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# 5.3   Double-Ended Queue
# 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](deque.assets/deque_operations.png){ class="animation-figure" }
![Operations in double-ended queue](deque.assets/deque_operations.png){ class="animation-figure" }
<p align="center"> Figure 5-7 &nbsp; Operations in Double-Ended Queue </p>
<p align="center"> Figure 5-7 &nbsp; Operations in double-ended queue </p>
## 5.3.1 &nbsp; Common Operations in Double-Ended Queue
## 5.3.1 &nbsp; 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.
<p align="center"> Table 5-3 &nbsp; Efficiency of Double-Ended Queue Operations </p>
<p align="center"> Table 5-3 &nbsp; Efficiency of double-ended queue operations </p>
<div class="center-table" markdown>
@@ -350,11 +350,11 @@ Similarly, we can directly use the double-ended queue classes implemented in pro
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## 5.3.2 &nbsp; Implementing a Double-Ended Queue *
## 5.3.2 &nbsp; 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. &nbsp; Implementation Based on Doubly Linked List
### 1. &nbsp; 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).
@@ -2136,7 +2136,7 @@ The implementation code is as follows:
}
```
### 2. &nbsp; Implementation Based on Array
### 2. &nbsp; 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.
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[class]{ArrayDeque}-[func]{}
```
## 5.3.3 &nbsp; Applications of Double-Ended Queue
## 5.3.3 &nbsp; 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**.