translation: Update chapter_stack_and_queue/deque.md (#1068)

* Update deque.md

* Update deque.md

* Update deque.md

docs-en/chapter_stack_and_queue/deque.md

@@ -1,23 +1,23 @@
 # Double-Ended Queue
 
-In a regular queue, we can only delete elements from the head or add elements to the tail. As shown in the figure below, a "double-ended queue (deque)" offers more flexibility, allowing the addition or removal of elements at both the head and the tail.
+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)
 
 ## Common Operations in Double-Ended Queue
 
-The common operations in a double-ended queue are listed below, and the specific method names depend on the programming language used.
+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 <id> &nbsp; Efficiency of Double-Ended Queue Operations </p>
 
 | Method Name   | Description                 | Time Complexity |
 | ------------- | --------------------------- | --------------- |
-| `pushFirst()` | Add an element to the front | $O(1)$          |
+| `pushFirst()` | Add an element to the head | $O(1)$          |
-| `pushLast()`  | Add an element to the rear  | $O(1)$          |
+| `pushLast()`  | Add an element to the tail  | $O(1)$          |
-| `popFirst()`  | Remove the front element    | $O(1)$          |
+| `popFirst()`  | Remove the first element    | $O(1)$          |
-| `popLast()`   | Remove the rear element     | $O(1)$          |
+| `popLast()`   | Remove the last element     | $O(1)$          |
-| `peekFirst()` | Access the front element    | $O(1)$          |
+| `peekFirst()` | Access the first element    | $O(1)$          |
-| `peekLast()`  | Access the rear element     | $O(1)$          |
+| `peekLast()`  | Access the last element     | $O(1)$          |
 
 Similarly, we can directly use the double-ended queue classes implemented in programming languages:
 
@@ -30,19 +30,19 @@ Similarly, we can directly use the double-ended queue classes implemented in pro
     deque: deque[int] = deque()
 
     # Enqueue elements
-    deque.append(2)      # Add to the rear
+    deque.append(2)      # Add to the tail
     deque.append(5)
     deque.append(4)
-    deque.appendleft(3)  # Add to the front
+    deque.appendleft(3)  # Add to the head
     deque.appendleft(1)
 
     # Access elements
-    front: int = deque[0]  # Front element
+    front: int = deque[0]  # The first element
-    rear: int = deque[-1]  # Rear element
+    rear: int = deque[-1]  # The last element
 
     # Dequeue elements
-    pop_front: int = deque.popleft()  # Front element dequeued
+    pop_front: int = deque.popleft()  # The first element dequeued
-    pop_rear: int = deque.pop()       # Rear element dequeued
+    pop_rear: int = deque.pop()       # The last element dequeued
 
     # Get the length of the deque
     size: int = len(deque)
@@ -58,19 +58,19 @@ Similarly, we can directly use the double-ended queue classes implemented in pro
     deque<int> deque;
 
     /* Enqueue elements */
-    deque.push_back(2);   // Add to the rear
+    deque.push_back(2);   // Add to the tail
     deque.push_back(5);
     deque.push_back(4);
-    deque.push_front(3);  // Add to the front
+    deque.push_front(3);  // Add to the head
     deque.push_front(1);
 
     /* Access elements */
-    int front = deque.front(); // Front element
+    int front = deque.front(); // The first element
-    int back = deque.back();   // Rear element
+    int back = deque.back();   // The last element
 
     /* Dequeue elements */
-    deque.pop_front();  // Front element dequeued
+    deque.pop_front();  // The first element dequeued
-    deque.pop_back();   // Rear element dequeued
+    deque.pop_back();   // The last element dequeued
 
     /* Get the length of the deque */
     int size = deque.size();
@@ -86,19 +86,19 @@ Similarly, we can directly use the double-ended queue classes implemented in pro
     Deque<Integer> deque = new LinkedList<>();
 
     /* Enqueue elements */
-    deque.offerLast(2);   // Add to the rear
+    deque.offerLast(2);   // Add to the tail
     deque.offerLast(5);
     deque.offerLast(4);
-    deque.offerFirst(3);  // Add to the front
+    deque.offerFirst(3);  // Add to the head
     deque.offerFirst(1);
 
     /* Access elements */
-    int peekFirst = deque.peekFirst();  // Front element
+    int peekFirst = deque.peekFirst();  // The first element
-    int peekLast = deque.peekLast();    // Rear element
+    int peekLast = deque.peekLast();    // The last element
 
     /* Dequeue elements */
-    int popFirst = deque.pollFirst();  // Front element dequeued
+    int popFirst = deque.pollFirst();  // The first element dequeued
-    int popLast = deque.pollLast();    // Rear element dequeued
+    int popLast = deque.pollLast();    // The last element dequeued
 
     /* Get the length of the deque */
     int size = deque.size();
@@ -115,19 +115,19 @@ Similarly, we can directly use the double-ended queue classes implemented in pro
     LinkedList<int> deque = new();
 
     /* Enqueue elements */
-    deque.AddLast(2);   // Add to the rear
+    deque.AddLast(2);   // Add to the tail
     deque.AddLast(5);
     deque.AddLast(4);
-    deque.AddFirst(3);  // Add to the front
+    deque.AddFirst(3);  // Add to the head
     deque.AddFirst(1);
 
     /* Access elements */
-    int peekFirst = deque.First.Value;  // Front element
+    int peekFirst = deque.First.Value;  // The first element
-    int peekLast = deque.Last.Value;    // Rear element
+    int peekLast = deque.Last.Value;    // The last element
 
     /* Dequeue elements */
-    deque.RemoveFirst();  // Front element dequeued
+    deque.RemoveFirst();  // The first element dequeued
-    deque.RemoveLast();   // Rear element dequeued
+    deque.RemoveLast();   // The last element dequeued
 
     /* Get the length of the deque */
     int size = deque.Count;
@@ -144,19 +144,19 @@ Similarly, we can directly use the double-ended queue classes implemented in pro
     deque := list.New()
 
     /* Enqueue elements */
-    deque.PushBack(2)      // Add to the rear
+    deque.PushBack(2)      // Add to the tail
     deque.PushBack(5)
     deque.PushBack(4)
-    deque.PushFront(3)     // Add to the front
+    deque.PushFront(3)     // Add to the head
     deque.PushFront(1)
 
     /* Access elements */
-    front := deque.Front() // Front element
+    front := deque.Front() // The first element
-    rear := deque.Back()   // Rear element
+    rear := deque.Back()   // The last element
 
     /* Dequeue elements */
-    deque.Remove(front)    // Front element dequeued
+    deque.Remove(front)    // The first element dequeued
-    deque.Remove(rear)     // Rear element dequeued
+    deque.Remove(rear)     // The last element dequeued
 
     /* Get the length of the deque */
     size := deque.Len()
@@ -173,20 +173,20 @@ Similarly, we can directly use the double-ended queue classes implemented in pro
     var deque: [Int] = []
 
     /* Enqueue elements */
-    deque.append(2) // Add to the rear
+    deque.append(2) // Add to the tail
     deque.append(5)
     deque.append(4)
-    deque.insert(3, at: 0) // Add to the front
+    deque.insert(3, at: 0) // Add to the head
     deque.insert(1, at: 0)
 
     /* Access elements */
-    let peekFirst = deque.first! // Front element
+    let peekFirst = deque.first! // The first element
-    let peekLast = deque.last!   // Rear element
+    let peekLast = deque.last!   // The last element
 
     /* Dequeue elements */
     // Using Array, popFirst has a complexity of O(n)
-    let popFirst = deque.removeFirst() // Front element dequeued
+    let popFirst = deque.removeFirst() // The first element dequeued
-    let popLast = deque.removeLast()   // Rear element dequeued
+    let popLast = deque.removeLast()   // The last element dequeued
 
     /* Get the length of the deque */
     let size = deque.count
@@ -211,13 +211,13 @@ Similarly, we can directly use the double-ended queue classes implemented in pro
     deque.unshift(1);
 
     /* Access elements */
-    const peekFirst = deque[0]; // Front element
+    const peekFirst = deque[0]; // The first element
-    const peekLast = deque[deque.length - 1]; // Rear 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(); // Front element dequeued
+    const popFront = deque.shift(); // The first element dequeued
-    const popBack = deque.pop();    // Rear element dequeued
+    const popBack = deque.pop();    // The last element dequeued
 
     /* Get the length of the deque */
     const size = deque.length;
@@ -242,13 +242,13 @@ Similarly, we can directly use the double-ended queue classes implemented in pro
     deque.unshift(1);
 
     /* Access elements */
-    const peekFirst: number = deque[0]; // Front element
+    const peekFirst: number = deque[0]; // The first element
-    const peekLast: number = deque[deque.length - 1]; // Rear 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; // Front element dequeued
+    const popFront: number = deque.shift() as number; // The first element dequeued
-    const popBack: number = deque.pop() as number;    // Rear element dequeued
+    const popBack: number = deque.pop() as number;    // The last element dequeued
 
     /* Get the length of the deque */
     const size: number = deque.length;
@@ -265,19 +265,19 @@ Similarly, we can directly use the double-ended queue classes implemented in pro
     Queue<int> deque = Queue<int>();
 
     /* Enqueue elements */
-    deque.addLast(2);  // Add to the rear
+    deque.addLast(2);  // Add to the tail
     deque.addLast(5);
     deque.addLast(4);
-    deque.addFirst(3); // Add to the front
+    deque.addFirst(3); // Add to the head
     deque.addFirst(1);
 
     /* Access elements */
-    int peekFirst = deque.first; // Front element
+    int peekFirst = deque.first; // The first element
-    int peekLast = deque.last;   // Rear element
+    int peekLast = deque.last;   // The last element
 
     /* Dequeue elements */
-    int popFirst = deque.removeFirst(); // Front element dequeued
+    int popFirst = deque.removeFirst(); // The first element dequeued
-    int popLast = deque.removeLast();   // Rear element dequeued
+    int popLast = deque.removeLast();   // The last element dequeued
 
     /* Get the length of the deque */
     int size = deque.length;
@@ -293,22 +293,22 @@ Similarly, we can directly use the double-ended queue classes implemented in pro
     let mut deque: VecDeque<u32> = VecDeque::new();
 
     /* Enqueue elements */
-    deque.push_back(2);  // Add to the rear
+    deque.push_back(2);  // Add to the tail
     deque.push_back(5);
     deque.push_back(4);
-    deque.push_front(3); // Add to the front
+    deque.push_front(3); // Add to the head
     deque.push_front(1);
 
     /* Access elements */
-    if let Some(front) = deque.front() { // Front element
+    if let Some(front) = deque.front() { // The first element
     }
-    if let Some(rear) = deque.back() {   // Rear element
+    if let Some(rear) = deque.back() {   // The last element
     }
 
     /* Dequeue elements */
-    if let Some(pop_front) = deque.pop_front() { // Front element dequeued
+    if let Some(pop_front) = deque.pop_front() { // The first element dequeued
     }
-    if let Some(pop_rear) = deque.pop_back() {   // Rear element dequeued
+    if let Some(pop_rear) = deque.pop_back() {   // The last element dequeued
     }
 
     /* Get the length of the deque */
@@ -330,19 +330,19 @@ Similarly, we can directly use the double-ended queue classes implemented in pro
 
     ```
 
-??? pythontutor "Code Visualization"
+??? pythontutor "Visualizing Code"
 
     https://pythontutor.com/render.html#code=from%20collections%20import%20deque%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%0A%20%20%20%20deq%20%3D%20deque%28%29%0A%0A%20%20%20%20%23%20%E5%85%83%E7%B4%A0%E5%85%A5%E9%98%9F%0A%20%20%20%20deq.append%282%29%20%20%23%20%E6%B7%BB%E5%8A%A0%E8%87%B3%E9%98%9F%E5%B0%BE%0A%20%20%20%20deq.append%285%29%0A%20%20%20%20deq.append%284%29%0A%20%20%20%20deq.appendleft%283%29%20%20%23%20%E6%B7%BB%E5%8A%A0%E8%87%B3%E9%98%9F%E9%A6%96%0A%20%20%20%20deq.appendleft%281%29%0A%20%20%20%20print%28%22%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%20deque%20%3D%22,%20deq%29%0A%0A%20%20%20%20%23%20%E8%AE%BF%E9%97%AE%E5%85%83%E7%B4%A0%0A%20%20%20%20front%20%3D%20deq%5B0%5D%20%20%23%20%E9%98%9F%E9%A6%96%E5%85%83%E7%B4%A0%0A%20%20%20%20print%28%22%E9%98%9F%E9%A6%96%E5%85%83%E7%B4%A0%20front%20%3D%22,%20front%29%0A%20%20%20%20rear%20%3D%20deq%5B-1%5D%20%20%23%20%E9%98%9F%E5%B0%BE%E5%85%83%E7%B4%A0%0A%20%20%20%20print%28%22%E9%98%9F%E5%B0%BE%E5%85%83%E7%B4%A0%20rear%20%3D%22,%20rear%29%0A%0A%20%20%20%20%23%20%E5%85%83%E7%B4%A0%E5%87%BA%E9%98%9F%0A%20%20%20%20pop_front%20%3D%20deq.popleft%28%29%20%20%23%20%E9%98%9F%E9%A6%96%E5%85%83%E7%B4%A0%E5%87%BA%E9%98%9F%0A%20%20%20%20print%28%22%E9%98%9F%E9%A6%96%E5%87%BA%E9%98%9F%E5%85%83%E7%B4%A0%20%20pop_front%20%3D%22,%20pop_front%29%0A%20%20%20%20print%28%22%E9%98%9F%E9%A6%96%E5%87%BA%E9%98%9F%E5%90%8E%20deque%20%3D%22,%20deq%29%0A%20%20%20%20pop_rear%20%3D%20deq.pop%28%29%20%20%23%20%E9%98%9F%E5%B0%BE%E5%85%83%E7%B4%A0%E5%87%BA%E9%98%9F%0A%20%20%20%20print%28%22%E9%98%9F%E5%B0%BE%E5%87%BA%E9%98%9F%E5%85%83%E7%B4%A0%20%20pop_rear%20%3D%22,%20pop_rear%29%0A%20%20%20%20print%28%22%E9%98%9F%E5%B0%BE%E5%87%BA%E9%98%9F%E5%90%8E%20deque%20%3D%22,%20deq%29%0A%0A%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%E7%9A%84%E9%95%BF%E5%BA%A6%0A%20%20%20%20size%20%3D%20len%28deq%29%0A%20%20%20%20print%28%22%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%E9%95%BF%E5%BA%A6%20size%20%3D%22,%20size%29%0A%0A%20%20%20%20%23%20%E5%88%A4%E6%96%AD%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%0A%20%20%20%20is_empty%20%3D%20len%28deq%29%20%3D%3D%200%0A%20%20%20%20print%28%22%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%20%3D%22,%20is_empty%29&cumulative=false&curInstr=3&heapPrimitives=nevernest&mode=display&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false
 
 ## Implementing a Double-Ended Queue *
 
-The implementation of a double-ended queue is similar to that of a regular queue, with the choice of either linked lists or arrays as the underlying data structure.
+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.
 
 ### 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 the head node (corresponding to dequeue operation) and adding new nodes after the tail node (corresponding to enqueue operation).
+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 another symmetric direction of operations. For this, we use a "doubly linked list" as the underlying data structure of the double-ended queue.
+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 below, 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.
 
@@ -394,6 +394,6 @@ The implementation only needs to add methods for "front enqueue" and "rear deque
 
 ## Applications of Double-Ended Queue
 
-The double-ended queue combines the logic of both stacks and queues, **thus it can implement all the application scenarios of these two, while offering greater flexibility**.
+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 the "undo" feature in software 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 length of the stack 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, which is 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.
+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.