雙向佇列是一種具有佇列和堆疊兩種特性的資料結構。在雙向佇列中，我們可以從兩端（即前端和後端）插入和刪除元素。這使得雙向佇列比一般的佇列和堆疊更為靈活。

雙向佇列的特性

• 元素可以從前端和後端添加。
• 元素可以從前端和後端移除。
• 插入和刪除操作都是複雜度。

使用陣列實作雙向佇列
以下是雙向佇列的基本結構和操作：

#include <iostream>
#define SIZE 10

class Deque {
private:
    int arr[SIZE];
    int front;
    int rear;
    int size;

public:
    Deque(int size) : front(-1), rear(0), size(size) {}

    bool isFull() {
        return ((front == 0 && rear == size - 1) || front == rear + 1);
    }

    bool isEmpty() {
        return (front == -1);
    }

    void insertFront(int key) {
        if (isFull()) {
            std::cout << "Deque is full" << std::endl;
            return;
        }
        if (front == -1) {
            front = rear = 0;
        } else if (front == 0) {
            front = size - 1;
        } else {
            front = front - 1;
        }
        arr[front] = key;
    }

    void insertRear(int key) {
        if (isFull()) {
            std::cout << "Deque is full" << std::endl;
            return;
        }
        if (front == -1) {
            front = rear = 0;
        } else if (rear == size - 1) {
            rear = 0;
        } else {
            rear = rear + 1;
        }
        arr[rear] = key;
    }

    void deleteFront() {
        if (isEmpty()) {
            std::cout << "Deque is empty" << std::endl;
            return;
        }
        if (front == rear) {
            front = rear = -1;
        } else if (front == size - 1) {
            front = 0;
        } else {
            front = front + 1;
        }
    }

    void deleteRear() {
        if (isEmpty()) {
            std::cout << "Deque is empty" << std::endl;
            return;
        }
        if (front == rear) {
            front = rear = -1;
        } else if (rear == 0) {
            rear = size - 1;
        } else {
            rear = rear - 1;
        }
    }

    int getFront() {
        if (isEmpty()) {
            std::cout << "Deque is empty" << std::endl;
            return -1;
        }
        return arr[front];
    }

    int getRear() {
        if (isEmpty() || rear < 0) {
            std::cout << "Deque is empty" << std::endl;
            return -1;
        }
        return arr[rear];
    }
};

int main() {
    Deque dq(5);
    dq.insertFront(1);
    dq.insertRear(2);
    dq.insertFront(3);
    dq.insertRear(4);
    std::cout << "Front element: " << dq.getFront() << std::endl;
    std::cout << "Rear element: " << dq.getRear() << std::endl;

    return 0;
}

總結
雙向佇列是一個非常靈活的資料結構，它允許我們在佇列的兩端進行操作。這在某些算法和問題中可能非常有用，特別是當我們需要同時具有佇列和堆疊的特性時。