Algorithms 101: Introduction to Double-Ended Queue

Introduction to Double-Ended Queue (双端队列的介绍)

A Double-Ended Queue (Deque) is a versatile data structure that allows elements to be inserted and removed from both ends, unlike a standard queue, where operations are restricted to one end for insertion (enqueue) and the other for removal (dequeue). This flexibility makes deques suitable for a wide range of applications, where operations need to be performed at both ends of the data structure.

双端队列（Deque，全称为Double-Ended Queue）是一种多功能的数据结构，允许从两端插入和删除元素。与标准队列不同，标准队列的操作仅限于在一端插入（入队）和另一端删除（出队），双端队列的灵活性使其适用于需要在数据结构两端执行操作的广泛应用场景。

Key Characteristics of Deque (双端队列的关键特性):

1. Bidirectional Operations (双向操作):

   • Elements can be added to or removed from both the front and rear of the deque.
   • 元素可以从双端队列的前端和后端进行添加或删除。

2. Dynamic Size (动态大小):

   • Deques can grow and shrink dynamically, depending on the implementation, allowing them to handle varying amounts of data efficiently.
   • 双端队列可以根据实现方式动态增长和缩小，从而高效地处理不同数量的数据。

3. Flexibility (灵活性):

   • A deque can function as a regular queue, stack, or a combination of both, depending on the operations performed.
   • 双端队列可以根据执行的操作，充当常规队列、栈或两者的组合。

Operations in Deque (双端队列的操作):

1. Insertion (插入):

   • insertFront(data): Inserts an element at the front of the deque.
   • insertLast(data): Inserts an element at the rear of the deque.
   • insertFront(data): 在双端队列的前端插入一个元素。
   • insertLast(data): 在双端队列的后端插入一个元素。

2. Deletion (删除):

   • deleteFront(): Removes and returns the front element of the deque.
   • deleteLast(): Removes and returns the rear element of the deque.
   • deleteFront(): 移除并返回双端队列的前端元素。
   • deleteLast(): 移除并返回双端队列的后端元素。

3. Access (访问):

   • getFront(): Returns the front element of the deque without removing it.
   • getRear(): Returns the rear element of the deque without removing it.
   • getFront(): 返回双端队列的前端元素，但不移除它。
   • getRear(): 返回双端队列的后端元素，但不移除它。

4. Size and Capacity (大小和容量):

   • isEmpty(): Checks if the deque is empty.
   • isFull(): Checks if the deque has reached its maximum capacity.
   • isEmpty(): 检查双端队列是否为空。
   • isFull(): 检查双端队列是否达到其最大容量。

Types of Deque (双端队列的类型):

1. Input-Restricted Deque (输入受限双端队列):

   • In this type, insertion is allowed only at one end, but deletion can be performed from both ends.
   • 在这种类型中，只允许在一端插入，但可以从两端删除。

2. Output-Restricted Deque (输出受限双端队列):

   • In this type, deletion is allowed only at one end, but insertion can be performed from both ends.
   • 在这种类型中，只允许在一端删除，但可以从两端插入。

Applications of Deque (双端队列的应用):

1. Sliding Window Problems (滑动窗口问题):

   • Deques are used to efficiently find the maximum or minimum in a sliding window of elements.
   • 双端队列用于在元素的滑动窗口中高效地查找最大值或最小值。

2. Palindrome Checking (回文检查):

   • Deques can be used to check if a sequence of characters is a palindrome by comparing elements from both ends.
   • 双端队列可以通过比较两端的元素来检查字符序列是否为回文。

3. Expression Parsing (表达式解析):

   • Deques help in evaluating expressions where operators and operands need to be processed from both ends.
   • 双端队列有助于解析表达式，其中操作符和操作数需要从两端处理。

4. Task Scheduling (任务调度):

   • Deques can be used to manage tasks that need to be processed in both FIFO (First-In, First-Out) and LIFO (Last-In, First-Out) order.
   • 双端队列可以用来管理需要按FIFO（先进先出）和LIFO（后进先出）顺序处理的任务。

Summary (总结):

A deque is a highly flexible and efficient data structure that combines the properties of both stacks and queues. Its ability to perform operations from both ends makes it particularly useful in scenarios where such flexibility is required.

双端队列是一种高度灵活和高效的数据结构，它结合了栈和队列的特性。它能够从两端执行操作，使其在需要这种灵活性的场景中尤为有用。