hello-algo/en/docs/chapter_stack_and_queue/deque.md

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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 Figure 5-7, a double-ended queue (deque) offers more flexibility, allowing the addition or removal of elements at both the head and the tail.

{ class="animation-figure" }

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:

=== "Python"

```python title="deque.py"
from collections import deque

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

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

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

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

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

# Check if the deque is empty
is_empty: bool = len(deq) == 0
```

=== "C++"

```cpp title="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();
```

=== "Java"

```java title="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();
```

=== "C#"

```csharp title="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;
```

=== "Go"

```go title="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
```

=== "Swift"

```swift title="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
```

=== "JS"

```javascript title="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;
```

=== "TS"

```typescript title="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;
```

=== "Dart"

```dart title="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;
```

=== "Rust"

```rust title="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();
```

=== "C"

```c title="deque.c"
// C does not provide a built-in deque
```

=== "Kotlin"

```kotlin title="deque.kt"

```

=== "Zig"

```zig title="deque.zig"

```

??? pythontutor "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 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.

=== "LinkedListDeque" { class="animation-figure" }

=== "pushLast()" { class="animation-figure" }

=== "pushFirst()" { class="animation-figure" }

=== "popLast()" { class="animation-figure" }

=== "popFirst()" { class="animation-figure" }

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

The implementation code is as follows:

=== "Python"

```python title="linkedlist_deque.py"
class ListNode:
    """Double-linked list node"""

    def __init__(self, val: int):
        """Constructor"""
        self.val: int = val
        self.next: ListNode | None = None  # Reference to successor node
        self.prev: ListNode | None = None  # Reference to predecessor node

class LinkedListDeque:
    """Double-ended queue class based on double-linked list"""

    def __init__(self):
        """Constructor"""
        self._front: ListNode | None = None  # Head node front
        self._rear: ListNode | None = None  # Tail node rear
        self._size: int = 0  # Length of the double-ended queue

    def size(self) -> int:
        """Get the length of the double-ended queue"""
        return self._size

    def is_empty(self) -> bool:
        """Determine if the double-ended queue is empty"""
        return self._size == 0

    def push(self, num: int, is_front: bool):
        """Enqueue operation"""
        node = ListNode(num)
        # If the list is empty, make front and rear both point to node
        if self.is_empty():
            self._front = self._rear = node
        # Front enqueue operation
        elif is_front:
            # Add node to the head of the list
            self._front.prev = node
            node.next = self._front
            self._front = node  # Update head node
        # Rear enqueue operation
        else:
            # Add node to the tail of the list
            self._rear.next = node
            node.prev = self._rear
            self._rear = node  # Update tail node
        self._size += 1  # Update queue length

    def push_first(self, num: int):
        """Front enqueue"""
        self.push(num, True)

    def push_last(self, num: int):
        """Rear enqueue"""
        self.push(num, False)

    def pop(self, is_front: bool) -> int:
        """Dequeue operation"""
        if self.is_empty():
            raise IndexError("Double-ended queue is empty")
        # Front dequeue operation
        if is_front:
            val: int = self._front.val  # Temporarily store the head node value
            # Remove head node
            fnext: ListNode | None = self._front.next
            if fnext != None:
                fnext.prev = None
                self._front.next = None
            self._front = fnext  # Update head node
        # Rear dequeue operation
        else:
            val: int = self._rear.val  # Temporarily store the tail node value
            # Remove tail node
            rprev: ListNode | None = self._rear.prev
            if rprev != None:
                rprev.next = None
                self._rear.prev = None
            self._rear = rprev  # Update tail node
        self._size -= 1  # Update queue length
        return val

    def pop_first(self) -> int:
        """Front dequeue"""
        return self.pop(True)

    def pop_last(self) -> int:
        """Rear dequeue"""
        return self.pop(False)

    def peek_first(self) -> int:
        """Access front element"""
        if self.is_empty():
            raise IndexError("Double-ended queue is empty")
        return self._front.val

    def peek_last(self) -> int:
        """Access rear element"""
        if self.is_empty():
            raise IndexError("Double-ended queue is empty")
        return self._rear.val

    def to_array(self) -> list[int]:
        """Return array for printing"""
        node = self._front
        res = [0] * self.size()
        for i in range(self.size()):
            res[i] = node.val
            node = node.next
        return res
```

=== "C++"

```cpp title="linkedlist_deque.cpp"
/* Double-linked list node */
struct DoublyListNode {
    int val;              // Node value
    DoublyListNode *next; // Pointer to successor node
    DoublyListNode *prev; // Pointer to predecessor node
    DoublyListNode(int val) : val(val), prev(nullptr), next(nullptr) {
    }
};

/* Double-ended queue class based on double-linked list */
class LinkedListDeque {
  private:
    DoublyListNode *front, *rear; // Front node front, back node rear
    int queSize = 0;              // Length of the double-ended queue

  public:
    /* Constructor */
    LinkedListDeque() : front(nullptr), rear(nullptr) {
    }

    /* Destructor */
    ~LinkedListDeque() {
        // Traverse the linked list, remove nodes, free memory
        DoublyListNode *pre, *cur = front;
        while (cur != nullptr) {
            pre = cur;
            cur = cur->next;
            delete pre;
        }
    }

    /* Get the length of the double-ended queue */
    int size() {
        return queSize;
    }

    /* Determine if the double-ended queue is empty */
    bool isEmpty() {
        return size() == 0;
    }

    /* Enqueue operation */
    void push(int num, bool isFront) {
        DoublyListNode *node = new DoublyListNode(num);
        // If the list is empty, make front and rear both point to node
        if (isEmpty())
            front = rear = node;
        // Front enqueue operation
        else if (isFront) {
            // Add node to the head of the list
            front->prev = node;
            node->next = front;
            front = node; // Update head node
        // Rear enqueue operation
        } else {
            // Add node to the tail of the list
            rear->next = node;
            node->prev = rear;
            rear = node; // Update tail node
        }
        queSize++; // Update queue length
    }

    /* Front enqueue */
    void pushFirst(int num) {
        push(num, true);
    }

    /* Rear enqueue */
    void pushLast(int num) {
        push(num, false);
    }

    /* Dequeue operation */
    int pop(bool isFront) {
        if (isEmpty())
            throw out_of_range("Queue is empty");
        int val;
        // Front dequeue operation
        if (isFront) {
            val = front->val; // Temporarily store the head node value
            // Remove head node
            DoublyListNode *fNext = front->next;
            if (fNext != nullptr) {
                fNext->prev = nullptr;
                front->next = nullptr;
            }
            delete front;
            front = fNext; // Update head node
        // Rear dequeue operation
        } else {
            val = rear->val; // Temporarily store the tail node value
            // Remove tail node
            DoublyListNode *rPrev = rear->prev;
            if (rPrev != nullptr) {
                rPrev->next = nullptr;
                rear->prev = nullptr;
            }
            delete rear;
            rear = rPrev; // Update tail node
        }
        queSize--; // Update queue length
        return val;
    }

    /* Front dequeue */
    int popFirst() {
        return pop(true);
    }

    /* Rear dequeue */
    int popLast() {
        return pop(false);
    }

    /* Access front element */
    int peekFirst() {
        if (isEmpty())
            throw out_of_range("Double-ended queue is empty");
        return front->val;
    }

    /* Access rear element */
    int peekLast() {
        if (isEmpty())
            throw out_of_range("Double-ended queue is empty");
        return rear->val;
    }

    /* Return array for printing */
    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;
    }
};
```

=== "Java"

```java title="linkedlist_deque.java"
/* Double-linked list node */
class ListNode {
    int val; // Node value
    ListNode next; // Reference to successor node
    ListNode prev; // Reference to predecessor node

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

/* Double-ended queue class based on double-linked list */
class LinkedListDeque {
    private ListNode front, rear; // Front node front, back node rear
    private int queSize = 0; // Length of the double-ended queue

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

    /* Get the length of the double-ended queue */
    public int size() {
        return queSize;
    }

    /* Determine if the double-ended queue is empty */
    public boolean isEmpty() {
        return size() == 0;
    }

    /* Enqueue operation */
    private void push(int num, boolean isFront) {
        ListNode node = new ListNode(num);
        // If the list is empty, make front and rear both point to node
        if (isEmpty())
            front = rear = node;
        // Front enqueue operation
        else if (isFront) {
            // Add node to the head of the list
            front.prev = node;
            node.next = front;
            front = node; // Update head node
        // Rear enqueue operation
        } else {
            // Add node to the tail of the list
            rear.next = node;
            node.prev = rear;
            rear = node; // Update tail node
        }
        queSize++; // Update queue length
    }

    /* Front enqueue */
    public void pushFirst(int num) {
        push(num, true);
    }

    /* Rear enqueue */
    public void pushLast(int num) {
        push(num, false);
    }

    /* Dequeue operation */
    private int pop(boolean isFront) {
        if (isEmpty())
            throw new IndexOutOfBoundsException();
        int val;
        // Front dequeue operation
        if (isFront) {
            val = front.val; // Temporarily store the head node value
            // Remove head node
            ListNode fNext = front.next;
            if (fNext != null) {
                fNext.prev = null;
                front.next = null;
            }
            front = fNext; // Update head node
        // Rear dequeue operation
        } else {
            val = rear.val; // Temporarily store the tail node value
            // Remove tail node
            ListNode rPrev = rear.prev;
            if (rPrev != null) {
                rPrev.next = null;
                rear.prev = null;
            }
            rear = rPrev; // Update tail node
        }
        queSize--; // Update queue length
        return val;
    }

    /* Front dequeue */
    public int popFirst() {
        return pop(true);
    }

    /* Rear dequeue */
    public int popLast() {
        return pop(false);
    }

    /* Access front element */
    public int peekFirst() {
        if (isEmpty())
            throw new IndexOutOfBoundsException();
        return front.val;
    }

    /* Access rear element */
    public int peekLast() {
        if (isEmpty())
            throw new IndexOutOfBoundsException();
        return rear.val;
    }

    /* Return array for printing */
    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;
    }
}
```

=== "C#"

```csharp title="linkedlist_deque.cs"
[class]{ListNode}-[func]{}

[class]{LinkedListDeque}-[func]{}
```

=== "Go"

```go title="linkedlist_deque.go"
[class]{linkedListDeque}-[func]{}
```

=== "Swift"

```swift title="linkedlist_deque.swift"
[class]{ListNode}-[func]{}

[class]{LinkedListDeque}-[func]{}
```

=== "JS"

```javascript title="linkedlist_deque.js"
[class]{ListNode}-[func]{}

[class]{LinkedListDeque}-[func]{}
```

=== "TS"

```typescript title="linkedlist_deque.ts"
[class]{ListNode}-[func]{}

[class]{LinkedListDeque}-[func]{}
```

=== "Dart"

```dart title="linkedlist_deque.dart"
[class]{ListNode}-[func]{}

[class]{LinkedListDeque}-[func]{}
```

=== "Rust"

```rust title="linkedlist_deque.rs"
[class]{ListNode}-[func]{}

[class]{LinkedListDeque}-[func]{}
```

=== "C"

```c title="linkedlist_deque.c"
[class]{DoublyListNode}-[func]{}

[class]{LinkedListDeque}-[func]{}
```

=== "Kotlin"

```kotlin title="linkedlist_deque.kt"
[class]{ListNode}-[func]{}

[class]{LinkedListDeque}-[func]{}
```

=== "Ruby"

```ruby title="linkedlist_deque.rb"
[class]{ListNode}-[func]{}

[class]{LinkedListDeque}-[func]{}
```

=== "Zig"

```zig title="linkedlist_deque.zig"
[class]{ListNode}-[func]{}

[class]{LinkedListDeque}-[func]{}
```

2.   Implementation based on array

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

=== "ArrayDeque" { class="animation-figure" }

=== "pushLast()" { class="animation-figure" }

=== "pushFirst()" { class="animation-figure" }

=== "popLast()" { class="animation-figure" }

=== "popFirst()" { class="animation-figure" }

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":

=== "Python"

```python title="array_deque.py"
class ArrayDeque:
    """Double-ended queue class based on circular array"""

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

    def capacity(self) -> int:
        """Get the capacity of the double-ended queue"""
        return len(self._nums)

    def size(self) -> int:
        """Get the length of the double-ended queue"""
        return self._size

    def is_empty(self) -> bool:
        """Determine if the double-ended queue is empty"""
        return self._size == 0

    def index(self, i: int) -> int:
        """Calculate circular array index"""
        # Implement circular array by modulo operation
        # When i exceeds the tail of the array, return to the head
        # When i exceeds the head of the array, return to the tail
        return (i + self.capacity()) % self.capacity()

    def push_first(self, num: int):
        """Front enqueue"""
        if self._size == self.capacity():
            print("Double-ended queue is full")
            return
        # Move the front pointer one position to the left
        # Implement front crossing the head of the array to return to the tail by modulo operation
        self._front = self.index(self._front - 1)
        # Add num to the front
        self._nums[self._front] = num
        self._size += 1

    def push_last(self, num: int):
        """Rear enqueue"""
        if self._size == self.capacity():
            print("Double-ended queue is full")
            return
        # Calculate rear pointer, pointing to rear index + 1
        rear = self.index(self._front + self._size)
        # Add num to the rear
        self._nums[rear] = num
        self._size += 1

    def pop_first(self) -> int:
        """Front dequeue"""
        num = self.peek_first()
        # Move front pointer one position backward
        self._front = self.index(self._front + 1)
        self._size -= 1
        return num

    def pop_last(self) -> int:
        """Rear dequeue"""
        num = self.peek_last()
        self._size -= 1
        return num

    def peek_first(self) -> int:
        """Access front element"""
        if self.is_empty():
            raise IndexError("Double-ended queue is empty")
        return self._nums[self._front]

    def peek_last(self) -> int:
        """Access rear element"""
        if self.is_empty():
            raise IndexError("Double-ended queue is empty")
        # Calculate rear element index
        last = self.index(self._front + self._size - 1)
        return self._nums[last]

    def to_array(self) -> list[int]:
        """Return array for printing"""
        # Only convert elements within valid length range
        res = []
        for i in range(self._size):
            res.append(self._nums[self.index(self._front + i)])
        return res
```

=== "C++"

```cpp title="array_deque.cpp"
/* Double-ended queue class based on circular array */
class ArrayDeque {
  private:
    vector<int> nums; // Array used to store elements of the double-ended queue
    int front;        // Front pointer, pointing to the front element
    int queSize;      // Length of the double-ended queue

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

    /* Get the capacity of the double-ended queue */
    int capacity() {
        return nums.size();
    }

    /* Get the length of the double-ended queue */
    int size() {
        return queSize;
    }

    /* Determine if the double-ended queue is empty */
    bool isEmpty() {
        return queSize == 0;
    }

    /* Calculate circular array index */
    int index(int i) {
        // Implement circular array by modulo operation
        // When i exceeds the tail of the array, return to the head
        // When i exceeds the head of the array, return to the tail
        return (i + capacity()) % capacity();
    }

    /* Front enqueue */
    void pushFirst(int num) {
        if (queSize == capacity()) {
            cout << "Double-ended queue is full" << endl;
            return;
        }
        // Move the front pointer one position to the left
        // Implement front crossing the head of the array to return to the tail by modulo operation
        front = index(front - 1);
        // Add num to the front
        nums[front] = num;
        queSize++;
    }

    /* Rear enqueue */
    void pushLast(int num) {
        if (queSize == capacity()) {
            cout << "Double-ended queue is full" << endl;
            return;
        }
        // Calculate rear pointer, pointing to rear index + 1
        int rear = index(front + queSize);
        // Add num to the rear
        nums[rear] = num;
        queSize++;
    }

    /* Front dequeue */
    int popFirst() {
        int num = peekFirst();
        // Move front pointer one position backward
        front = index(front + 1);
        queSize--;
        return num;
    }

    /* Rear dequeue */
    int popLast() {
        int num = peekLast();
        queSize--;
        return num;
    }

    /* Access front element */
    int peekFirst() {
        if (isEmpty())
            throw out_of_range("Double-ended queue is empty");
        return nums[front];
    }

    /* Access rear element */
    int peekLast() {
        if (isEmpty())
            throw out_of_range("Double-ended queue is empty");
        // Calculate rear element index
        int last = index(front + queSize - 1);
        return nums[last];
    }

    /* Return array for printing */
    vector<int> toVector() {
        // Only convert elements within valid length range
        vector<int> res(queSize);
        for (int i = 0, j = front; i < queSize; i++, j++) {
            res[i] = nums[index(j)];
        }
        return res;
    }
};
```

=== "Java"

```java title="array_deque.java"
/* Double-ended queue class based on circular array */
class ArrayDeque {
    private int[] nums; // Array used to store elements of the double-ended queue
    private int front; // Front pointer, pointing to the front element
    private int queSize; // Length of the double-ended queue

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

    /* Get the capacity of the double-ended queue */
    public int capacity() {
        return nums.length;
    }

    /* Get the length of the double-ended queue */
    public int size() {
        return queSize;
    }

    /* Determine if the double-ended queue is empty */
    public boolean isEmpty() {
        return queSize == 0;
    }

    /* Calculate circular array index */
    private int index(int i) {
        // Implement circular array by modulo operation
        // When i exceeds the tail of the array, return to the head
        // When i exceeds the head of the array, return to the tail
        return (i + capacity()) % capacity();
    }

    /* Front enqueue */
    public void pushFirst(int num) {
        if (queSize == capacity()) {
            System.out.println("Double-ended queue is full");
            return;
        }
        // Move the front pointer one position to the left
        // Implement front crossing the head of the array to return to the tail by modulo operation
        front = index(front - 1);
        // Add num to the front
        nums[front] = num;
        queSize++;
    }

    /* Rear enqueue */
    public void pushLast(int num) {
        if (queSize == capacity()) {
            System.out.println("Double-ended queue is full");
            return;
        }
        // Calculate rear pointer, pointing to rear index + 1
        int rear = index(front + queSize);
        // Add num to the rear
        nums[rear] = num;
        queSize++;
    }

    /* Front dequeue */
    public int popFirst() {
        int num = peekFirst();
        // Move front pointer one position backward
        front = index(front + 1);
        queSize--;
        return num;
    }

    /* Rear dequeue */
    public int popLast() {
        int num = peekLast();
        queSize--;
        return num;
    }

    /* Access front element */
    public int peekFirst() {
        if (isEmpty())
            throw new IndexOutOfBoundsException();
        return nums[front];
    }

    /* Access rear element */
    public int peekLast() {
        if (isEmpty())
            throw new IndexOutOfBoundsException();
        // Calculate rear element index
        int last = index(front + queSize - 1);
        return nums[last];
    }

    /* Return array for printing */
    public int[] toArray() {
        // Only convert elements within valid length range
        int[] res = new int[queSize];
        for (int i = 0, j = front; i < queSize; i++, j++) {
            res[i] = nums[index(j)];
        }
        return res;
    }
}
```

=== "C#"

```csharp title="array_deque.cs"
[class]{ArrayDeque}-[func]{}
```

=== "Go"

```go title="array_deque.go"
[class]{arrayDeque}-[func]{}
```

=== "Swift"

```swift title="array_deque.swift"
[class]{ArrayDeque}-[func]{}
```

=== "JS"

```javascript title="array_deque.js"
[class]{ArrayDeque}-[func]{}
```

=== "TS"

```typescript title="array_deque.ts"
[class]{ArrayDeque}-[func]{}
```

=== "Dart"

```dart title="array_deque.dart"
[class]{ArrayDeque}-[func]{}
```

=== "Rust"

```rust title="array_deque.rs"
[class]{ArrayDeque}-[func]{}
```

=== "C"

```c title="array_deque.c"
[class]{ArrayDeque}-[func]{}
```

=== "Kotlin"

```kotlin title="array_deque.kt"
[class]{ArrayDeque}-[func]{}
```

=== "Ruby"

```ruby title="array_deque.rb"
[class]{ArrayDeque}-[func]{}
```

=== "Zig"

```zig title="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.