length;

/* Check if the deque is empty */
bool isEmpty = deque.isEmpty;
deque.rs
/* Initialize the deque */
let mut deque: VecDeque<u32> = VecDeque::new();

/* Enqueue elements */
deque.push_back(2);  // Add to the tail
deque.push_back(5);
deque.push_back(4);
deque.push_front(3); // Add to the head
deque.push_front(1);

/* Access elements */
if let Some(front) = deque.front() { // The first element
}
if let Some(rear) = deque.back() {   // The last element
}

/* Dequeue elements */
if let Some(pop_front) = deque.pop_front() { // The first element dequeued
}
if let Some(pop_rear) = deque.pop_back() {   // The last element dequeued
}

/* Get the length of the deque */
let size = deque.len();

/* Check if the deque is empty */
let is_empty = deque.is_empty();
deque.c
// C does not provide a built-in deque
deque.kt

deque.zig

Visualizing Code

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5.3.2   Implementing a double-ended queue *

The implementation of a double-ended queue is similar to that of a regular queue, it can be based on either a linked list or an array as the underlying data structure.

1.   Implementation based on doubly linked list

Recall from the previous section that we used a regular singly linked list to implement a queue, as it conveniently allows for deleting from the head (corresponding to the dequeue operation) and adding new elements after the tail (corresponding to the enqueue operation).

For a double-ended queue, both the head and the tail can perform enqueue and dequeue operations. In other words, a double-ended queue needs to implement operations in the opposite direction as well. For this, we use a "doubly linked list" as the underlying data structure of the double-ended queue.

As shown in the Figure 5-8 , we treat the head and tail nodes of the doubly linked list as the front and rear of the double-ended queue, respectively, and implement the functionality to add and remove nodes at both ends.

Implementing Double-Ended Queue with Doubly Linked List for Enqueue and Dequeue Operations

linkedlist_deque_push_last

linkedlist_deque_push_first

linkedlist_deque_pop_last

linkedlist_deque_pop_first

Figure 5-8   Implementing Double-Ended Queue with Doubly Linked List for Enqueue and Dequeue Operations

The implementation code is as follows:

linkedlist_deque.py
class ListNode:
    """双向链表节点"""

    def __init__(self, val: int):
        """构造方法"""
        self.val: int = val
        self.next: ListNode | None = None  # 后继节点引用
        self.prev: ListNode | None = None  # 前驱节点引用

class LinkedListDeque:
    """基于双向链表实现的双向队列"""

    def __init__(self):
        """构造方法"""
        self._front: ListNode | None = None  # 头节点 front
        self._rear: ListNode | None = None  # 尾节点 rear
        self._size: int = 0  # 双向队列的长度

    def size(self) -> int:
        """获取双向队列的长度"""
        return self._size

    def is_empty(self) -> bool:
        """判断双向队列是否为空"""
        return self._size == 0

    def push(self, num: int, is_front: bool):
        """入队操作"""
        node = ListNode(num)
        # 若链表为空,则令 front 和 rear 都指向 node
        if self.is_empty():
            self._front = self._rear = node
        # 队首入队操作
        elif is_front:
            # 将 node 添加至链表头部
            self._front.prev = node
            node.next = self._front
            self._front = node  # 更新头节点
        # 队尾入队操作
        else:
            # 将 node 添加至链表尾部
            self._rear.next = node
            node.prev = self._rear
            self._rear = node  # 更新尾节点
        self._size += 1  # 更新队列长度

    def push_first(self, num: int):
        """队首入队"""
        self.push(num, True)

    def push_last(self, num: int):
        """队尾入队"""
        self.push(num, False)

    def pop(self, is_front: bool) -> int:
        """出队操作"""
        if self.is_empty():
            raise IndexError("双向队列为空")
        # 队首出队操作
        if is_front:
            val: int = self._front.val  # 暂存头节点值
            # 删除头节点
            fnext: ListNode | None = self._front.next
            if fnext != None:
                fnext.prev = None
                self._front.next = None
            self._front = fnext  # 更新头节点
        # 队尾出队操作
        else:
            val: int = self._rear.val  # 暂存尾节点值
            # 删除尾节点
            rprev: ListNode | None = self._rear.prev
            if rprev != None:
                rprev.next = None
                self._rear.prev = None
            self._rear = rprev  # 更新尾节点
        self._size -= 1  # 更新队列长度
        return val

    def pop_first(self) -> int:
        """队首出队"""
        return self.pop(True)

    def pop_last(self) -> int:
        """队尾出队"""
        return self.pop(False)

    def peek_first(self) -> int:
        """访问队首元素"""
        if self.is_empty():
            raise IndexError("双向队列为空")
        return self._front.val

    def peek_last(self) -> int:
        """访问队尾元素"""
        if self.is_empty():
            raise IndexError("双向队列为空")
        return self._rear.val

    def to_array(self) -> list[int]:
        """返回数组用于打印"""
        node = self._front
        res = [0] * self.size()
        for i in range(self.size()):
            res[i] = node.val
            node = node.next
        return res
linkedlist_deque.cpp
/* 双向链表节点 */
struct DoublyListNode {
    int val;              // 节点值
    DoublyListNode *next; // 后继节点指针
    DoublyListNode *prev; // 前驱节点指针
    DoublyListNode(int val) : val(val), prev(nullptr), next(nullptr) {
    }
};

/* 基于双向链表实现的双向队列 */
class LinkedListDeque {
  private:
    DoublyListNode *front, *rear; // 头节点 front ,尾节点 rear
    int queSize = 0;              // 双向队列的长度

  public:
    /* 构造方法 */
    LinkedListDeque() : front(nullptr), rear(nullptr) {
    }

    /* 析构方法 */
    ~LinkedListDeque() {
        // 遍历链表删除节点,释放内存
        DoublyListNode *pre, *cur = front;
        while (cur != nullptr) {
            pre = cur;
            cur = cur->next;
            delete pre;
        }
    }

    /* 获取双向队列的长度 */
    int size() {
        return queSize;
    }

    /* 判断双向队列是否为空 */
    bool isEmpty() {
        return size() == 0;
    }

    /* 入队操作 */
    void push(int num, bool isFront) {
        DoublyListNode *node = new DoublyListNode(num);
        // 若链表为空,则令 front 和 rear 都指向 node
        if (isEmpty())
            front = rear = node;
        // 队首入队操作
        else if (isFront) {
            // 将 node 添加至链表头部
            front->prev = node;
            node->next = front;
            front = node; // 更新头节点
        // 队尾入队操作
        } else {
            // 将 node 添加至链表尾部
            rear->next = node;
            node->prev = rear;
            rear = node; // 更新尾节点
        }
        queSize++; // 更新队列长度
    }

    /* 队首入队 */
    void pushFirst(int num) {
        push(num, true);
    }

    /* 队尾入队 */
    void pushLast(int num) {
        push(num, false);
    }

    /* 出队操作 */
    int pop(bool isFront) {
        if (isEmpty())
            throw out_of_range("队列为空");
        int val;
        // 队首出队操作
        if (isFront) {
            val = front->val; // 暂存头节点值
            // 删除头节点
            DoublyListNode *fNext = front->next;
            if (fNext != nullptr) {
                fNext->prev = nullptr;
                front->next = nullptr;
            }
            delete front;
            front = fNext; // 更新头节点
        // 队尾出队操作
        } else {
            val = rear->val; // 暂存尾节点值
            // 删除尾节点
            DoublyListNode *rPrev = rear->prev;
            if (rPrev != nullptr) {
                rPrev->next = nullptr;
                rear->prev = nullptr;
            }
            delete rear;
            rear = rPrev; // 更新尾节点
        }
        queSize--; // 更新队列长度
        return val;
    }

    /* 队首出队 */
    int popFirst() {
        return pop(true);
    }

    /* 队尾出队 */
    int popLast() {
        return pop(false);
    }

    /* 访问队首元素 */
    int peekFirst() {
        if (isEmpty())
            throw out_of_range("双向队列为空");
        return front->val;
    }

    /* 访问队尾元素 */
    int peekLast() {
        if (isEmpty())
            throw out_of_range("双向队列为空");
        return rear->val;
    }

    /* 返回数组用于打印 */
    vector<int> toVector() {
        DoublyListNode *node = front;
        vector<int> res(size());
        for (int i = 0; i < res.size(); i++) {
            res[i] = node->val;
            node = node->next;
        }
        return res;
    }
};
linkedlist_deque.java
/* 双向链表节点 */
class ListNode {
    int val; // 节点值
    ListNode next; // 后继节点引用
    ListNode prev; // 前驱节点引用

    ListNode(int val) {
        this.val = val;
        prev = next = null;
    }
}

/* 基于双向链表实现的双向队列 */
class LinkedListDeque {
    private ListNode front, rear; // 头节点 front ,尾节点 rear
    private int queSize = 0; // 双向队列的长度

    public LinkedListDeque() {
        front = rear = null;
    }

    /* 获取双向队列的长度 */
    public int size() {
        return queSize;
    }

    /* 判断双向队列是否为空 */
    public boolean isEmpty() {
        return size() == 0;
    }

    /* 入队操作 */
    private void push(int num, boolean isFront) {
        ListNode node = new ListNode(num);
        // 若链表为空,则令 front 和 rear 都指向 node
        if (isEmpty())
            front = rear = node;
        // 队首入队操作
        else if (isFront) {
            // 将 node 添加至链表头部
            front.prev = node;
            node.next = front;
            front = node; // 更新头节点
        // 队尾入队操作
        } else {
            // 将 node 添加至链表尾部
            rear.next = node;
            node.prev = rear;
            rear = node; // 更新尾节点
        }
        queSize++; // 更新队列长度
    }

    /* 队首入队 */
    public void pushFirst(int num) {
        push(num, true);
    }

    /* 队尾入队 */
    public void pushLast(int num) {
        push(num, false);
    }

    /* 出队操作 */
    private int pop(boolean isFront) {
        if (isEmpty())
            throw new IndexOutOfBoundsException();
        int val;
        // 队首出队操作
        if (isFront) {
            val = front.val; // 暂存头节点值
            // 删除头节点
            ListNode fNext = front.next;
            if (fNext != null) {
                fNext.prev = null;
                front.next = null;
            }
            front = fNext; // 更新头节点
        // 队尾出队操作
        } else {
            val = rear.val; // 暂存尾节点值
            // 删除尾节点
            ListNode rPrev = rear.prev;
            if (rPrev != null) {
                rPrev.next = null;
                rear.prev = null;
            }
            rear = rPrev; // 更新尾节点
        }
        queSize--; // 更新队列长度
        return val;
    }

    /* 队首出队 */
    public int popFirst() {
        return pop(true);
    }

    /* 队尾出队 */
    public int popLast() {
        return pop(false);
    }

    /* 访问队首元素 */
    public int peekFirst() {
        if (isEmpty())
            throw new IndexOutOfBoundsException();
        return front.val;
    }

    /* 访问队尾元素 */
    public int peekLast() {
        if (isEmpty())
            throw new IndexOutOfBoundsException();
        return rear.val;
    }

    /* 返回数组用于打印 */
    public int[] toArray() {
        ListNode node = front;
        int[] res = new int[size()];
        for (int i = 0; i < res.length; i++) {
            res[i] = node.val;
            node = node.next;
        }
        return res;
    }
}
linkedlist_deque.cs
/* 双向链表节点 */
class ListNode(int val) {
    public int val = val;       // 节点值
    public ListNode? next = null; // 后继节点引用
    public ListNode? prev = null; // 前驱节点引用
}

/* 基于双向链表实现的双向队列 */
class LinkedListDeque {
    ListNode? front, rear; // 头节点 front, 尾节点 rear
    int queSize = 0;      // 双向队列的长度

    public LinkedListDeque() {
        front = null;
        rear = null;
    }

    /* 获取双向队列的长度 */
    public int Size() {
        return queSize;
    }

    /* 判断双向队列是否为空 */
    public bool IsEmpty() {
        return Size() == 0;
    }

    /* 入队操作 */
    void Push(int num, bool isFront) {
        ListNode node = new(num);
        // 若链表为空,则令 front 和 rear 都指向 node
        if (IsEmpty()) {
            front = node;
            rear = node;
        }
        // 队首入队操作
        else if (isFront) {
            // 将 node 添加至链表头部
            front!.prev = node;
            node.next = front;
            front = node; // 更新头节点                           
        }
        // 队尾入队操作
        else {
            // 将 node 添加至链表尾部
            rear!.next = node;
            node.prev = rear;
            rear = node;  // 更新尾节点
        }

        queSize++; // 更新队列长度
    }

    /* 队首入队 */
    public void PushFirst(int num) {
        Push(num, true);
    }

    /* 队尾入队 */
    public void PushLast(int num) {
        Push(num, false);
    }

    /* 出队操作 */
    int? Pop(bool isFront) {
        if (IsEmpty())
            throw new Exception();
        int? val;
        // 队首出队操作
        if (isFront) {
            val = front?.val; // 暂存头节点值
            // 删除头节点
            ListNode? fNext = front?.next;
            if (fNext != null) {
                fNext.prev = null;
                front!.next = null;
            }
            front = fNext;   // 更新头节点
        }
        // 队尾出队操作
        else {
            val = rear?.val;  // 暂存尾节点值
            // 删除尾节点
            ListNode? rPrev = rear?.prev;
            if (rPrev != null) {
                rPrev.next = null;
                rear!.prev = null;
            }
            rear = rPrev;    // 更新尾节点
        }

        queSize--; // 更新队列长度
        return val;
    }

    /* 队首出队 */
    public int? PopFirst() {
        return Pop(true);
    }

    /* 队尾出队 */
    public int? PopLast() {
        return Pop(false);
    }

    /* 访问队首元素 */
    public int? PeekFirst() {
        if (IsEmpty())
            throw new Exception();
        return front?.val;
    }

    /* 访问队尾元素 */
    public int? PeekLast() {
        if (IsEmpty())
            throw new Exception();
        return rear?.val;
    }

    /* 返回数组用于打印 */
    public int?[] ToArray() {
        ListNode? node = front;
        int?[] res = new int?[Size()];
        for (int i = 0; i < res.Length; i++) {
            res[i] = node?.val;
            node = node?.next;
        }

        return res;
    }
}
linkedlist_deque.go
/* 基于双向链表实现的双向队列 */
type linkedListDeque struct {
    // 使用内置包 list
    data *list.List
}

/* 初始化双端队列 */
func newLinkedListDeque() *linkedListDeque {
    return &linkedListDeque{
        data: list.New(),
    }
}

/* 队首元素入队 */
func (s *linkedListDeque) pushFirst(value any) {
    s.data.PushFront(value)
}

/* 队尾元素入队 */
func (s *linkedListDeque) pushLast(value any) {
    s.data.PushBack(value)
}

/* 队首元素出队 */
func (s *linkedListDeque) popFirst() any {
    if s.isEmpty() {
        return nil
    }
    e := s.data.Front()
    s.data.Remove(e)
    return e.Value
}

/* 队尾元素出队 */
func (s *linkedListDeque) popLast() any {
    if s.isEmpty() {
        return nil
    }
    e := s.data.Back()
    s.data.Remove(e)
    return e.Value
}

/* 访问队首元素 */
func (s *linkedListDeque) peekFirst() any {
    if s.isEmpty() {
        return nil
    }
    e := s.data.Front()
    return e.Value
}

/* 访问队尾元素 */
func (s *linkedListDeque) peekLast() any {
    if s.isEmpty() {
        return nil
    }
    e := s.data.Back()
    return e.Value
}

/* 获取队列的长度 */
func (s *linkedListDeque) size() int {
    return s.data.Len()
}

/* 判断队列是否为空 */
func (s *linkedListDeque) isEmpty() bool {
    return s.data.Len() == 0
}

/* 获取 List 用于打印 */
func (s *linkedListDeque) toList() *list.List {
    return s.data
}
linkedlist_deque.swift
/* 双向链表节点 */
class ListNode {
    var val: Int // 节点值
    var next: ListNode? // 后继节点引用
    weak var prev: ListNode? // 前驱节点引用

    init(val: Int) {
        self.val = val
    }
}

/* 基于双向链表实现的双向队列 */
class LinkedListDeque {
    private var front: ListNode? // 头节点 front
    private var rear: ListNode? // 尾节点 rear
    private var _size: Int // 双向队列的长度

    init() {
        _size = 0
    }

    /* 获取双向队列的长度 */
    func size() -> Int {
        _size
    }

    /* 判断双向队列是否为空 */
    func isEmpty() -> Bool {
        size() == 0
    }

    /* 入队操作 */
    private func push(num: Int, isFront: Bool) {
        let node = ListNode(val: num)
        // 若链表为空,则令 front 和 rear 都指向 node
        if isEmpty() {
            front = node
            rear = node
        }
        // 队首入队操作
        else if isFront {
            // 将 node 添加至链表头部
            front?.prev = node
            node.next = front
            front = node // 更新头节点
        }
        // 队尾入队操作
        else {
            // 将 node 添加至链表尾部
            rear?.next = node
            node.prev = rear
            rear = node // 更新尾节点
        }
        _size += 1 // 更新队列长度
    }

    /* 队首入队 */
    func pushFirst(num: Int) {
        push(num: num, isFront: true)
    }

    /* 队尾入队 */
    func pushLast(num: Int) {
        push(num: num, isFront: false)
    }

    /* 出队操作 */
    private func pop(isFront: Bool) -> Int {
        if isEmpty() {
            fatalError("双向队列为空")
        }
        let val: Int
        // 队首出队操作
        if isFront {
            val = front!.val // 暂存头节点值
            // 删除头节点
            let fNext = front?.next
            if fNext != nil {
                fNext?.prev = nil
                front?.next = nil
            }
            front = fNext // 更新头节点
        }
        // 队尾出队操作
        else {
            val = rear!.val // 暂存尾节点值
            // 删除尾节点
            let rPrev = rear?.prev
            if rPrev != nil {
                rPrev?.next = nil
                rear?.prev = nil
            }
            rear = rPrev // 更新尾节点
        }
        _size -= 1 // 更新队列长度
        return val
    }

    /* 队首出队 */
    func popFirst() -> Int {
        pop(isFront: true)
    }

    /* 队尾出队 */
    func popLast() -> Int {
        pop(isFront: false)
    }

    /* 访问队首元素 */
    func peekFirst() -> Int {
        if isEmpty() {
            fatalError("双向队列为空")
        }
        return front!.val
    }

    /* 访问队尾元素 */
    func peekLast() -> Int {
        if isEmpty() {
            fatalError("双向队列为空")
        }
        return rear!.val
    }

    /* 返回数组用于打印 */
    func toArray() -> [Int] {
        var node = front
        var res = Array(repeating: 0, count: size())
        for i in res.indices {
            res[i] = node!.val
            node = node?.next
        }
        return res
    }
}
linkedlist_deque.js
/* 双向链表节点 */
class ListNode {
    prev; // 前驱节点引用 (指针)
    next; // 后继节点引用 (指针)
    val; // 节点值

    constructor(val) {
        this.val = val;
        this.next = null;
        this.prev = null;
    }
}

/* 基于双向链表实现的双向队列 */
class LinkedListDeque {
    #front; // 头节点 front
    #rear; // 尾节点 rear
    #queSize; // 双向队列的长度

    constructor() {
        this.#front = null;
        this.#rear = null;
        this.#queSize = 0;
    }

    /* 队尾入队操作 */
    pushLast(val) {
        const node = new ListNode(val);
        // 若链表为空,则令 front 和 rear 都指向 node
        if (this.#queSize === 0) {
            this.#front = node;
            this.#rear = node;
        } else {
            // 将 node 添加至链表尾部
            this.#rear.next = node;
            node.prev = this.#rear;
            this.#rear = node; // 更新尾节点
        }
        this.#queSize++;
    }

    /* 队首入队操作 */
    pushFirst(val) {
        const node = new ListNode(val);
        // 若链表为空,则令 front 和 rear 都指向 node
        if (this.#queSize === 0) {
            this.#front = node;
            this.#rear = node;
        } else {
            // 将 node 添加至链表头部
            this.#front.prev = node;
            node.next = this.#front;
            this.#front = node; // 更新头节点
        }
        this.#queSize++;
    }

    /* 队尾出队操作 */
    popLast() {
        if (this.#queSize === 0) {
            return null;
        }
        const value = this.#rear.val; // 存储尾节点值
        // 删除尾节点
        let temp = this.#rear.prev;
        if (temp !== null) {
            temp.next = null;
            this.#rear.prev = null;
        }
        this.#rear = temp; // 更新尾节点
        this.#queSize--;
        return value;
    }

    /* 队首出队操作 */
    popFirst() {
        if (this.#queSize === 0) {
            return null;
        }
        const value = this.#front.val; // 存储尾节点值
        // 删除头节点
        let temp = this.#front.next;
        if (temp !== null) {
            temp.prev = null;
            this.#front.next = null;
        }
        this.#front = temp; // 更新头节点
        this.#queSize--;
        return value;
    }

    /* 访问队尾元素 */
    peekLast() {
        return this.#queSize === 0 ? null : this.#rear.val;
    }

    /* 访问队首元素 */
    peekFirst() {
        return this.#queSize === 0 ? null : this.#front.val;
    }

    /* 获取双向队列的长度 */
    size() {
        return this.#queSize;
    }

    /* 判断双向队列是否为空 */
    isEmpty() {
        return this.#queSize === 0;
    }

    /* 打印双向队列 */
    print() {
        const arr = [];
        let temp = this.#front;
        while (temp !== null) {
            arr.push(temp.val);
            temp = temp.next;
        }
        console.log('[' + arr.join(', ') + ']');
    }
}
linkedlist_deque.ts
/* 双向链表节点 */
class ListNode {
    prev: ListNode; // 前驱节点引用 (指针)
    next: ListNode; // 后继节点引用 (指针)
    val: number; // 节点值

    constructor(val: number) {
        this.val = val;
        this.next = null;
        this.prev = null;
    }
}

/* 基于双向链表实现的双向队列 */
class LinkedListDeque {
    private front: ListNode; // 头节点 front
    private rear: ListNode; // 尾节点 rear
    private queSize: number; // 双向队列的长度

    constructor() {
        this.front = null;
        this.rear = null;
        this.queSize = 0;
    }

    /* 队尾入队操作 */
    pushLast(val: number): void {
        const node: ListNode = new ListNode(val);
        // 若链表为空,则令 front 和 rear 都指向 node
        if (this.queSize === 0) {
            this.front = node;
            this.rear = node;
        } else {
            // 将 node 添加至链表尾部
            this.rear.next = node;
            node.prev = this.rear;
            this.rear = node; // 更新尾节点
        }
        this.queSize++;
    }

    /* 队首入队操作 */
    pushFirst(val: number): void {
        const node: ListNode = new ListNode(val);
        // 若链表为空,则令 front 和 rear 都指向 node
        if (this.queSize === 0) {
            this.front = node;
            this.rear = node;
        } else {
            // 将 node 添加至链表头部
            this.front.prev = node;
            node.next = this.front;
            this.front = node; // 更新头节点
        }
        this.queSize++;
    }

    /* 队尾出队操作 */
    popLast(): number {
        if (this.queSize === 0) {
            return null;
        }
        const value: number = this.rear.val; // 存储尾节点值
        // 删除尾节点
        let temp: ListNode = this.rear.prev;
        if (temp !== null) {
            temp.next = null;
            this.rear.prev = null;
        }
        this.rear = temp; // 更新尾节点
        this.queSize--;
        return value;
    }

    /* 队首出队操作 */
    popFirst(): number {
        if (this.queSize === 0) {
            return null;
        }
        const value: number = this.front.val; // 存储尾节点值
        // 删除头节点
        let temp: ListNode = this.front.next;
        if (temp !== null) {
            temp.prev = null;
            this.front.next = null;
        }
        this.front = temp; // 更新头节点
        this.queSize--;
        return value;
    }

    /* 访问队尾元素 */
    peekLast(): number {
        return this.queSize === 0 ? null : this.rear.val;
    }

    /* 访问队首元素 */
    peekFirst(): number {
        return this.queSize === 0 ? null : this.front.val;
    }

    /* 获取双向队列的长度 */
    size(): number {
        return this.queSize;
    }

    /* 判断双向队列是否为空 */
    isEmpty(): boolean {
        return this.queSize === 0;
    }

    /* 打印双向队列 */
    print(): void {
        const arr: number[] = [];
        let temp: ListNode = this.front;
        while (temp !== null) {
            arr.push(temp.val);
            temp = temp.next;
        }
        console.log('[' + arr.join(', ') + ']');
    }
}
linkedlist_deque.dart
/* 双向链表节点 */
class ListNode {
  int val; // 节点值
  ListNode? next; // 后继节点引用
  ListNode? prev; // 前驱节点引用

  ListNode(this.val, {this.next, this.prev});
}

/* 基于双向链表实现的双向对列 */
class LinkedListDeque {
  late ListNode? _front; // 头节点 _front
  late ListNode? _rear; // 尾节点 _rear
  int _queSize = 0; // 双向队列的长度

  LinkedListDeque() {
    this._front = null;
    this._rear = null;
  }

  /* 获取双向队列长度 */
  int size() {
    return this._queSize;
  }

  /* 判断双向队列是否为空 */
  bool isEmpty() {
    return size() == 0;
  }

  /* 入队操作 */
  void push(int _num, bool isFront) {
    final ListNode node = ListNode(_num);
    if (isEmpty()) {
      // 若链表为空,则令 _front 和 _rear 都指向 node
      _front = _rear = node;
    } else if (isFront) {
      // 队首入队操作
      // 将 node 添加至链表头部
      _front!.prev = node;
      node.next = _front;
      _front = node; // 更新头节点
    } else {
      // 队尾入队操作
      // 将 node 添加至链表尾部
      _rear!.next = node;
      node.prev = _rear;
      _rear = node; // 更新尾节点
    }
    _queSize++; // 更新队列长度
  }

  /* 队首入队 */
  void pushFirst(int _num) {
    push(_num, true);
  }

  /* 队尾入队 */
  void pushLast(int _num) {
    push(_num, false);
  }

  /* 出队操作 */
  int? pop(bool isFront) {
    // 若队列为空,直接返回 null
    if (isEmpty()) {
      return null;
    }
    final int val;
    if (isFront) {
      // 队首出队操作
      val = _front!.val; // 暂存头节点值
      // 删除头节点
      ListNode? fNext = _front!.next;
      if (fNext != null) {
        fNext.prev = null;
        _front!.next = null;
      }
      _front = fNext; // 更新头节点
    } else {
      // 队尾出队操作
      val = _rear!.val; // 暂存尾节点值
      // 删除尾节点
      ListNode? rPrev = _rear!.prev;
      if (rPrev != null) {
        rPrev.next = null;
        _rear!.prev = null;
      }
      _rear = rPrev; // 更新尾节点
    }
    _queSize--; // 更新队列长度
    return val;
  }

  /* 队首出队 */
  int? popFirst() {
    return pop(true);
  }

  /* 队尾出队 */
  int? popLast() {
    return pop(false);
  }

  /* 访问队首元素 */
  int? peekFirst() {
    return _front?.val;
  }

  /* 访问队尾元素 */
  int? peekLast() {
    return _rear?.val;
  }

  /* 返回数组用于打印 */
  List<int> toArray() {
    ListNode? node = _front;
    final List<int> res = [];
    for (int i = 0; i < _queSize; i++) {
      res.add(node!.val);
      node = node.next;
    }
    return res;
  }
}
linkedlist_deque.rs
/* 双向链表节点 */
pub struct ListNode<T> {
    pub val: T,                                 // 节点值
    pub next: Option<Rc<RefCell<ListNode<T>>>>, // 后继节点指针
    pub prev: Option<Rc<RefCell<ListNode<T>>>>, // 前驱节点指针
}

impl<T> ListNode<T> {
    pub fn new(val: T) -> Rc<RefCell<ListNode<T>>> {
        Rc::new(RefCell::new(ListNode {
            val,
            next: None,
            prev: None,
        }))
    }
}

/* 基于双向链表实现的双向队列 */
#[allow(dead_code)]
pub struct LinkedListDeque<T> {
    front: Option<Rc<RefCell<ListNode<T>>>>, // 头节点 front
    rear: Option<Rc<RefCell<ListNode<T>>>>,  // 尾节点 rear
    que_size: usize,                         // 双向队列的长度
}

impl<T: Copy> LinkedListDeque<T> {
    pub fn new() -> Self {
        Self {
            front: None,
            rear: None,
            que_size: 0,
        }
    }

    /* 获取双向队列的长度 */
    pub fn size(&self) -> usize {
        return self.que_size;
    }

    /* 判断双向队列是否为空 */
    pub fn is_empty(&self) -> bool {
        return self.size() == 0;
    }

    /* 入队操作 */
    pub fn push(&mut self, num: T, is_front: bool) {
        let node = ListNode::new(num);
        // 队首入队操作
        if is_front {
            match self.front.take() {
                // 若链表为空,则令 front 和 rear 都指向 node
                None => {
                    self.rear = Some(node.clone());
                    self.front = Some(node);
                }
                // 将 node 添加至链表头部
                Some(old_front) => {
                    old_front.borrow_mut().prev = Some(node.clone());
                    node.borrow_mut().next = Some(old_front);
                    self.front = Some(node); // 更新头节点
                }
            }
        }
        // 队尾入队操作
        else {
            match self.rear.take() {
                // 若链表为空,则令 front 和 rear 都指向 node
                None => {
                    self.front = Some(node.clone());
                    self.rear = Some(node);
                }
                // 将 node 添加至链表尾部
                Some(old_rear) => {
                    old_rear.borrow_mut().next = Some(node.clone());
                    node.borrow_mut().prev = Some(old_rear);
                    self.rear = Some(node); // 更新尾节点
                }
            }
        }
        self.que_size += 1; // 更新队列长度
    }

    /* 队首入队 */
    pub fn push_first(&mut self, num: T) {
        self.push(num, true);
    }

    /* 队尾入队 */
    pub fn push_last(&mut self, num: T) {
        self.push(num, false);
    }

    /* 出队操作 */
    pub fn pop(&mut self, is_front: bool) -> Option<T> {
        // 若队列为空,直接返回 None
        if self.is_empty() {
            return None;
        };
        // 队首出队操作
        if is_front {
            self.front.take().map(|old_front| {
                match old_front.borrow_mut().next.take() {
                    Some(new_front) => {
                        new_front.borrow_mut().prev.take();
                        self.front = Some(new_front); // 更新头节点
                    }
                    None => {
                        self.rear.take();
                    }
                }
                self.que_size -= 1; // 更新队列长度
                Rc::try_unwrap(old_front).ok().unwrap().into_inner().val
            })
        }
        // 队尾出队操作
        else {
            self.rear.take().map(|old_rear| {
                match old_rear.borrow_mut().prev.take() {
                    Some(new_rear) => {
                        new_rear.borrow_mut().next.take();
                        self.rear = Some(new_rear); // 更新尾节点
                    }
                    None => {
                        self.front.take();
                    }
                }
                self.que_size -= 1; // 更新队列长度
                Rc::try_unwrap(old_rear).ok().unwrap().into_inner().val
            })
        }
    }

    /* 队首出队 */
    pub fn pop_first(&mut self) -> Option<T> {
        return self.pop(true);
    }

    /* 队尾出队 */
    pub fn pop_last(&mut self) -> Option<T> {
        return self.pop(false);
    }

    /* 访问队首元素 */
    pub fn peek_first(&self) -> Option<&Rc<RefCell<ListNode<T>>>> {
        self.front.as_ref()
    }

    /* 访问队尾元素 */
    pub fn peek_last(&self) -> Option<&Rc<RefCell<ListNode<T>>>> {
        self.rear.as_ref()
    }

    /* 返回数组用于打印 */
    pub fn to_array(&self, head: Option<&Rc<RefCell<ListNode<T>>>>) -> Vec<T> {
        if let Some(node) = head {
            let mut nums = self.to_array(node.borrow().next.as_ref());
            nums.insert(0, node.borrow().val);
            return nums;
        }
        return Vec::new();
    }
}
linkedlist_deque.c
/* 双向链表节点 */
typedef struct DoublyListNode {
    int val;                     // 节点值
    struct DoublyListNode *next; // 后继节点
    struct DoublyListNode *prev; // 前驱节点
} DoublyListNode;

/* 构造函数 */
DoublyListNode *newDoublyListNode(int num) {
    DoublyListNode *new = (DoublyListNode *)malloc(sizeof(DoublyListNode));
    new->val = num;
    new->next = NULL;
    new->prev = NULL;
    return new;
}

/* 析构函数 */
void delDoublyListNode(DoublyListNode *node) {
    free(node);
}

/* 基于双向链表实现的双向队列 */
typedef struct {
    DoublyListNode *front, *rear; // 头节点 front ,尾节点 rear
    int queSize;                  // 双向队列的长度
} LinkedListDeque;

/* 构造函数 */
LinkedListDeque *newLinkedListDeque() {
    LinkedListDeque *deque = (LinkedListDeque *)malloc(sizeof(LinkedListDeque));
    deque->front = NULL;
    deque->rear = NULL;
    deque->queSize = 0;
    return deque;
}

/* 析构函数 */
void delLinkedListdeque(LinkedListDeque *deque) {
    // 释放所有节点
    for (int i = 0; i < deque->queSize && deque->front != NULL; i++) {
        DoublyListNode *tmp = deque->front;
        deque->front = deque->front->next;
        free(tmp);
    }
    // 释放 deque 结构体
    free(deque);
}

/* 获取队列的长度 */
int size(LinkedListDeque *deque) {
    return deque->queSize;
}

/* 判断队列是否为空 */
bool empty(LinkedListDeque *deque) {
    return (size(deque) == 0);
}

/* 入队 */
void push(LinkedListDeque *deque, int num, bool isFront) {
    DoublyListNode *node = newDoublyListNode(num);
    // 若链表为空,则令 front 和 rear 都指向node
    if (empty(deque)) {
        deque->front = deque->rear = node;
    }
    // 队首入队操作
    else if (isFront) {
        // 将 node 添加至链表头部
        deque->front->prev = node;
        node->next = deque->front;
        deque->front = node; // 更新头节点
    }
    // 队尾入队操作
    else {
        // 将 node 添加至链表尾部
        deque->rear->next = node;
        node->prev = deque->rear;
        deque->rear = node;
    }
    deque->queSize++; // 更新队列长度
}

/* 队首入队 */
void pushFirst(LinkedListDeque *deque, int num) {
    push(deque, num, true);
}

/* 队尾入队 */
void pushLast(LinkedListDeque *deque, int num) {
    push(deque, num, false);
}

/* 访问队首元素 */
int peekFirst(LinkedListDeque *deque) {
    assert(size(deque) && deque->front);
    return deque->front->val;
}

/* 访问队尾元素 */
int peekLast(LinkedListDeque *deque) {
    assert(size(deque) && deque->rear);
    return deque->rear->val;
}

/* 出队 */
int pop(LinkedListDeque *deque, bool isFront) {
    if (empty(deque))
        return -1;
    int val;
    // 队首出队操作
    if (isFront) {
        val = peekFirst(deque); // 暂存头节点值
        DoublyListNode *fNext = deque->front->next;
        if (fNext) {
            fNext->prev = NULL;
            deque->front->next = NULL;
        }
        delDoublyListNode(deque->front);
        deque->front = fNext; // 更新头节点
    }
    // 队尾出队操作
    else {
        val = peekLast(deque); // 暂存尾节点值
        DoublyListNode *rPrev = deque->rear->prev;
        if (rPrev) {
            rPrev->next = NULL;
            deque->rear->prev = NULL;
        }
        delDoublyListNode(deque->rear);
        deque->rear = rPrev; // 更新尾节点
    }
    deque->queSize--; // 更新队列长度
    return val;
}

/* 队首出队 */
int popFirst(LinkedListDeque *deque) {
    return pop(deque, true);
}

/* 队尾出队 */
int popLast(LinkedListDeque *deque) {
    return pop(deque, false);
}

/* 打印队列 */
void printLinkedListDeque(LinkedListDeque *deque) {
    int *arr = malloc(sizeof(int) * deque->queSize);
    // 拷贝链表中的数据到数组
    int i;
    DoublyListNode *node;
    for (i = 0, node = deque->front; i < deque->queSize; i++) {
        arr[i] = node->val;
        node = node->next;
    }
    printArray(arr, deque->queSize);
    free(arr);
}
linkedlist_deque.kt
/* 双向链表节点 */
class ListNode(var _val: Int) {
    // 节点值
    var next: ListNode? = null // 后继节点引用
    var prev: ListNode? = null // 前驱节点引用
}

/* 基于双向链表实现的双向队列 */
class LinkedListDeque {
    private var front: ListNode? = null // 头节点 front
    private var rear: ListNode? = null // 尾节点 rear
    private var queSize: Int = 0 // 双向队列的长度

    /* 获取双向队列的长度 */
    fun size(): Int {
        return queSize
    }

    /* 判断双向队列是否为空 */
    fun isEmpty(): Boolean {
        return size() == 0
    }

    /* 入队操作 */
    fun push(num: Int, isFront: Boolean) {
        val node = ListNode(num)
        // 若链表为空,则令 front 和 rear 都指向 node
        if (isEmpty()) {
            rear = node
            front = rear
            // 队首入队操作
        } else if (isFront) {
            // 将 node 添加至链表头部
            front?.prev = node
            node.next = front
            front = node // 更新头节点
            // 队尾入队操作
        } else {
            // 将 node 添加至链表尾部
            rear?.next = node
            node.prev = rear
            rear = node // 更新尾节点
        }
        queSize++ // 更新队列长度
    }

    /* 队首入队 */
    fun pushFirst(num: Int) {
        push(num, true)
    }

    /* 队尾入队 */
    fun pushLast(num: Int) {
        push(num, false)
    }

    /* 出队操作 */
    fun pop(isFront: Boolean): Int {
        if (isEmpty()) 
            throw IndexOutOfBoundsException()
        val _val: Int
        // 队首出队操作
        if (isFront) {
            _val = front!!._val // 暂存头节点值
            // 删除头节点
            val fNext = front!!.next
            if (fNext != null) {
                fNext.prev = null
                front!!.next = null
            }
            front = fNext // 更新头节点
            // 队尾出队操作
        } else {
            _val = rear!!._val // 暂存尾节点值
            // 删除尾节点
            val rPrev = rear!!.prev
            if (rPrev != null) {
                rPrev.next = null
                rear!!.prev = null
            }
            rear = rPrev // 更新尾节点
        }
        queSize-- // 更新队列长度
        return _val
    }

    /* 队首出队 */
    fun popFirst(): Int {
        return pop(true)
    }

    /* 队尾出队 */
    fun popLast(): Int {
        return pop(false)
    }

    /* 访问队首元素 */
    fun peekFirst(): Int {
        if (isEmpty()) throw IndexOutOfBoundsException()
        return front!!._val
    }

    /* 访问队尾元素 */
    fun peekLast(): Int {
        if (isEmpty()) throw IndexOutOfBoundsException()
        return rear!!._val
    }

    /* 返回数组用于打印 */
    fun toArray(): IntArray {
        var node = front
        val res = IntArray(size())
        for (i in res.indices) {
            res[i] = node!!._val
            node = node.next
        }
        return res
    }
}
linkedlist_deque.rb
=begin
File: linkedlist_deque.rb
Created Time: 2024-04-06
Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
=end

### 双向链表节点
class ListNode
  attr_accessor :val
  attr_accessor :next # 后继节点引用
  attr_accessor :prev # 前躯节点引用

  ### 构造方法 ###
  def initialize(val)
    @val = val
  end
end

### 基于双向链表实现的双向队列 ###
class LinkedListDeque
  ### 获取双向队列的长度 ###
  attr_reader :size

  ### 构造方法 ###
  def initialize
    @front = nil  # 头节点 front
    @rear = nil   # 尾节点 rear
    @size = 0     # 双向队列的长度
  end

  ### 判断双向队列是否为空 ###
  def is_empty?
    size.zero?
  end

  ### 入队操作 ###
  def push(num, is_front)
    node = ListNode.new(num)
    # 若链表为空, 则令 front 和 rear 都指向 node
    if is_empty?
      @front = @rear = node
    # 队首入队操作
    elsif is_front
      # 将 node 添加至链表头部
      @front.prev = node
      node.next = @front
      @front = node # 更新头节点
    # 队尾入队操作
    else
      # 将 node 添加至链表尾部
      @rear.next = node
      node.prev = @rear
      @rear = node # 更新尾节点
    end
    @size += 1 # 更新队列长度
  end

  ### 队首入队 ###
  def push_first(num)
    push(num, true)
  end

  ### 队尾入队 ###
  def push_last(num)
    push(num, false)
  end

  ### 出队操作 ###
  def pop(is_front)
    raise IndexError, '双向队列为空' if is_empty?

    # 队首出队操作
    if is_front
      val = @front.val # 暂存头节点值
      # 删除头节点
      fnext = @front.next
      unless fnext.nil?
        fnext.prev = nil
        @front.next = nil
      end
      @front = fnext # 更新头节点
    # 队尾出队操作
    else
      val = @rear.val # 暂存尾节点值
      # 删除尾节点
      rprev = @rear.prev
      unless rprev.nil?
        rprev.next = nil
        @rear.prev = nil
      end
      @rear = rprev # 更新尾节点
    end
    @size -= 1 # 更新队列长度

    val
  end

  ### 队首出队 ###
  def pop_first
    pop(true)
  end

  ### 队首出队 ###
  def pop_last
    pop(false)
  end

  ### 访问队首元素 ###
  def peek_first
    raise IndexError, '双向队列为空' if is_empty?

    @front.val
  end

  ### 访问队尾元素 ###
  def peek_last
    raise IndexError, '双向队列为空' if is_empty?

    @rear.val
  end

  ### 返回数组用于打印 ###
  def to_array
    node = @front
    res = Array.new(size, 0)
    for i in 0...size
      res[i] = node.val
      node = node.next
    end
    res
  end
end
linkedlist_deque.zig
// 双向链表节点
fn ListNode(comptime T: type) type {
    return struct {
        const Self = @This();

        val: T = undefined,     // 节点值
        next: ?*Self = null,    // 后继节点指针
        prev: ?*Self = null,    // 前驱节点指针

        // Initialize a list node with specific value
        pub fn init(self: *Self, x: i32) void {
            self.val = x;
            self.next = null;
            self.prev = null;
        }
    };
}

// 基于双向链表实现的双向队列
fn LinkedListDeque(comptime T: type) type {
    return struct {
        const Self = @This();

        front: ?*ListNode(T) = null,                    // 头节点 front
        rear: ?*ListNode(T) = null,                     // 尾节点 rear
        que_size: usize = 0,                             // 双向队列的长度
        mem_arena: ?std.heap.ArenaAllocator = null,
        mem_allocator: std.mem.Allocator = undefined,   // 内存分配器

        // 构造函数(分配内存+初始化队列)
        pub fn init(self: *Self, allocator: std.mem.Allocator) !void {
            if (self.mem_arena == null) {
                self.mem_arena = std.heap.ArenaAllocator.init(allocator);
                self.mem_allocator = self.mem_arena.?.allocator();
            }
            self.front = null;
            self.rear = null;
            self.que_size = 0;
        }

        // 析构函数(释放内存)
        pub fn deinit(self: *Self) void {
            if (self.mem_arena == null) return;
            self.mem_arena.?.deinit();
        }

        // 获取双向队列的长度
        pub fn size(self: *Self) usize {
            return self.que_size;
        }

        // 判断双向队列是否为空
        pub fn isEmpty(self: *Self) bool {
            return self.size() == 0;
        }

        // 入队操作
        pub fn push(self: *Self, num: T, is_front: bool) !void {
            var node = try self.mem_allocator.create(ListNode(T));
            node.init(num);
            // 若链表为空,则令 front 和 rear 都指向 node
            if (self.isEmpty()) {
                self.front = node;
                self.rear = node;
            // 队首入队操作
            } else if (is_front) {
                // 将 node 添加至链表头部
                self.front.?.prev = node;
                node.next = self.front;
                self.front = node;  // 更新头节点
            // 队尾入队操作
            } else {
                // 将 node 添加至链表尾部
                self.rear.?.next = node;
                node.prev = self.rear;
                self.rear = node;   // 更新尾节点
            }
            self.que_size += 1;      // 更新队列长度
        } 

        // 队首入队
        pub fn pushFirst(self: *Self, num: T) !void {
            try self.push(num, true);
        } 

        // 队尾入队
        pub fn pushLast(self: *Self, num: T) !void {
            try self.push(num, false);
        } 

        // 出队操作
        pub fn pop(self: *Self, is_front: bool) T {
            if (self.isEmpty()) @panic("双向队列为空");
            var val: T = undefined;
            // 队首出队操作
            if (is_front) {
                val = self.front.?.val;     // 暂存头节点值
                // 删除头节点
                var fNext = self.front.?.next;
                if (fNext != null) {
                    fNext.?.prev = null;
                    self.front.?.next = null;
                }
                self.front = fNext;         // 更新头节点
            // 队尾出队操作
            } else {
                val = self.rear.?.val;      // 暂存尾节点值
                // 删除尾节点
                var rPrev = self.rear.?.prev;
                if (rPrev != null) {
                    rPrev.?.next = null;
                    self.rear.?.prev = null;
                }
                self.rear = rPrev;          // 更新尾节点
            }
            self.que_size -= 1;              // 更新队列长度
            return val;
        } 

        // 队首出队
        pub fn popFirst(self: *Self) T {
            return self.pop(true);
        } 

        // 队尾出队
        pub fn popLast(self: *Self) T {
            return self.pop(false);
        } 

        // 访问队首元素
        pub fn peekFirst(self: *Self) T {
            if (self.isEmpty()) @panic("双向队列为空");
            return self.front.?.val;
        }  

        // 访问队尾元素
        pub fn peekLast(self: *Self) T {
            if (self.isEmpty()) @panic("双向队列为空");
            return self.rear.?.val;
        }

        // 返回数组用于打印
        pub fn toArray(self: *Self) ![]T {
            var node = self.front;
            var res = try self.mem_allocator.alloc(T, self.size());
            @memset(res, @as(T, 0));
            var i: usize = 0;
            while (i < res.len) : (i += 1) {
                res[i] = node.?.val;
                node = node.?.next;
            }
            return res;
        }
    };
}

2.   Implementation based on array

As shown in the Figure 5-9 , similar to implementing a queue with an array, we can also use a circular array to implement a double-ended queue.

Implementing Double-Ended Queue with Array for Enqueue and Dequeue Operations

array_deque_push_last

array_deque_push_first

array_deque_pop_last

array_deque_pop_first

Figure 5-9   Implementing Double-Ended Queue with Array for Enqueue and Dequeue Operations

The implementation only needs to add methods for "front enqueue" and "rear dequeue":

array_deque.py
class ArrayDeque:
    """基于环形数组实现的双向队列"""

    def __init__(self, capacity: int):
        """构造方法"""
        self._nums: list[int] = [0] * capacity
        self._front: int = 0
        self._size: int = 0

    def capacity(self) -> int:
        """获取双向队列的容量"""
        return len(self._nums)

    def size(self) -> int:
        """获取双向队列的长度"""
        return self._size

    def is_empty(self) -> bool:
        """判断双向队列是否为空"""
        return self._size == 0

    def index(self, i: int) -> int:
        """计算环形数组索引"""
        # 通过取余操作实现数组首尾相连
        # 当 i 越过数组尾部后,回到头部
        # 当 i 越过数组头部后,回到尾部
        return (i + self.capacity()) % self.capacity()

    def push_first(self, num: int):
        """队首入队"""
        if self._size == self.capacity():
            print("双向队列已满")
            return
        # 队首指针向左移动一位
        # 通过取余操作实现 front 越过数组头部后回到尾部
        self._front = self.index(self._front - 1)
        # 将 num 添加至队首
        self._nums[self._front] = num
        self._size += 1

    def push_last(self, num: int):
        """队尾入队"""
        if self._size == self.capacity():
            print("双向队列已满")
            return
        # 计算队尾指针,指向队尾索引 + 1
        rear = self.index(self._front + self._size)
        # 将 num 添加至队尾
        self._nums[rear] = num
        self._size += 1

    def pop_first(self) -> int:
        """队首出队"""
        num = self.peek_first()
        # 队首指针向后移动一位
        self._front = self.index(self._front + 1)
        self._size -= 1
        return num

    def pop_last(self) -> int:
        """队尾出队"""
        num = self.peek_last()
        self._size -= 1
        return num

    def peek_first(self) -> int:
        """访问队首元素"""
        if self.is_empty():
            raise IndexError("双向队列为空")
        return self._nums[self._front]

    def peek_last(self) -> int:
        """访问队尾元素"""
        if self.is_empty():
            raise IndexError("双向队列为空")
        # 计算尾元素索引
        last = self.index(self._front + self._size - 1)
        return self._nums[last]

    def to_array(self) -> list[int]:
        """返回数组用于打印"""
        # 仅转换有效长度范围内的列表元素
        res = []
        for i in range(self._size):
            res.append(self._nums[self.index(self._front + i)])
        return res
array_deque.cpp
/* 基于环形数组实现的双向队列 */
class ArrayDeque {
  private:
    vector<int> nums; // 用于存储双向队列元素的数组
    int front;        // 队首指针,指向队首元素
    int queSize;      // 双向队列长度

  public:
    /* 构造方法 */
    ArrayDeque(int capacity) {
        nums.resize(capacity);
        front = queSize = 0;
    }

    /* 获取双向队列的容量 */
    int capacity() {
        return nums.size();
    }

    /* 获取双向队列的长度 */
    int size() {
        return queSize;
    }

    /* 判断双向队列是否为空 */
    bool isEmpty() {
        return queSize == 0;
    }

    /* 计算环形数组索引 */
    int index(int i) {
        // 通过取余操作实现数组首尾相连
        // 当 i 越过数组尾部后,回到头部
        // 当 i 越过数组头部后,回到尾部
        return (i + capacity()) % capacity();
    }

    /* 队首入队 */
    void pushFirst(int num) {
        if (queSize == capacity()) {
            cout << "双向队列已满" << endl;
            return;
        }
        // 队首指针向左移动一位
        // 通过取余操作实现 front 越过数组头部后回到尾部
        front = index(front - 1);
        // 将 num 添加至队首
        nums[front] = num;
        queSize++;
    }

    /* 队尾入队 */
    void pushLast(int num) {
        if (queSize == capacity()) {
            cout << "双向队列已满" << endl;
            return;
        }
        // 计算队尾指针,指向队尾索引 + 1
        int rear = index(front + queSize);
        // 将 num 添加至队尾
        nums[rear] = num;
        queSize++;
    }

    /* 队首出队 */
    int popFirst() {
        int num = peekFirst();
        // 队首指针向后移动一位
        front = index(front + 1);
        queSize--;
        return num;
    }

    /* 队尾出队 */
    int popLast() {
        int num = peekLast();
        queSize--;
        return num;
    }

    /* 访问队首元素 */
    int peekFirst() {
        if (isEmpty())
            throw out_of_range("双向队列为空");
        return nums[front];
    }

    /* 访问队尾元素 */
    int peekLast() {
        if (isEmpty())
            throw out_of_range("双向队列为空");
        // 计算尾元素索引
        int last = index(front + queSize - 1);
        return nums[last];
    }

    /* 返回数组用于打印 */
    vector<int> toVector() {
        // 仅转换有效长度范围内的列表元素
        vector<int> res(queSize);
        for (int i = 0, j = front; i < queSize; i++, j++) {
            res[i] = nums[index(j)];
        }
        return res;
    }
};
array_deque.java
/* 基于环形数组实现的双向队列 */
class ArrayDeque {
    private int[] nums; // 用于存储双向队列元素的数组
    private int front; // 队首指针,指向队首元素
    private int queSize; // 双向队列长度

    /* 构造方法 */
    public ArrayDeque(int capacity) {
        this.nums = new int[capacity];
        front = queSize = 0;
    }

    /* 获取双向队列的容量 */
    public int capacity() {
        return nums.length;
    }

    /* 获取双向队列的长度 */
    public int size() {
        return queSize;
    }

    /* 判断双向队列是否为空 */
    public boolean isEmpty() {
        return queSize == 0;
    }

    /* 计算环形数组索引 */
    private int index(int i) {
        // 通过取余操作实现数组首尾相连
        // 当 i 越过数组尾部后,回到头部
        // 当 i 越过数组头部后,回到尾部
        return (i + capacity()) % capacity();
    }

    /* 队首入队 */
    public void pushFirst(int num) {
        if (queSize == capacity()) {
            System.out.println("双向队列已满");
            return;
        }
        // 队首指针向左移动一位
        // 通过取余操作实现 front 越过数组头部后回到尾部
        front = index(front - 1);
        // 将 num 添加至队首
        nums[front] = num;
        queSize++;
    }

    /* 队尾入队 */
    public void pushLast(int num) {
        if (queSize == capacity()) {
            System.out.println("双向队列已满");
            return;
        }
        // 计算队尾指针,指向队尾索引 + 1
        int rear = index(front + queSize);
        // 将 num 添加至队尾
        nums[rear] = num;
        queSize++;
    }

    /* 队首出队 */
    public int popFirst() {
        int num = peekFirst();
        // 队首指针向后移动一位
        front = index(front + 1);
        queSize--;
        return num;
    }

    /* 队尾出队 */
    public int popLast() {
        int num = peekLast();
        queSize--;
        return num;
    }

    /* 访问队首元素 */
    public int peekFirst() {
        if (isEmpty())
            throw new IndexOutOfBoundsException();
        return nums[front];
    }

    /* 访问队尾元素 */
    public int peekLast() {
        if (isEmpty())
            throw new IndexOutOfBoundsException();
        // 计算尾元素索引
        int last = index(front + queSize - 1);
        return nums[last];
    }

    /* 返回数组用于打印 */
    public int[] toArray() {
        // 仅转换有效长度范围内的列表元素
        int[] res = new int[queSize];
        for (int i = 0, j = front; i < queSize; i++, j++) {
            res[i] = nums[index(j)];
        }
        return res;
    }
}
array_deque.cs
/* 基于环形数组实现的双向队列 */
class ArrayDeque {
    int[] nums;  // 用于存储双向队列元素的数组
    int front;   // 队首指针,指向队首元素
    int queSize; // 双向队列长度

    /* 构造方法 */
    public ArrayDeque(int capacity) {
        nums = new int[capacity];
        front = queSize = 0;
    }

    /* 获取双向队列的容量 */
    int Capacity() {
        return nums.Length;
    }

    /* 获取双向队列的长度 */
    public int Size() {
        return queSize;
    }

    /* 判断双向队列是否为空 */
    public bool IsEmpty() {
        return queSize == 0;
    }

    /* 计算环形数组索引 */
    int Index(int i) {
        // 通过取余操作实现数组首尾相连
        // 当 i 越过数组尾部后,回到头部
        // 当 i 越过数组头部后,回到尾部
        return (i + Capacity()) % Capacity();
    }

    /* 队首入队 */
    public void PushFirst(int num) {
        if (queSize == Capacity()) {
            Console.WriteLine("双向队列已满");
            return;
        }
        // 队首指针向左移动一位
        // 通过取余操作实现 front 越过数组头部后回到尾部
        front = Index(front - 1);
        // 将 num 添加至队首
        nums[front] = num;
        queSize++;
    }

    /* 队尾入队 */
    public void PushLast(int num) {
        if (queSize == Capacity()) {
            Console.WriteLine("双向队列已满");
            return;
        }
        // 计算队尾指针,指向队尾索引 + 1
        int rear = Index(front + queSize);
        // 将 num 添加至队尾
        nums[rear] = num;
        queSize++;
    }

    /* 队首出队 */
    public int PopFirst() {
        int num = PeekFirst();
        // 队首指针向后移动一位
        front = Index(front + 1);
        queSize--;
        return num;
    }

    /* 队尾出队 */
    public int PopLast() {
        int num = PeekLast();
        queSize--;
        return num;
    }

    /* 访问队首元素 */
    public int PeekFirst() {
        if (IsEmpty()) {
            throw new InvalidOperationException();
        }
        return nums[front];
    }

    /* 访问队尾元素 */
    public int PeekLast() {
        if (IsEmpty()) {
            throw new InvalidOperationException();
        }
        // 计算尾元素索引
        int last = Index(front + queSize - 1);
        return nums[last];
    }

    /* 返回数组用于打印 */
    public int[] ToArray() {
        // 仅转换有效长度范围内的列表元素
        int[] res = new int[queSize];
        for (int i = 0, j = front; i < queSize; i++, j++) {
            res[i] = nums[Index(j)];
        }
        return res;
    }
}
array_deque.go
/* 基于环形数组实现的双向队列 */
type arrayDeque struct {
    nums        []int // 用于存储双向队列元素的数组
    front       int   // 队首指针,指向队首元素
    queSize     int   // 双向队列长度
    queCapacity int   // 队列容量(即最大容纳元素数量)
}

/* 初始化队列 */
func newArrayDeque(queCapacity int) *arrayDeque {
    return &arrayDeque{
        nums:        make([]int, queCapacity),
        queCapacity: queCapacity,
        front:       0,
        queSize:     0,
    }
}

/* 获取双向队列的长度 */
func (q *arrayDeque) size() int {
    return q.queSize
}

/* 判断双向队列是否为空 */
func (q *arrayDeque) isEmpty() bool {
    return q.queSize == 0
}

/* 计算环形数组索引 */
func (q *arrayDeque) index(i int) int {
    // 通过取余操作实现数组首尾相连
    // 当 i 越过数组尾部后,回到头部
    // 当 i 越过数组头部后,回到尾部
    return (i + q.queCapacity) % q.queCapacity
}

/* 队首入队 */
func (q *arrayDeque) pushFirst(num int) {
    if q.queSize == q.queCapacity {
        fmt.Println("双向队列已满")
        return
    }
    // 队首指针向左移动一位
    // 通过取余操作实现 front 越过数组头部后回到尾部
    q.front = q.index(q.front - 1)
    // 将 num 添加至队首
    q.nums[q.front] = num
    q.queSize++
}

/* 队尾入队 */
func (q *arrayDeque) pushLast(num int) {
    if q.queSize == q.queCapacity {
        fmt.Println("双向队列已满")
        return
    }
    // 计算队尾指针,指向队尾索引 + 1
    rear := q.index(q.front + q.queSize)
    // 将 num 添加至队尾
    q.nums[rear] = num
    q.queSize++
}

/* 队首出队 */
func (q *arrayDeque) popFirst() any {
    num := q.peekFirst()
    // 队首指针向后移动一位
    q.front = q.index(q.front + 1)
    q.queSize--
    return num
}

/* 队尾出队 */
func (q *arrayDeque) popLast() any {
    num := q.peekLast()
    q.queSize--
    return num
}

/* 访问队首元素 */
func (q *arrayDeque) peekFirst() any {
    if q.isEmpty() {
        return nil
    }
    return q.nums[q.front]
}

/* 访问队尾元素 */
func (q *arrayDeque) peekLast() any {
    if q.isEmpty() {
        return nil
    }
    // 计算尾元素索引
    last := q.index(q.front + q.queSize - 1)
    return q.nums[last]
}

/* 获取 Slice 用于打印 */
func (q *arrayDeque) toSlice() []int {
    // 仅转换有效长度范围内的列表元素
    res := make([]int, q.queSize)
    for i, j := 0, q.front; i < q.queSize; i++ {
        res[i] = q.nums[q.index(j)]
        j++
    }
    return res
}
array_deque.swift
/* 基于环形数组实现的双向队列 */
class ArrayDeque {
    private var nums: [Int] // 用于存储双向队列元素的数组
    private var front: Int // 队首指针,指向队首元素
    private var _size: Int // 双向队列长度

    /* 构造方法 */
    init(capacity: Int) {
        nums = Array(repeating: 0, count: capacity)
        front = 0
        _size = 0
    }

    /* 获取双向队列的容量 */
    func capacity() -> Int {
        nums.count
    }

    /* 获取双向队列的长度 */
    func size() -> Int {
        _size
    }

    /* 判断双向队列是否为空 */
    func isEmpty() -> Bool {
        size() == 0
    }

    /* 计算环形数组索引 */
    private func index(i: Int) -> Int {
        // 通过取余操作实现数组首尾相连
        // 当 i 越过数组尾部后,回到头部
        // 当 i 越过数组头部后,回到尾部
        (i + capacity()) % capacity()
    }

    /* 队首入队 */
    func pushFirst(num: Int) {
        if size() == capacity() {
            print("双向队列已满")
            return
        }
        // 队首指针向左移动一位
        // 通过取余操作实现 front 越过数组头部后回到尾部
        front = index(i: front - 1)
        // 将 num 添加至队首
        nums[front] = num
        _size += 1
    }

    /* 队尾入队 */
    func pushLast(num: Int) {
        if size() == capacity() {
            print("双向队列已满")
            return
        }
        // 计算队尾指针,指向队尾索引 + 1
        let rear = index(i: front + size())
        // 将 num 添加至队尾
        nums[rear] = num
        _size += 1
    }

    /* 队首出队 */
    func popFirst() -> Int {
        let num = peekFirst()
        // 队首指针向后移动一位
        front = index(i: front + 1)
        _size -= 1
        return num
    }

    /* 队尾出队 */
    func popLast() -> Int {
        let num = peekLast()
        _size -= 1
        return num
    }

    /* 访问队首元素 */
    func peekFirst() -> Int {
        if isEmpty() {
            fatalError("双向队列为空")
        }
        return nums[front]
    }

    /* 访问队尾元素 */
    func peekLast() -> Int {
        if isEmpty() {
            fatalError("双向队列为空")
        }
        // 计算尾元素索引
        let last = index(i: front + size() - 1)
        return nums[last]
    }

    /* 返回数组用于打印 */
    func toArray() -> [Int] {
        // 仅转换有效长度范围内的列表元素
        (front ..< front + size()).map { nums[index(i: $0)] }
    }
}
array_deque.js
/* 基于环形数组实现的双向队列 */
class ArrayDeque {
    #nums; // 用于存储双向队列元素的数组
    #front; // 队首指针,指向队首元素
    #queSize; // 双向队列长度

    /* 构造方法 */
    constructor(capacity) {
        this.#nums = new Array(capacity);
        this.#front = 0;
        this.#queSize = 0;
    }

    /* 获取双向队列的容量 */
    capacity() {
        return this.#nums.length;
    }

    /* 获取双向队列的长度 */
    size() {
        return this.#queSize;
    }

    /* 判断双向队列是否为空 */
    isEmpty() {
        return this.#queSize === 0;
    }

    /* 计算环形数组索引 */
    index(i) {
        // 通过取余操作实现数组首尾相连
        // 当 i 越过数组尾部后,回到头部
        // 当 i 越过数组头部后,回到尾部
        return (i + this.capacity()) % this.capacity();
    }

    /* 队首入队 */
    pushFirst(num) {
        if (this.#queSize === this.capacity()) {
            console.log('双向队列已满');
            return;
        }
        // 队首指针向左移动一位
        // 通过取余操作实现 front 越过数组头部后回到尾部
        this.#front = this.index(this.#front - 1);
        // 将 num 添加至队首
        this.#nums[this.#front] = num;
        this.#queSize++;
    }

    /* 队尾入队 */
    pushLast(num) {
        if (this.#queSize === this.capacity()) {
            console.log('双向队列已满');
            return;
        }
        // 计算队尾指针,指向队尾索引 + 1
        const rear = this.index(this.#front + this.#queSize);
        // 将 num 添加至队尾
        this.#nums[rear] = num;
        this.#queSize++;
    }

    /* 队首出队 */
    popFirst() {
        const num = this.peekFirst();
        // 队首指针向后移动一位
        this.#front = this.index(this.#front + 1);
        this.#queSize--;
        return num;
    }

    /* 队尾出队 */
    popLast() {
        const num = this.peekLast();
        this.#queSize--;
        return num;
    }

    /* 访问队首元素 */
    peekFirst() {
        if (this.isEmpty()) throw new Error('The Deque Is Empty.');
        return this.#nums[this.#front];
    }

    /* 访问队尾元素 */
    peekLast() {
        if (this.isEmpty()) throw new Error('The Deque Is Empty.');
        // 计算尾元素索引
        const last = this.index(this.#front + this.#queSize - 1);
        return this.#nums[last];
    }

    /* 返回数组用于打印 */
    toArray() {
        // 仅转换有效长度范围内的列表元素
        const res = [];
        for (let i = 0, j = this.#front; i < this.#queSize; i++, j++) {
            res[i] = this.#nums[this.index(j)];
        }
        return res;
    }
}
array_deque.ts
/* 基于环形数组实现的双向队列 */
class ArrayDeque {
    private nums: number[]; // 用于存储双向队列元素的数组
    private front: number; // 队首指针,指向队首元素
    private queSize: number; // 双向队列长度

    /* 构造方法 */
    constructor(capacity: number) {
        this.nums = new Array(capacity);
        this.front = 0;
        this.queSize = 0;
    }

    /* 获取双向队列的容量 */
    capacity(): number {
        return this.nums.length;
    }

    /* 获取双向队列的长度 */
    size(): number {
        return this.queSize;
    }

    /* 判断双向队列是否为空 */
    isEmpty(): boolean {
        return this.queSize === 0;
    }

    /* 计算环形数组索引 */
    index(i: number): number {
        // 通过取余操作实现数组首尾相连
        // 当 i 越过数组尾部后,回到头部
        // 当 i 越过数组头部后,回到尾部
        return (i + this.capacity()) % this.capacity();
    }

    /* 队首入队 */
    pushFirst(num: number): void {
        if (this.queSize === this.capacity()) {
            console.log('双向队列已满');
            return;
        }
        // 队首指针向左移动一位
        // 通过取余操作实现 front 越过数组头部后回到尾部
        this.front = this.index(this.front - 1);
        // 将 num 添加至队首
        this.nums[this.front] = num;
        this.queSize++;
    }

    /* 队尾入队 */
    pushLast(num: number): void {
        if (this.queSize === this.capacity()) {
            console.log('双向队列已满');
            return;
        }
        // 计算队尾指针,指向队尾索引 + 1
        const rear: number = this.index(this.front + this.queSize);
        // 将 num 添加至队尾
        this.nums[rear] = num;
        this.queSize++;
    }

    /* 队首出队 */
    popFirst(): number {
        const num: number = this.peekFirst();
        // 队首指针向后移动一位
        this.front = this.index(this.front + 1);
        this.queSize--;
        return num;
    }

    /* 队尾出队 */
    popLast(): number {
        const num: number = this.peekLast();
        this.queSize--;
        return num;
    }

    /* 访问队首元素 */
    peekFirst(): number {
        if (this.isEmpty()) throw new Error('The Deque Is Empty.');
        return this.nums[this.front];
    }

    /* 访问队尾元素 */
    peekLast(): number {
        if (this.isEmpty()) throw new Error('The Deque Is Empty.');
        // 计算尾元素索引
        const last = this.index(this.front + this.queSize - 1);
        return this.nums[last];
    }

    /* 返回数组用于打印 */
    toArray(): number[] {
        // 仅转换有效长度范围内的列表元素
        const res: number[] = [];
        for (let i = 0, j = this.front; i < this.queSize; i++, j++) {
            res[i] = this.nums[this.index(j)];
        }
        return res;
    }
}
array_deque.dart
/* 基于环形数组实现的双向队列 */
class ArrayDeque {
  late List<int> _nums; // 用于存储双向队列元素的数组
  late int _front; // 队首指针,指向队首元素
  late int _queSize; // 双向队列长度

  /* 构造方法 */
  ArrayDeque(int capacity) {
    this._nums = List.filled(capacity, 0);
    this._front = this._queSize = 0;
  }

  /* 获取双向队列的容量 */
  int capacity() {
    return _nums.length;
  }

  /* 获取双向队列的长度 */
  int size() {
    return _queSize;
  }

  /* 判断双向队列是否为空 */
  bool isEmpty() {
    return _queSize == 0;
  }

  /* 计算环形数组索引 */
  int index(int i) {
    // 通过取余操作实现数组首尾相连
    // 当 i 越过数组尾部后,回到头部
    // 当 i 越过数组头部后,回到尾部
    return (i + capacity()) % capacity();
  }

  /* 队首入队 */
  void pushFirst(int _num) {
    if (_queSize == capacity()) {
      throw Exception("双向队列已满");
    }
    // 队首指针向左移动一位
    // 通过取余操作实现 _front 越过数组头部后回到尾部
    _front = index(_front - 1);
    // 将 _num 添加至队首
    _nums[_front] = _num;
    _queSize++;
  }

  /* 队尾入队 */
  void pushLast(int _num) {
    if (_queSize == capacity()) {
      throw Exception("双向队列已满");
    }
    // 计算队尾指针,指向队尾索引 + 1
    int rear = index(_front + _queSize);
    // 将 _num 添加至队尾
    _nums[rear] = _num;
    _queSize++;
  }

  /* 队首出队 */
  int popFirst() {
    int _num = peekFirst();
    // 队首指针向右移动一位
    _front = index(_front + 1);
    _queSize--;
    return _num;
  }

  /* 队尾出队 */
  int popLast() {
    int _num = peekLast();
    _queSize--;
    return _num;
  }

  /* 访问队首元素 */
  int peekFirst() {
    if (isEmpty()) {
      throw Exception("双向队列为空");
    }
    return _nums[_front];
  }

  /* 访问队尾元素 */
  int peekLast() {
    if (isEmpty()) {
      throw Exception("双向队列为空");
    }
    // 计算尾元素索引
    int last = index(_front + _queSize - 1);
    return _nums[last];
  }

  /* 返回数组用于打印 */
  List<int> toArray() {
    // 仅转换有效长度范围内的列表元素
    List<int> res = List.filled(_queSize, 0);
    for (int i = 0, j = _front; i < _queSize; i++, j++) {
      res[i] = _nums[index(j)];
    }
    return res;
  }
}
array_deque.rs
/* 基于环形数组实现的双向队列 */
struct ArrayDeque {
    nums: Vec<i32>,  // 用于存储双向队列元素的数组
    front: usize,    // 队首指针,指向队首元素
    que_size: usize, // 双向队列长度
}

impl ArrayDeque {
    /* 构造方法 */
    pub fn new(capacity: usize) -> Self {
        Self {
            nums: vec![0; capacity],
            front: 0,
            que_size: 0,
        }
    }

    /* 获取双向队列的容量 */
    pub fn capacity(&self) -> usize {
        self.nums.len()
    }

    /* 获取双向队列的长度 */
    pub fn size(&self) -> usize {
        self.que_size
    }

    /* 判断双向队列是否为空 */
    pub fn is_empty(&self) -> bool {
        self.que_size == 0
    }

    /* 计算环形数组索引 */
    fn index(&self, i: i32) -> usize {
        // 通过取余操作实现数组首尾相连
        // 当 i 越过数组尾部后,回到头部
        // 当 i 越过数组头部后,回到尾部
        return ((i + self.capacity() as i32) % self.capacity() as i32) as usize;
    }

    /* 队首入队 */
    pub fn push_first(&mut self, num: i32) {
        if self.que_size == self.capacity() {
            println!("双向队列已满");
            return;
        }
        // 队首指针向左移动一位
        // 通过取余操作实现 front 越过数组头部后回到尾部
        self.front = self.index(self.front as i32 - 1);
        // 将 num 添加至队首
        self.nums[self.front] = num;
        self.que_size += 1;
    }

    /* 队尾入队 */
    pub fn push_last(&mut self, num: i32) {
        if self.que_size == self.capacity() {
            println!("双向队列已满");
            return;
        }
        // 计算队尾指针,指向队尾索引 + 1
        let rear = self.index(self.front as i32 + self.que_size as i32);
        // 将 num 添加至队尾
        self.nums[rear] = num;
        self.que_size += 1;
    }

    /* 队首出队 */
    fn pop_first(&mut self) -> i32 {
        let num = self.peek_first();
        // 队首指针向后移动一位
        self.front = self.index(self.front as i32 + 1);
        self.que_size -= 1;
        num
    }

    /* 队尾出队 */
    fn pop_last(&mut self) -> i32 {
        let num = self.peek_last();
        self.que_size -= 1;
        num
    }

    /* 访问队首元素 */
    fn peek_first(&self) -> i32 {
        if self.is_empty() {
            panic!("双向队列为空")
        };
        self.nums[self.front]
    }

    /* 访问队尾元素 */
    fn peek_last(&self) -> i32 {
        if self.is_empty() {
            panic!("双向队列为空")
        };
        // 计算尾元素索引
        let last = self.index(self.front as i32 + self.que_size as i32 - 1);
        self.nums[last]
    }

    /* 返回数组用于打印 */
    fn to_array(&self) -> Vec<i32> {
        // 仅转换有效长度范围内的列表元素
        let mut res = vec![0; self.que_size];
        let mut j = self.front;
        for i in 0..self.que_size {
            res[i] = self.nums[self.index(j as i32)];
            j += 1;
        }
        res
    }
}
array_deque.c
/* 基于环形数组实现的双向队列 */
typedef struct {
    int *nums;       // 用于存储队列元素的数组
    int front;       // 队首指针,指向队首元素
    int queSize;     // 尾指针,指向队尾 + 1
    int queCapacity; // 队列容量
} ArrayDeque;

/* 构造函数 */
ArrayDeque *newArrayDeque(int capacity) {
    ArrayDeque *deque = (ArrayDeque *)malloc(sizeof(ArrayDeque));
    // 初始化数组
    deque->queCapacity = capacity;
    deque->nums = (int *)malloc(sizeof(int) * deque->queCapacity);
    deque->front = deque->queSize = 0;
    return deque;
}

/* 析构函数 */
void delArrayDeque(ArrayDeque *deque) {
    free(deque->nums);
    free(deque);
}

/* 获取双向队列的容量 */
int capacity(ArrayDeque *deque) {
    return deque->queCapacity;
}

/* 获取双向队列的长度 */
int size(ArrayDeque *deque) {
    return deque->queSize;
}

/* 判断双向队列是否为空 */
bool empty(ArrayDeque *deque) {
    return deque->queSize == 0;
}

/* 计算环形数组索引 */
int dequeIndex(ArrayDeque *deque, int i) {
    // 通过取余操作实现数组首尾相连
    // 当 i 越过数组尾部时,回到头部
    // 当 i 越过数组头部后,回到尾部
    return ((i + capacity(deque)) % capacity(deque));
}

/* 队首入队 */
void pushFirst(ArrayDeque *deque, int num) {
    if (deque->queSize == capacity(deque)) {
        printf("双向队列已满\r\n");
        return;
    }
    // 队首指针向左移动一位
    // 通过取余操作实现 front 越过数组头部回到尾部
    deque->front = dequeIndex(deque, deque->front - 1);
    // 将 num 添加到队首
    deque->nums[deque->front] = num;
    deque->queSize++;
}

/* 队尾入队 */
void pushLast(ArrayDeque *deque, int num) {
    if (deque->queSize == capacity(deque)) {
        printf("双向队列已满\r\n");
        return;
    }
    // 计算队尾指针,指向队尾索引 + 1
    int rear = dequeIndex(deque, deque->front + deque->queSize);
    // 将 num 添加至队尾
    deque->nums[rear] = num;
    deque->queSize++;
}

/* 访问队首元素 */
int peekFirst(ArrayDeque *deque) {
    // 访问异常:双向队列为空
    assert(empty(deque) == 0);
    return deque->nums[deque->front];
}

/* 访问队尾元素 */
int peekLast(ArrayDeque *deque) {
    // 访问异常:双向队列为空
    assert(empty(deque) == 0);
    int last = dequeIndex(deque, deque->front + deque->queSize - 1);
    return deque->nums[last];
}

/* 队首出队 */
int popFirst(ArrayDeque *deque) {
    int num = peekFirst(deque);
    // 队首指针向后移动一位
    deque->front = dequeIndex(deque, deque->front + 1);
    deque->queSize--;
    return num;
}

/* 队尾出队 */
int popLast(ArrayDeque *deque) {
    int num = peekLast(deque);
    deque->queSize--;
    return num;
}
array_deque.kt
/* 构造方法 */
class ArrayDeque(capacity: Int) {
    private var nums: IntArray = IntArray(capacity) // 用于存储双向队列元素的数组
    private var front: Int = 0 // 队首指针,指向队首元素
    private var queSize: Int = 0 // 双向队列长度

    /* 获取双向队列的容量 */
    fun capacity(): Int {
        return nums.size
    }

    /* 获取双向队列的长度 */
    fun size(): Int {
        return queSize
    }

    /* 判断双向队列是否为空 */
    fun isEmpty(): Boolean {
        return queSize == 0
    }

    /* 计算环形数组索引 */
    private fun index(i: Int): Int {
        // 通过取余操作实现数组首尾相连
        // 当 i 越过数组尾部后,回到头部
        // 当 i 越过数组头部后,回到尾部
        return (i + capacity()) % capacity()
    }

    /* 队首入队 */
    fun pushFirst(num: Int) {
        if (queSize == capacity()) {
            println("双向队列已满")
            return
        }
        // 队首指针向左移动一位
        // 通过取余操作实现 front 越过数组头部后回到尾部
        front = index(front - 1)
        // 将 num 添加至队首
        nums[front] = num
        queSize++
    }

    /* 队尾入队 */
    fun pushLast(num: Int) {
        if (queSize == capacity()) {
            println("双向队列已满")
            return
        }
        // 计算队尾指针,指向队尾索引 + 1
        val rear = index(front + queSize)
        // 将 num 添加至队尾
        nums[rear] = num
        queSize++
    }

    /* 队首出队 */
    fun popFirst(): Int {
        val num = peekFirst()
        // 队首指针向后移动一位
        front = index(front + 1)
        queSize--
        return num
    }

    /* 队尾出队 */
    fun popLast(): Int {
        val num = peekLast()
        queSize--
        return num
    }

    /* 访问队首元素 */
    fun peekFirst(): Int {
        if (isEmpty()) throw IndexOutOfBoundsException()
        return nums[front]
    }

    /* 访问队尾元素 */
    fun peekLast(): Int {
        if (isEmpty()) throw IndexOutOfBoundsException()
        // 计算尾元素索引
        val last = index(front + queSize - 1)
        return nums[last]
    }

    /* 返回数组用于打印 */
    fun toArray(): IntArray {
        // 仅转换有效长度范围内的列表元素
        val res = IntArray(queSize)
        var i = 0
        var j = front
        while (i < queSize) {
            res[i] = nums[index(j)]
            i++
            j++
        }
        return res
    }
}
array_deque.rb
### 基于环形数组实现的双向队列 ###
class ArrayDeque
  ### 获取双向队列的长度 ###
  attr_reader :size

  ### 构造方法 ###
  def initialize(capacity)
    @nums = Array.new(capacity, 0)
    @front = 0
    @size = 0
  end

  ### 获取双向队列的容量 ###
  def capacity
    @nums.length
  end

  ### 判断双向队列是否为空 ###
  def is_empty?
    size.zero?
  end

  ### 队首入队 ###
  def push_first(num)
    if size == capacity
      puts '双向队列已满'
      return
    end

    # 队首指针向左移动一位
    # 通过取余操作实现 front 越过数组头部后回到尾部
    @front = index(@front - 1)
    # 将 num 添加至队首
    @nums[@front] = num
    @size += 1
  end

  ### 队尾入队 ###
  def push_last(num)
    if size == capacity
      puts '双向队列已满'
      return
    end

    # 计算队尾指针,指向队尾索引 + 1
    rear = index(@front + size)
    # 将 num 添加至队尾
    @nums[rear] = num
    @size += 1
  end

  ### 队首出队 ###
  def pop_first
    num = peek_first
    # 队首指针向后移动一位
    @front = index(@front + 1)
    @size -= 1
    num
  end

  ### 队尾出队 ###
  def pop_last
    num = peek_last
    @size -= 1
    num
  end

  ### 访问队首元素 ###
  def peek_first
    raise IndexError, '双向队列为空' if is_empty?

    @nums[@front]
  end

  ### 访问队尾元素 ###
  def peek_last
    raise IndexError, '双向队列为空' if is_empty?

    # 计算尾元素索引
    last = index(@front + size - 1)
    @nums[last]
  end

  ### 返回数组用于打印 ###
  def to_array
    # 仅转换有效长度范围内的列表元素
    res = []
    for i in 0...size
      res << @nums[index(@front + i)]
    end
    res
  end

  private

  ### 计算环形数组索引 ###
  def index(i)
    # 通过取余操作实现数组首尾相连
    # 当 i 越过数组尾部后,回到头部
    # 当 i 越过数组头部后,回到尾部
    (i + capacity) % capacity
  end
end
array_deque.zig
[class]{ArrayDeque}-[func]{}

5.3.3   Applications of double-ended queue

The double-ended queue combines the logic of both stacks and queues, thus, it can implement all their respective use cases while offering greater flexibility.

We know that software's "undo" feature is typically implemented using a stack: the system pushes each change operation onto the stack and then pops to implement undoing. However, considering the limitations of system resources, software often restricts the number of undo steps (for example, only allowing the last 50 steps). When the stack length exceeds 50, the software needs to perform a deletion operation at the bottom of the stack (the front of the queue). But a regular stack cannot perform this function, where a double-ended queue becomes necessary. Note that the core logic of "undo" still follows the Last-In-First-Out principle of a stack, but a double-ended queue can more flexibly implement some additional logic.

Feel free to drop your insights, questions or suggestions