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623 lines
17 KiB
Markdown
623 lines
17 KiB
Markdown
---
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comments: true
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---
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# 5.3. 双向队列
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对于队列，我们只能在头部删除或在尾部添加元素，而「双向队列 Deque」更加灵活，在其头部和尾部都能执行元素添加或删除操作。
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<p align="center"> Fig. 双向队列的操作 </p>
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## 5.3.1. 双向队列常用操作
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双向队列的常用操作见下表，方法名需根据特定语言来确定。
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<p align="center"> Table. 双向队列的常用操作 </p>
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<div class="center-table" markdown>
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| 方法名 | 描述 | 时间复杂度 |
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| ------------ | ---------------- | ---------- |
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| pushFirst() | 将元素添加至队首 | $O(1)$ |
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| pushLast() | 将元素添加至队尾 | $O(1)$ |
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| pollFirst() | 删除队首元素 | $O(1)$ |
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| pollLast() | 删除队尾元素 | $O(1)$ |
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| peekFirst() | 访问队首元素 | $O(1)$ |
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| peekLast() | 访问队尾元素 | $O(1)$ |
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| size() | 获取队列的长度 | $O(1)$ |
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| isEmpty() | 判断队列是否为空 | $O(1)$ |
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</div>
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相同地，我们可以直接使用编程语言实现好的双向队列类。
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=== "Java"
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```java title="deque.java"
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/* 初始化双向队列 */
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Deque<Integer> deque = new LinkedList<>();
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/* 元素入队 */
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deque.offerLast(2); // 添加至队尾
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deque.offerLast(5);
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deque.offerLast(4);
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deque.offerFirst(3); // 添加至队首
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deque.offerFirst(1);
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/* 访问元素 */
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int peekFirst = deque.peekFirst(); // 队首元素
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int peekLast = deque.peekLast(); // 队尾元素
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/* 元素出队 */
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int pollFirst = deque.pollFirst(); // 队首元素出队
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int pollLast = deque.pollLast(); // 队尾元素出队
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/* 获取双向队列的长度 */
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int size = deque.size();
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/* 判断双向队列是否为空 */
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boolean isEmpty = deque.isEmpty();
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```
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=== "C++"
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```cpp title="deque.cpp"
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/* 初始化双向队列 */
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deque<int> deque;
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/* 元素入队 */
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deque.push_back(2); // 添加至队尾
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deque.push_back(5);
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deque.push_back(4);
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deque.push_front(3); // 添加至队首
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deque.push_front(1);
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/* 访问元素 */
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int front = deque.front(); // 队首元素
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int back = deque.back(); // 队尾元素
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/* 元素出队 */
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deque.pop_front(); // 队首元素出队
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deque.pop_back(); // 队尾元素出队
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/* 获取双向队列的长度 */
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int size = deque.size();
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/* 判断双向队列是否为空 */
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bool empty = deque.empty();
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```
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=== "Python"
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```python title="deque.py"
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""" 初始化双向队列 """
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duque = deque()
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""" 元素入队 """
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duque.append(2) # 添加至队尾
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duque.append(5)
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duque.append(4)
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duque.appendleft(3) # 添加至队首
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duque.appendleft(1)
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""" 访问元素 """
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front = duque[0] # 队首元素
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rear = duque[-1] # 队尾元素
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""" 元素出队 """
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pop_front = duque.popleft() # 队首元素出队
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pop_rear = duque.pop() # 队尾元素出队
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""" 获取双向队列的长度 """
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size = len(duque)
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""" 判断双向队列是否为空 """
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is_empty = len(duque) == 0
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```
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=== "Go"
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```go title="deque_test.go"
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/* 初始化双向队列 */
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// 在 Go 中，将 list 作为双向队列使用
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deque := list.New()
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/* 元素入队 */
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deque.PushBack(2) // 添加至队尾
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deque.PushBack(5)
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deque.PushBack(4)
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deque.PushFront(3) // 添加至队首
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deque.PushFront(1)
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/* 访问元素 */
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front := deque.Front() // 队首元素
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rear := deque.Back() // 队尾元素
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/* 元素出队 */
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deque.Remove(front) // 队首元素出队
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deque.Remove(rear) // 队尾元素出队
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/* 获取双向队列的长度 */
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size := deque.Len()
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/* 判断双向队列是否为空 */
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isEmpty := deque.Len() == 0
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```
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=== "JavaScript"
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```javascript title="deque.js"
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/* 初始化双向队列 */
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// JavaScript 没有内置的双端队列，只能把 Array 当作双端队列来使用
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const deque = [];
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/* 元素入队 */
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deque.push(2);
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deque.push(5);
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deque.push(4);
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// 请注意，由于是数组，unshift() 方法的时间复杂度为 O(n)
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deque.unshift(3);
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deque.unshift(1);
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console.log("双向队列 deque = ", deque);
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/* 访问元素 */
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const peekFirst = deque[0];
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console.log("队首元素 peekFirst = " + peekFirst);
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const peekLast = deque[deque.length - 1];
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console.log("队尾元素 peekLast = " + peekLast);
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/* 元素出队 */
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// 请注意，由于是数组，shift() 方法的时间复杂度为 O(n)
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const popFront = deque.shift();
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console.log("队首出队元素 popFront = " + popFront + "，队首出队后 deque = " + deque);
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const popBack = deque.pop();
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console.log("队尾出队元素 popBack = " + popBack + "，队尾出队后 deque = " + deque);
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/* 获取双向队列的长度 */
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const size = deque.length;
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console.log("双向队列长度 size = " + size);
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/* 判断双向队列是否为空 */
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const isEmpty = size === 0;
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console.log("双向队列是否为空 = " + isEmpty);
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```
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=== "TypeScript"
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```typescript title="deque.ts"
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/* 初始化双向队列 */
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// TypeScript 没有内置的双端队列，只能把 Array 当作双端队列来使用
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const deque: number[] = [];
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/* 元素入队 */
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deque.push(2);
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deque.push(5);
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deque.push(4);
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// 请注意，由于是数组，unshift() 方法的时间复杂度为 O(n)
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deque.unshift(3);
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deque.unshift(1);
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console.log("双向队列 deque = ", deque);
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/* 访问元素 */
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const peekFirst: number = deque[0];
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console.log("队首元素 peekFirst = " + peekFirst);
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const peekLast: number = deque[deque.length - 1];
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console.log("队尾元素 peekLast = " + peekLast);
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/* 元素出队 */
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// 请注意，由于是数组，shift() 方法的时间复杂度为 O(n)
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const popFront: number = deque.shift() as number;
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console.log("队首出队元素 popFront = " + popFront + "，队首出队后 deque = " + deque);
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const popBack: number = deque.pop() as number;
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console.log("队尾出队元素 popBack = " + popBack + "，队尾出队后 deque = " + deque);
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/* 获取双向队列的长度 */
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const size: number = deque.length;
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console.log("双向队列长度 size = " + size);
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/* 判断双向队列是否为空 */
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const isEmpty: boolean = size === 0;
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console.log("双向队列是否为空 = " + isEmpty);
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```
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=== "C"
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```c title="deque.c"
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```
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=== "C#"
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```csharp title="deque.cs"
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/* 初始化双向队列 */
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// 在 C# 中，将链表 LinkedList 看作双向队列来使用
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LinkedList<int> deque = new LinkedList<int>();
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/* 元素入队 */
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deque.AddLast(2); // 添加至队尾
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deque.AddLast(5);
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deque.AddLast(4);
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deque.AddFirst(3); // 添加至队首
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deque.AddFirst(1);
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/* 访问元素 */
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int peekFirst = deque.First.Value; // 队首元素
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int peekLast = deque.Last.Value; // 队尾元素
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/* 元素出队 */
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deque.RemoveFirst(); // 队首元素出队
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deque.RemoveLast(); // 队尾元素出队
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/* 获取双向队列的长度 */
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int size = deque.Count;
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/* 判断双向队列是否为空 */
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bool isEmpty = deque.Count == 0;
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```
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=== "Swift"
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```swift title="deque.swift"
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/* 初始化双向队列 */
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// Swift 没有内置的双向队列类，可以把 Array 当作双向队列来使用
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var deque: [Int] = []
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/* 元素入队 */
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deque.append(2) // 添加至队尾
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deque.append(5)
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deque.append(4)
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deque.insert(3, at: 0) // 添加至队首
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deque.insert(1, at: 0)
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/* 访问元素 */
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let peekFirst = deque.first! // 队首元素
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let peekLast = deque.last! // 队尾元素
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/* 元素出队 */
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// 使用 Array 模拟时 pollFirst 的复杂度为 O(n)
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let pollFirst = deque.removeFirst() // 队首元素出队
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let pollLast = deque.removeLast() // 队尾元素出队
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/* 获取双向队列的长度 */
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let size = deque.count
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/* 判断双向队列是否为空 */
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let isEmpty = deque.isEmpty
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```
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=== "Zig"
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```zig title="deque.zig"
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```
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## 5.3.2. 双向队列实现
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双向队列需要一种可以在两端添加、两端删除的数据结构。与队列的实现方法类似，双向队列也可以使用双向链表和循环数组来实现。
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### 基于双向链表的实现
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我们将双向链表的头结点和尾结点分别看作双向队列的队首和队尾，并且实现在两端都能添加与删除结点。
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=== "LinkedListDeque"
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=== "pushLast()"
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=== "pushFirst()"
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=== "pollLast()"
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=== "pollFirst()"
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以下是使用双向链表实现双向队列的示例代码。
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=== "Java"
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```java title="linkedlist_deque.java"
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[class]{ListNode}-[func]{}
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[class]{LinkedListDeque}-[func]{}
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```
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=== "C++"
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```cpp title="linkedlist_deque.cpp"
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```
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=== "Python"
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```python title="linkedlist_deque.py"
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```
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=== "Go"
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```go title="linkedlist_deque.go"
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```
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=== "JavaScript"
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```javascript title="linkedlist_deque.js"
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/* 双向链表结点 */
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class ListNode {
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prev; // 前驱结点引用 (指针)
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next; // 后继结点引用 (指针)
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val; // 结点值
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constructor(val) {
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this.val = val;
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this.next = null;
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this.prev = null;
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}
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}
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/* 基于双向链表实现的双向队列 */
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class LinkedListDeque {
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front; // 头结点 front
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rear; // 尾结点 rear
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len; // 双向队列的长度
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constructor() {
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this.front = null;
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this.rear = null;
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this.len = 0;
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}
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/* 队尾入队操作 */
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pushLast(val) {
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const node = new ListNode(val);
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// 若链表为空，则令 front, rear 都指向 node
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if (this.len === 0) {
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this.front = node;
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this.rear = node;
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} else {
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// 将 node 添加至链表尾部
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this.rear.next = node;
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node.prev = this.rear;
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this.rear = node; // 更新尾结点
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}
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this.len++;
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}
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/* 队首入队操作 */
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pushFirst(val) {
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const node = new ListNode(val);
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// 若链表为空，则令 front, rear 都指向 node
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if (this.len === 0) {
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this.front = node;
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this.rear = node;
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} else {
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// 将 node 添加至链表头部
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this.front.prev = node;
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node.next = this.front;
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this.front = node; // 更新头结点
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}
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this.len++;
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}
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/* 队尾出队操作 */
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pollLast() {
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if (this.len === 0) {
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return null;
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}
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const value = this.rear.val; // 存储尾结点值
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// 删除尾结点
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let temp = this.rear.prev;
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if (temp !== null) {
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temp.next = null;
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this.rear.prev = null;
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}
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this.rear = temp; // 更新尾结点
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this.len--;
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return value;
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}
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/* 队首出队操作 */
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pollFirst() {
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if (this.len === 0) {
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return null;
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}
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const value = this.front.val; // 存储尾结点值
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// 删除头结点
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let temp = this.front.next;
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if (temp !== null) {
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temp.prev = null;
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this.front.next = null;
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}
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this.front = temp; // 更新头结点
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this.len--;
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return value;
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}
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/* 访问队尾元素 */
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peekLast() {
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return this.len === 0 ? null : this.rear.val;
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}
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/* 访问队首元素 */
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peekFirst() {
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return this.len === 0 ? null : this.front.val;
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}
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/* 获取双向队列的长度 */
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size() {
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return this.len;
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}
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/* 判断双向队列是否为空 */
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isEmpty() {
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return this.len === 0;
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}
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/* 打印双向队列 */
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print() {
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const arr = [];
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let temp = this.front;
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while (temp !== null) {
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arr.push(temp.val);
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temp = temp.next;
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}
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console.log("[" + arr.join(", ") + "]");
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}
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}
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```
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=== "TypeScript"
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```typescript title="linkedlist_deque.ts"
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/* 双向链表结点 */
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class ListNode {
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prev: ListNode; // 前驱结点引用 (指针)
|
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next: ListNode; // 后继结点引用 (指针)
|
||
val: number; // 结点值
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||
|
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constructor(val: number) {
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||
this.val = val;
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||
this.next = null;
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||
this.prev = null;
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}
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||
}
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|
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/* 基于双向链表实现的双向队列 */
|
||
class LinkedListDeque {
|
||
front: ListNode; // 头结点 front
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||
rear: ListNode; // 尾结点 rear
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||
len: number; // 双向队列的长度
|
||
|
||
constructor() {
|
||
this.front = null;
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this.rear = null;
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||
this.len = 0;
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||
}
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/* 队尾入队操作 */
|
||
pushLast(val: number): void {
|
||
const node: ListNode = new ListNode(val);
|
||
// 若链表为空，则令 front, rear 都指向 node
|
||
if (this.len === 0) {
|
||
this.front = node;
|
||
this.rear = node;
|
||
} else {
|
||
// 将 node 添加至链表尾部
|
||
this.rear.next = node;
|
||
node.prev = this.rear;
|
||
this.rear = node; // 更新尾结点
|
||
}
|
||
this.len++;
|
||
}
|
||
|
||
/* 队首入队操作 */
|
||
pushFirst(val: number): void {
|
||
const node: ListNode = new ListNode(val);
|
||
// 若链表为空，则令 front, rear 都指向 node
|
||
if (this.len === 0) {
|
||
this.front = node;
|
||
this.rear = node;
|
||
} else {
|
||
// 将 node 添加至链表头部
|
||
this.front.prev = node;
|
||
node.next = this.front;
|
||
this.front = node; // 更新头结点
|
||
}
|
||
this.len++;
|
||
}
|
||
|
||
/* 队尾出队操作 */
|
||
pollLast(): number {
|
||
if (this.len === 0) {
|
||
return null;
|
||
}
|
||
const value: number = this.rear.val; // 存储尾结点值
|
||
// 删除尾结点
|
||
let temp: ListNode = this.rear.prev;
|
||
if (temp !== null) {
|
||
temp.next = null;
|
||
this.rear.prev = null;
|
||
}
|
||
this.rear = temp; // 更新尾结点
|
||
this.len--;
|
||
return value;
|
||
}
|
||
|
||
/* 队首出队操作 */
|
||
pollFirst(): number {
|
||
if (this.len === 0) {
|
||
return null;
|
||
}
|
||
const value: number = this.front.val; // 存储尾结点值
|
||
// 删除头结点
|
||
let temp: ListNode = this.front.next;
|
||
if (temp !== null) {
|
||
temp.prev = null;
|
||
this.front.next = null;
|
||
}
|
||
this.front = temp; // 更新头结点
|
||
this.len--;
|
||
return value;
|
||
}
|
||
|
||
/* 访问队尾元素 */
|
||
peekLast(): number {
|
||
return this.len === 0 ? null : this.rear.val;
|
||
}
|
||
|
||
/* 访问队首元素 */
|
||
peekFirst(): number {
|
||
return this.len === 0 ? null : this.front.val;
|
||
}
|
||
|
||
/* 获取双向队列的长度 */
|
||
size(): number {
|
||
return this.len;
|
||
}
|
||
|
||
/* 判断双向队列是否为空 */
|
||
isEmpty(): boolean {
|
||
return this.len === 0;
|
||
}
|
||
|
||
/* 打印双向队列 */
|
||
print(): void {
|
||
const arr: number[] = [];
|
||
let temp: ListNode = this.front;
|
||
while (temp !== null) {
|
||
arr.push(temp.val);
|
||
temp = temp.next;
|
||
}
|
||
console.log("[" + arr.join(", ") + "]");
|
||
}
|
||
}
|
||
```
|
||
|
||
=== "C"
|
||
|
||
```c title="linkedlist_deque.c"
|
||
|
||
```
|
||
|
||
=== "C#"
|
||
|
||
```csharp title="linkedlist_deque.cs"
|
||
|
||
```
|
||
|
||
=== "Swift"
|
||
|
||
```swift title="linkedlist_deque.swift"
|
||
|
||
```
|
||
|
||
=== "Zig"
|
||
|
||
```zig title="linkedlist_deque.zig"
|
||
|
||
```
|