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---
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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，我们仅能在头部删除或在尾部添加元素。然而，「双向队列 Deque」提供了更高的灵活性，允许在头部和尾部执行元素的添加或删除操作。
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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如下表所示，具体的方法名称需要根据所使用的编程语言来确定。
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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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| popFirst() | 删除队首元素 | $O(1)$ |
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| popLast() | 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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</div>
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同样地，我们可以直接使用编程语言中已实现的双向队列类。
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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 popFirst = deque.pollFirst(); // 队首元素出队
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int popLast = 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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deque: Deque[int] = collections.deque()
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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.appendleft(3) # 添加至队首
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deque.appendleft(1)
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# 访问元素
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front: int = deque[0] # 队首元素
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rear: int = deque[-1] # 队尾元素
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# 元素出队
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pop_front: int = deque.popleft() # 队首元素出队
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pop_rear: int = deque.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: int = len(deque)
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# 判断双向队列是否为空
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is_empty: bool = len(deque) == 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 popFirst 的复杂度为 O(n)
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let popFirst = deque.removeFirst() // 队首元素出队
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let popLast = 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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双向队列的实现与队列类似，可以选择链表或数组作为底层数据结构。
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### 基于双向链表的实现
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回顾上一节内容，我们使用普通单向链表来实现队列，因为它可以方便地删除头节点（对应出队操作）和在尾节点后添加新节点（对应入队操作）。
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对于双向队列而言，头部和尾部都可以执行入队和出队操作。换句话说，双向队列需要实现另一个对称方向的操作。为此，我们采用「双向链表」作为双向队列的底层数据结构。
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我们将双向链表的头节点和尾节点视为双向队列的队首和队尾，同时实现在两端添加和删除节点的功能。
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=== "LinkedListDeque"
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=== "pushLast()"
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=== "pushFirst()"
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=== "popLast()"
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=== "popFirst()"
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以下是具体实现代码。
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=== "Java"
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```java title="linkedlist_deque.java"
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/* 双向链表节点 */
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class ListNode {
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int val; // 节点值
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ListNode next; // 后继节点引用（指针）
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ListNode prev; // 前驱节点引用（指针）
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ListNode(int val) {
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this.val = val;
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prev = next = 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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private ListNode front, rear; // 头节点 front ，尾节点 rear
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private int queSize = 0; // 双向队列的长度
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public LinkedListDeque() {
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front = rear = null;
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}
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/* 获取双向队列的长度 */
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public int size() {
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return queSize;
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}
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/* 判断双向队列是否为空 */
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public boolean isEmpty() {
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return size() == 0;
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}
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/* 入队操作 */
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private void push(int num, boolean isFront) {
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ListNode node = new ListNode(num);
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// 若链表为空，则令 front, rear 都指向 node
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if (isEmpty())
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front = rear = node;
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// 队首入队操作
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else if (isFront) {
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// 将 node 添加至链表头部
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front.prev = node;
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node.next = front;
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front = node; // 更新头节点
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// 队尾入队操作
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} else {
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// 将 node 添加至链表尾部
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rear.next = node;
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node.prev = rear;
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rear = node; // 更新尾节点
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}
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queSize++; // 更新队列长度
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}
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/* 队首入队 */
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public void pushFirst(int num) {
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push(num, true);
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}
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/* 队尾入队 */
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public void pushLast(int num) {
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push(num, false);
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}
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/* 出队操作 */
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private Integer pop(boolean isFront) {
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// 若队列为空，直接返回 null
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if (isEmpty())
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return null;
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int val;
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// 队首出队操作
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if (isFront) {
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val = front.val; // 暂存头节点值
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// 删除头节点
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ListNode fNext = front.next;
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if (fNext != null) {
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fNext.prev = null;
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front.next = null;
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}
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front = fNext; // 更新头节点
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// 队尾出队操作
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} else {
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val = rear.val; // 暂存尾节点值
|
|
|
// 删除尾节点
|
|
|
ListNode rPrev = rear.prev;
|
|
|
if (rPrev != null) {
|
|
|
rPrev.next = null;
|
|
|
rear.prev = null;
|
|
|
}
|
|
|
rear = rPrev; // 更新尾节点
|
|
|
}
|
|
|
queSize--; // 更新队列长度
|
|
|
return val;
|
|
|
}
|
|
|
|
|
|
/* 队首出队 */
|
|
|
public Integer popFirst() {
|
|
|
return pop(true);
|
|
|
}
|
|
|
|
|
|
/* 队尾出队 */
|
|
|
public Integer popLast() {
|
|
|
return pop(false);
|
|
|
}
|
|
|
|
|
|
/* 访问队首元素 */
|
|
|
public Integer peekFirst() {
|
|
|
return isEmpty() ? null : front.val;
|
|
|
}
|
|
|
|
|
|
/* 访问队尾元素 */
|
|
|
public Integer peekLast() {
|
|
|
return isEmpty() ? null : rear.val;
|
|
|
}
|
|
|
|
|
|
/* 返回数组用于打印 */
|
|
|
public int[] toArray() {
|
|
|
ListNode node = front;
|
|
|
int[] res = new int[size()];
|
|
|
for (int i = 0; i < res.length; i++) {
|
|
|
res[i] = node.val;
|
|
|
node = node.next;
|
|
|
}
|
|
|
return res;
|
|
|
}
|
|
|
}
|
|
|
```
|
|
|
|
|
|
=== "C++"
|
|
|
|
|
|
```cpp title="linkedlist_deque.cpp"
|
|
|
/* 双向链表节点 */
|
|
|
struct DoublyListNode {
|
|
|
int val; // 节点值
|
|
|
DoublyListNode *next; // 后继节点指针
|
|
|
DoublyListNode *prev; // 前驱节点指针
|
|
|
DoublyListNode(int val) : val(val), prev(nullptr), next(nullptr) {
|
|
|
}
|
|
|
};
|
|
|
|
|
|
/* 基于双向链表实现的双向队列 */
|
|
|
class LinkedListDeque {
|
|
|
private:
|
|
|
DoublyListNode *front, *rear; // 头节点 front ，尾节点 rear
|
|
|
int queSize = 0; // 双向队列的长度
|
|
|
|
|
|
public:
|
|
|
/* 构造方法 */
|
|
|
LinkedListDeque() : front(nullptr), rear(nullptr) {
|
|
|
}
|
|
|
|
|
|
/* 析构方法 */
|
|
|
~LinkedListDeque() {
|
|
|
// 遍历链表删除节点，释放内存
|
|
|
DoublyListNode *pre, *cur = front;
|
|
|
while (cur != nullptr) {
|
|
|
pre = cur;
|
|
|
cur = cur->next;
|
|
|
delete pre;
|
|
|
}
|
|
|
}
|
|
|
|
|
|
/* 获取双向队列的长度 */
|
|
|
int size() {
|
|
|
return queSize;
|
|
|
}
|
|
|
|
|
|
/* 判断双向队列是否为空 */
|
|
|
bool isEmpty() {
|
|
|
return size() == 0;
|
|
|
}
|
|
|
|
|
|
/* 入队操作 */
|
|
|
void push(int num, bool isFront) {
|
|
|
DoublyListNode *node = new DoublyListNode(num);
|
|
|
// 若链表为空，则令 front, rear 都指向 node
|
|
|
if (isEmpty())
|
|
|
front = rear = node;
|
|
|
// 队首入队操作
|
|
|
else if (isFront) {
|
|
|
// 将 node 添加至链表头部
|
|
|
front->prev = node;
|
|
|
node->next = front;
|
|
|
front = node; // 更新头节点
|
|
|
// 队尾入队操作
|
|
|
} else {
|
|
|
// 将 node 添加至链表尾部
|
|
|
rear->next = node;
|
|
|
node->prev = rear;
|
|
|
rear = node; // 更新尾节点
|
|
|
}
|
|
|
queSize++; // 更新队列长度
|
|
|
}
|
|
|
|
|
|
/* 队首入队 */
|
|
|
void pushFirst(int num) {
|
|
|
push(num, true);
|
|
|
}
|
|
|
|
|
|
/* 队尾入队 */
|
|
|
void pushLast(int num) {
|
|
|
push(num, false);
|
|
|
}
|
|
|
|
|
|
/* 出队操作 */
|
|
|
int pop(bool isFront) {
|
|
|
// 若队列为空，直接返回 -1
|
|
|
if (isEmpty())
|
|
|
return -1;
|
|
|
int val;
|
|
|
// 队首出队操作
|
|
|
if (isFront) {
|
|
|
val = front->val; // 暂存头节点值
|
|
|
// 删除头节点
|
|
|
DoublyListNode *fNext = front->next;
|
|
|
if (fNext != nullptr) {
|
|
|
fNext->prev = nullptr;
|
|
|
front->next = nullptr;
|
|
|
delete front;
|
|
|
}
|
|
|
front = fNext; // 更新头节点
|
|
|
// 队尾出队操作
|
|
|
} else {
|
|
|
val = rear->val; // 暂存尾节点值
|
|
|
// 删除尾节点
|
|
|
DoublyListNode *rPrev = rear->prev;
|
|
|
if (rPrev != nullptr) {
|
|
|
rPrev->next = nullptr;
|
|
|
rear->prev = nullptr;
|
|
|
delete rear;
|
|
|
}
|
|
|
rear = rPrev; // 更新尾节点
|
|
|
}
|
|
|
queSize--; // 更新队列长度
|
|
|
return val;
|
|
|
}
|
|
|
|
|
|
/* 队首出队 */
|
|
|
int popFirst() {
|
|
|
return pop(true);
|
|
|
}
|
|
|
|
|
|
/* 队尾出队 */
|
|
|
int popLast() {
|
|
|
return pop(false);
|
|
|
}
|
|
|
|
|
|
/* 访问队首元素 */
|
|
|
int peekFirst() {
|
|
|
return isEmpty() ? -1 : front->val;
|
|
|
}
|
|
|
|
|
|
/* 访问队尾元素 */
|
|
|
int peekLast() {
|
|
|
return isEmpty() ? -1 : rear->val;
|
|
|
}
|
|
|
|
|
|
/* 返回数组用于打印 */
|
|
|
vector<int> toVector() {
|
|
|
DoublyListNode *node = front;
|
|
|
vector<int> res(size());
|
|
|
for (int i = 0; i < res.size(); i++) {
|
|
|
res[i] = node->val;
|
|
|
node = node->next;
|
|
|
}
|
|
|
return res;
|
|
|
}
|
|
|
};
|
|
|
```
|
|
|
|
|
|
=== "Python"
|
|
|
|
|
|
```python title="linkedlist_deque.py"
|
|
|
class ListNode:
|
|
|
"""双向链表节点"""
|
|
|
|
|
|
def __init__(self, val: int) -> None:
|
|
|
"""构造方法"""
|
|
|
self.val: int = val
|
|
|
self.next: ListNode | None = None # 后继节点引用（指针）
|
|
|
self.prev: ListNode | None = None # 前驱节点引用（指针）
|
|
|
|
|
|
class LinkedListDeque:
|
|
|
"""基于双向链表实现的双向队列"""
|
|
|
|
|
|
def __init__(self) -> None:
|
|
|
"""构造方法"""
|
|
|
self.front: ListNode | None = None # 头节点 front
|
|
|
self.rear: ListNode | None = None # 尾节点 rear
|
|
|
self.__size: int = 0 # 双向队列的长度
|
|
|
|
|
|
def size(self) -> int:
|
|
|
"""获取双向队列的长度"""
|
|
|
return self.__size
|
|
|
|
|
|
def is_empty(self) -> bool:
|
|
|
"""判断双向队列是否为空"""
|
|
|
return self.size() == 0
|
|
|
|
|
|
def push(self, num: int, is_front: bool) -> None:
|
|
|
"""入队操作"""
|
|
|
node = ListNode(num)
|
|
|
# 若链表为空，则令 front, rear 都指向 node
|
|
|
if self.is_empty():
|
|
|
self.front = self.rear = node
|
|
|
# 队首入队操作
|
|
|
elif is_front:
|
|
|
# 将 node 添加至链表头部
|
|
|
self.front.prev = node
|
|
|
node.next = self.front
|
|
|
self.front = node # 更新头节点
|
|
|
# 队尾入队操作
|
|
|
else:
|
|
|
# 将 node 添加至链表尾部
|
|
|
self.rear.next = node
|
|
|
node.prev = self.rear
|
|
|
self.rear = node # 更新尾节点
|
|
|
self.__size += 1 # 更新队列长度
|
|
|
|
|
|
def push_first(self, num: int) -> None:
|
|
|
"""队首入队"""
|
|
|
self.push(num, True)
|
|
|
|
|
|
def push_last(self, num: int) -> None:
|
|
|
"""队尾入队"""
|
|
|
self.push(num, False)
|
|
|
|
|
|
def pop(self, is_front: bool) -> int:
|
|
|
"""出队操作"""
|
|
|
# 若队列为空，直接返回 None
|
|
|
if self.is_empty():
|
|
|
return None
|
|
|
# 队首出队操作
|
|
|
if is_front:
|
|
|
val: int = self.front.val # 暂存头节点值
|
|
|
# 删除头节点
|
|
|
fnext: ListNode | None = self.front.next
|
|
|
if fnext != None:
|
|
|
fnext.prev = None
|
|
|
self.front.next = None
|
|
|
self.front = fnext # 更新头节点
|
|
|
# 队尾出队操作
|
|
|
else:
|
|
|
val: int = self.rear.val # 暂存尾节点值
|
|
|
# 删除尾节点
|
|
|
rprev: ListNode | None = self.rear.prev
|
|
|
if rprev != None:
|
|
|
rprev.next = None
|
|
|
self.rear.prev = None
|
|
|
self.rear = rprev # 更新尾节点
|
|
|
self.__size -= 1 # 更新队列长度
|
|
|
return val
|
|
|
|
|
|
def pop_first(self) -> int:
|
|
|
"""队首出队"""
|
|
|
return self.pop(True)
|
|
|
|
|
|
def pop_last(self) -> int:
|
|
|
"""队尾出队"""
|
|
|
return self.pop(False)
|
|
|
|
|
|
def peek_first(self) -> int:
|
|
|
"""访问队首元素"""
|
|
|
return None if self.is_empty() else self.front.val
|
|
|
|
|
|
def peek_last(self) -> int:
|
|
|
"""访问队尾元素"""
|
|
|
return None if self.is_empty() else self.rear.val
|
|
|
|
|
|
def to_array(self) -> list[int]:
|
|
|
"""返回数组用于打印"""
|
|
|
node: ListNode | None = self.front
|
|
|
res: list[int] = [0] * self.size()
|
|
|
for i in range(self.size()):
|
|
|
res[i] = node.val
|
|
|
node = node.next
|
|
|
return res
|
|
|
```
|
|
|
|
|
|
=== "Go"
|
|
|
|
|
|
```go title="linkedlist_deque.go"
|
|
|
/* 基于双向链表实现的双向队列 */
|
|
|
type linkedListDeque struct {
|
|
|
// 使用内置包 list
|
|
|
data *list.List
|
|
|
}
|
|
|
|
|
|
/* 初始化双端队列 */
|
|
|
func newLinkedListDeque() *linkedListDeque {
|
|
|
return &linkedListDeque{
|
|
|
data: list.New(),
|
|
|
}
|
|
|
}
|
|
|
|
|
|
/* 队首元素入队 */
|
|
|
func (s *linkedListDeque) pushFirst(value any) {
|
|
|
s.data.PushFront(value)
|
|
|
}
|
|
|
|
|
|
/* 队尾元素入队 */
|
|
|
func (s *linkedListDeque) pushLast(value any) {
|
|
|
s.data.PushBack(value)
|
|
|
}
|
|
|
|
|
|
/* 队首元素出队 */
|
|
|
func (s *linkedListDeque) popFirst() any {
|
|
|
if s.isEmpty() {
|
|
|
return nil
|
|
|
}
|
|
|
e := s.data.Front()
|
|
|
s.data.Remove(e)
|
|
|
return e.Value
|
|
|
}
|
|
|
|
|
|
/* 队尾元素出队 */
|
|
|
func (s *linkedListDeque) popLast() any {
|
|
|
if s.isEmpty() {
|
|
|
return nil
|
|
|
}
|
|
|
e := s.data.Back()
|
|
|
s.data.Remove(e)
|
|
|
return e.Value
|
|
|
}
|
|
|
|
|
|
/* 访问队首元素 */
|
|
|
func (s *linkedListDeque) peekFirst() any {
|
|
|
if s.isEmpty() {
|
|
|
return nil
|
|
|
}
|
|
|
e := s.data.Front()
|
|
|
return e.Value
|
|
|
}
|
|
|
|
|
|
/* 访问队尾元素 */
|
|
|
func (s *linkedListDeque) peekLast() any {
|
|
|
if s.isEmpty() {
|
|
|
return nil
|
|
|
}
|
|
|
e := s.data.Back()
|
|
|
return e.Value
|
|
|
}
|
|
|
|
|
|
/* 获取队列的长度 */
|
|
|
func (s *linkedListDeque) size() int {
|
|
|
return s.data.Len()
|
|
|
}
|
|
|
|
|
|
/* 判断队列是否为空 */
|
|
|
func (s *linkedListDeque) isEmpty() bool {
|
|
|
return s.data.Len() == 0
|
|
|
}
|
|
|
|
|
|
/* 获取 List 用于打印 */
|
|
|
func (s *linkedListDeque) toList() *list.List {
|
|
|
return s.data
|
|
|
}
|
|
|
```
|
|
|
|
|
|
=== "JavaScript"
|
|
|
|
|
|
```javascript title="linkedlist_deque.js"
|
|
|
/* 双向链表节点 */
|
|
|
class ListNode {
|
|
|
prev; // 前驱节点引用 (指针)
|
|
|
next; // 后继节点引用 (指针)
|
|
|
val; // 节点值
|
|
|
|
|
|
constructor(val) {
|
|
|
this.val = val;
|
|
|
this.next = null;
|
|
|
this.prev = null;
|
|
|
}
|
|
|
}
|
|
|
|
|
|
/* 基于双向链表实现的双向队列 */
|
|
|
class LinkedListDeque {
|
|
|
#front; // 头节点 front
|
|
|
#rear; // 尾节点 rear
|
|
|
#queSize; // 双向队列的长度
|
|
|
|
|
|
constructor() {
|
|
|
this.#front = null;
|
|
|
this.#rear = null;
|
|
|
this.#queSize = 0;
|
|
|
}
|
|
|
|
|
|
/* 队尾入队操作 */
|
|
|
pushLast(val) {
|
|
|
const node = new ListNode(val);
|
|
|
// 若链表为空，则令 front, rear 都指向 node
|
|
|
if (this.#queSize === 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; // 更新尾节点
|
|
|
}
|
|
|
this.#queSize++;
|
|
|
}
|
|
|
|
|
|
/* 队首入队操作 */
|
|
|
pushFirst(val) {
|
|
|
const node = new ListNode(val);
|
|
|
// 若链表为空，则令 front, rear 都指向 node
|
|
|
if (this.#queSize === 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; // 更新头节点
|
|
|
}
|
|
|
this.#queSize++;
|
|
|
}
|
|
|
|
|
|
/* 队尾出队操作 */
|
|
|
popLast() {
|
|
|
if (this.#queSize === 0) {
|
|
|
return null;
|
|
|
}
|
|
|
const value = this.#rear.val; // 存储尾节点值
|
|
|
// 删除尾节点
|
|
|
let temp = this.#rear.prev;
|
|
|
if (temp !== null) {
|
|
|
temp.next = null;
|
|
|
this.#rear.prev = null;
|
|
|
}
|
|
|
this.#rear = temp; // 更新尾节点
|
|
|
this.#queSize--;
|
|
|
return value;
|
|
|
}
|
|
|
|
|
|
/* 队首出队操作 */
|
|
|
popFirst() {
|
|
|
if (this.#queSize === 0) {
|
|
|
return null;
|
|
|
}
|
|
|
const value = this.#front.val; // 存储尾节点值
|
|
|
// 删除头节点
|
|
|
let temp = this.#front.next;
|
|
|
if (temp !== null) {
|
|
|
temp.prev = null;
|
|
|
this.#front.next = null;
|
|
|
}
|
|
|
this.#front = temp; // 更新头节点
|
|
|
this.#queSize--;
|
|
|
return value;
|
|
|
}
|
|
|
|
|
|
/* 访问队尾元素 */
|
|
|
peekLast() {
|
|
|
return this.#queSize === 0 ? null : this.#rear.val;
|
|
|
}
|
|
|
|
|
|
/* 访问队首元素 */
|
|
|
peekFirst() {
|
|
|
return this.#queSize === 0 ? null : this.#front.val;
|
|
|
}
|
|
|
|
|
|
/* 获取双向队列的长度 */
|
|
|
size() {
|
|
|
return this.#queSize;
|
|
|
}
|
|
|
|
|
|
/* 判断双向队列是否为空 */
|
|
|
isEmpty() {
|
|
|
return this.#queSize === 0;
|
|
|
}
|
|
|
|
|
|
/* 打印双向队列 */
|
|
|
print() {
|
|
|
const arr = [];
|
|
|
let temp = this.#front;
|
|
|
while (temp !== null) {
|
|
|
arr.push(temp.val);
|
|
|
temp = temp.next;
|
|
|
}
|
|
|
console.log("[" + arr.join(", ") + "]");
|
|
|
}
|
|
|
}
|
|
|
```
|
|
|
|
|
|
=== "TypeScript"
|
|
|
|
|
|
```typescript title="linkedlist_deque.ts"
|
|
|
/* 双向链表节点 */
|
|
|
class ListNode {
|
|
|
prev: ListNode; // 前驱节点引用 (指针)
|
|
|
next: ListNode; // 后继节点引用 (指针)
|
|
|
val: number; // 节点值
|
|
|
|
|
|
constructor(val: number) {
|
|
|
this.val = val;
|
|
|
this.next = null;
|
|
|
this.prev = null;
|
|
|
}
|
|
|
}
|
|
|
|
|
|
/* 基于双向链表实现的双向队列 */
|
|
|
class LinkedListDeque {
|
|
|
private front: ListNode; // 头节点 front
|
|
|
private rear: ListNode; // 尾节点 rear
|
|
|
private queSize: number; // 双向队列的长度
|
|
|
|
|
|
constructor() {
|
|
|
this.front = null;
|
|
|
this.rear = null;
|
|
|
this.queSize = 0;
|
|
|
}
|
|
|
|
|
|
/* 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.queSize === 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; // 更新尾节点
|
|
|
}
|
|
|
this.queSize++;
|
|
|
}
|
|
|
|
|
|
/* 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.queSize === 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; // 更新头节点
|
|
|
}
|
|
|
this.queSize++;
|
|
|
}
|
|
|
|
|
|
/* 队尾出队操作 */
|
|
|
popLast(): number {
|
|
|
if (this.queSize === 0) {
|
|
|
return null;
|
|
|
}
|
|
|
const value: number = this.rear.val; // 存储尾节点值
|
|
|
// 删除尾节点
|
|
|
let temp: ListNode = this.rear.prev;
|
|
|
if (temp !== null) {
|
|
|
temp.next = null;
|
|
|
this.rear.prev = null;
|
|
|
}
|
|
|
this.rear = temp; // 更新尾节点
|
|
|
this.queSize--;
|
|
|
return value;
|
|
|
}
|
|
|
|
|
|
/* 队首出队操作 */
|
|
|
popFirst(): number {
|
|
|
if (this.queSize === 0) {
|
|
|
return null;
|
|
|
}
|
|
|
const value: number = this.front.val; // 存储尾节点值
|
|
|
// 删除头节点
|
|
|
let temp: ListNode = this.front.next;
|
|
|
if (temp !== null) {
|
|
|
temp.prev = null;
|
|
|
this.front.next = null;
|
|
|
}
|
|
|
this.front = temp; // 更新头节点
|
|
|
this.queSize--;
|
|
|
return value;
|
|
|
}
|
|
|
|
|
|
/* 访问队尾元素 */
|
|
|
peekLast(): number {
|
|
|
return this.queSize === 0 ? null : this.rear.val;
|
|
|
}
|
|
|
|
|
|
/* 访问队首元素 */
|
|
|
peekFirst(): number {
|
|
|
return this.queSize === 0 ? null : this.front.val;
|
|
|
}
|
|
|
|
|
|
/* 获取双向队列的长度 */
|
|
|
size(): number {
|
|
|
return this.queSize;
|
|
|
}
|
|
|
|
|
|
/* 判断双向队列是否为空 */
|
|
|
isEmpty(): boolean {
|
|
|
return this.queSize === 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"
|
|
|
[class]{ListNode}-[func]{}
|
|
|
|
|
|
[class]{LinkedListDeque}-[func]{}
|
|
|
```
|
|
|
|
|
|
=== "C#"
|
|
|
|
|
|
```csharp title="linkedlist_deque.cs"
|
|
|
[class]{ListNode}-[func]{}
|
|
|
|
|
|
[class]{LinkedListDeque}-[func]{}
|
|
|
```
|
|
|
|
|
|
=== "Swift"
|
|
|
|
|
|
```swift title="linkedlist_deque.swift"
|
|
|
/* 双向链表节点 */
|
|
|
class ListNode {
|
|
|
var val: Int // 节点值
|
|
|
var next: ListNode? // 后继节点引用（指针）
|
|
|
var prev: ListNode? // 前驱节点引用（指针）
|
|
|
|
|
|
init(val: Int) {
|
|
|
self.val = val
|
|
|
}
|
|
|
}
|
|
|
|
|
|
/* 基于双向链表实现的双向队列 */
|
|
|
class LinkedListDeque {
|
|
|
private var front: ListNode? // 头节点 front
|
|
|
private var rear: ListNode? // 尾节点 rear
|
|
|
private var queSize: Int // 双向队列的长度
|
|
|
|
|
|
init() {
|
|
|
queSize = 0
|
|
|
}
|
|
|
|
|
|
/* 获取双向队列的长度 */
|
|
|
func size() -> Int {
|
|
|
queSize
|
|
|
}
|
|
|
|
|
|
/* 判断双向队列是否为空 */
|
|
|
func isEmpty() -> Bool {
|
|
|
size() == 0
|
|
|
}
|
|
|
|
|
|
/* 入队操作 */
|
|
|
private func push(num: Int, isFront: Bool) {
|
|
|
let node = ListNode(val: num)
|
|
|
// 若链表为空，则令 front, rear 都指向 node
|
|
|
if isEmpty() {
|
|
|
front = node
|
|
|
rear = node
|
|
|
}
|
|
|
// 队首入队操作
|
|
|
else if isFront {
|
|
|
// 将 node 添加至链表头部
|
|
|
front?.prev = node
|
|
|
node.next = front
|
|
|
front = node // 更新头节点
|
|
|
}
|
|
|
// 队尾入队操作
|
|
|
else {
|
|
|
// 将 node 添加至链表尾部
|
|
|
rear?.next = node
|
|
|
node.prev = rear
|
|
|
rear = node // 更新尾节点
|
|
|
}
|
|
|
queSize += 1 // 更新队列长度
|
|
|
}
|
|
|
|
|
|
/* 队首入队 */
|
|
|
func pushFirst(num: Int) {
|
|
|
push(num: num, isFront: true)
|
|
|
}
|
|
|
|
|
|
/* 队尾入队 */
|
|
|
func pushLast(num: Int) {
|
|
|
push(num: num, isFront: false)
|
|
|
}
|
|
|
|
|
|
/* 出队操作 */
|
|
|
private func pop(isFront: Bool) -> Int {
|
|
|
if isEmpty() {
|
|
|
fatalError("双向队列为空")
|
|
|
}
|
|
|
let val: Int
|
|
|
// 队首出队操作
|
|
|
if isFront {
|
|
|
val = front!.val // 暂存头节点值
|
|
|
// 删除头节点
|
|
|
let fNext = front?.next
|
|
|
if fNext != nil {
|
|
|
fNext?.prev = nil
|
|
|
front?.next = nil
|
|
|
}
|
|
|
front = fNext // 更新头节点
|
|
|
}
|
|
|
// 队尾出队操作
|
|
|
else {
|
|
|
val = rear!.val // 暂存尾节点值
|
|
|
// 删除尾节点
|
|
|
let rPrev = rear?.prev
|
|
|
if rPrev != nil {
|
|
|
rPrev?.next = nil
|
|
|
rear?.prev = nil
|
|
|
}
|
|
|
rear = rPrev // 更新尾节点
|
|
|
}
|
|
|
queSize -= 1 // 更新队列长度
|
|
|
return val
|
|
|
}
|
|
|
|
|
|
/* 队首出队 */
|
|
|
func popFirst() -> Int {
|
|
|
pop(isFront: true)
|
|
|
}
|
|
|
|
|
|
/* 队尾出队 */
|
|
|
func popLast() -> Int {
|
|
|
pop(isFront: false)
|
|
|
}
|
|
|
|
|
|
/* 访问队首元素 */
|
|
|
func peekFirst() -> Int? {
|
|
|
isEmpty() ? nil : front?.val
|
|
|
}
|
|
|
|
|
|
/* 访问队尾元素 */
|
|
|
func peekLast() -> Int? {
|
|
|
isEmpty() ? nil : rear?.val
|
|
|
}
|
|
|
|
|
|
/* 返回数组用于打印 */
|
|
|
func toArray() -> [Int] {
|
|
|
var node = front
|
|
|
var res = Array(repeating: 0, count: size())
|
|
|
for i in res.indices {
|
|
|
res[i] = node!.val
|
|
|
node = node?.next
|
|
|
}
|
|
|
return res
|
|
|
}
|
|
|
}
|
|
|
```
|
|
|
|
|
|
=== "Zig"
|
|
|
|
|
|
```zig title="linkedlist_deque.zig"
|
|
|
// 双向链表节点
|
|
|
fn ListNode(comptime T: type) type {
|
|
|
return struct {
|
|
|
const Self = @This();
|
|
|
|
|
|
val: T = undefined, // 节点值
|
|
|
next: ?*Self = null, // 后继节点引用（指针）
|
|
|
prev: ?*Self = null, // 前驱节点引用（指针）
|
|
|
|
|
|
// Initialize a list node with specific value
|
|
|
pub fn init(self: *Self, x: i32) void {
|
|
|
self.val = x;
|
|
|
self.next = null;
|
|
|
self.prev = null;
|
|
|
}
|
|
|
};
|
|
|
}
|
|
|
|
|
|
// 基于双向链表实现的双向队列
|
|
|
fn LinkedListDeque(comptime T: type) type {
|
|
|
return struct {
|
|
|
const Self = @This();
|
|
|
|
|
|
front: ?*ListNode(T) = null, // 头节点 front
|
|
|
rear: ?*ListNode(T) = null, // 尾节点 rear
|
|
|
que_size: usize = 0, // 双向队列的长度
|
|
|
mem_arena: ?std.heap.ArenaAllocator = null,
|
|
|
mem_allocator: std.mem.Allocator = undefined, // 内存分配器
|
|
|
|
|
|
// 构造方法（分配内存+初始化队列）
|
|
|
pub fn init(self: *Self, allocator: std.mem.Allocator) !void {
|
|
|
if (self.mem_arena == null) {
|
|
|
self.mem_arena = std.heap.ArenaAllocator.init(allocator);
|
|
|
self.mem_allocator = self.mem_arena.?.allocator();
|
|
|
}
|
|
|
self.front = null;
|
|
|
self.rear = null;
|
|
|
self.que_size = 0;
|
|
|
}
|
|
|
|
|
|
// 析构方法（释放内存）
|
|
|
pub fn deinit(self: *Self) void {
|
|
|
if (self.mem_arena == null) return;
|
|
|
self.mem_arena.?.deinit();
|
|
|
}
|
|
|
|
|
|
// 获取双向队列的长度
|
|
|
pub fn size(self: *Self) usize {
|
|
|
return self.que_size;
|
|
|
}
|
|
|
|
|
|
// 判断双向队列是否为空
|
|
|
pub fn isEmpty(self: *Self) bool {
|
|
|
return self.size() == 0;
|
|
|
}
|
|
|
|
|
|
// 入队操作
|
|
|
pub fn push(self: *Self, num: T, is_front: bool) !void {
|
|
|
var node = try self.mem_allocator.create(ListNode(T));
|
|
|
node.init(num);
|
|
|
// 若链表为空，则令 front, rear 都指向 node
|
|
|
if (self.isEmpty()) {
|
|
|
self.front = node;
|
|
|
self.rear = node;
|
|
|
// 队首入队操作
|
|
|
} else if (is_front) {
|
|
|
// 将 node 添加至链表头部
|
|
|
self.front.?.prev = node;
|
|
|
node.next = self.front;
|
|
|
self.front = node; // 更新头节点
|
|
|
// 队尾入队操作
|
|
|
} else {
|
|
|
// 将 node 添加至链表尾部
|
|
|
self.rear.?.next = node;
|
|
|
node.prev = self.rear;
|
|
|
self.rear = node; // 更新尾节点
|
|
|
}
|
|
|
self.que_size += 1; // 更新队列长度
|
|
|
}
|
|
|
|
|
|
// 队首入队
|
|
|
pub fn pushFirst(self: *Self, num: T) !void {
|
|
|
try self.push(num, true);
|
|
|
}
|
|
|
|
|
|
// 队尾入队
|
|
|
pub fn pushLast(self: *Self, num: T) !void {
|
|
|
try self.push(num, false);
|
|
|
}
|
|
|
|
|
|
// 出队操作
|
|
|
pub fn pop(self: *Self, is_front: bool) T {
|
|
|
if (self.isEmpty()) @panic("双向队列为空");
|
|
|
var val: T = undefined;
|
|
|
// 队首出队操作
|
|
|
if (is_front) {
|
|
|
val = self.front.?.val; // 暂存头节点值
|
|
|
// 删除头节点
|
|
|
var fNext = self.front.?.next;
|
|
|
if (fNext != null) {
|
|
|
fNext.?.prev = null;
|
|
|
self.front.?.next = null;
|
|
|
}
|
|
|
self.front = fNext; // 更新头节点
|
|
|
// 队尾出队操作
|
|
|
} else {
|
|
|
val = self.rear.?.val; // 暂存尾节点值
|
|
|
// 删除尾节点
|
|
|
var rPrev = self.rear.?.prev;
|
|
|
if (rPrev != null) {
|
|
|
rPrev.?.next = null;
|
|
|
self.rear.?.prev = null;
|
|
|
}
|
|
|
self.rear = rPrev; // 更新尾节点
|
|
|
}
|
|
|
self.que_size -= 1; // 更新队列长度
|
|
|
return val;
|
|
|
}
|
|
|
|
|
|
// 队首出队
|
|
|
pub fn popFirst(self: *Self) T {
|
|
|
return self.pop(true);
|
|
|
}
|
|
|
|
|
|
// 队尾出队
|
|
|
pub fn popLast(self: *Self) T {
|
|
|
return self.pop(false);
|
|
|
}
|
|
|
|
|
|
// 访问队首元素
|
|
|
pub fn peekFirst(self: *Self) T {
|
|
|
if (self.isEmpty()) @panic("双向队列为空");
|
|
|
return self.front.?.val;
|
|
|
}
|
|
|
|
|
|
// 访问队尾元素
|
|
|
pub fn peekLast(self: *Self) T {
|
|
|
if (self.isEmpty()) @panic("双向队列为空");
|
|
|
return self.rear.?.val;
|
|
|
}
|
|
|
|
|
|
// 返回数组用于打印
|
|
|
pub fn toArray(self: *Self) ![]T {
|
|
|
var node = self.front;
|
|
|
var res = try self.mem_allocator.alloc(T, self.size());
|
|
|
std.mem.set(T, res, @as(T, 0));
|
|
|
var i: usize = 0;
|
|
|
while (i < res.len) : (i += 1) {
|
|
|
res[i] = node.?.val;
|
|
|
node = node.?.next;
|
|
|
}
|
|
|
return res;
|
|
|
}
|
|
|
};
|
|
|
}
|
|
|
```
|
|
|
|
|
|
### 基于数组的实现
|
|
|
|
|
|
与基于数组实现队列类似，我们也可以使用环形数组来实现双向队列。在队列的实现基础上，仅需增加“队首入队”和“队尾出队”的方法。
|
|
|
|
|
|
=== "ArrayDeque"
|
|
|
|
|
|
|
|
|
=== "pushLast()"
|
|
|
|
|
|
|
|
|
=== "pushFirst()"
|
|
|
|
|
|
|
|
|
=== "popLast()"
|
|
|
|
|
|
|
|
|
=== "popFirst()"
|
|
|
|
|
|
|
|
|
以下是具体实现代码。
|
|
|
|
|
|
=== "Java"
|
|
|
|
|
|
```java title="array_deque.java"
|
|
|
/* 基于环形数组实现的双向队列 */
|
|
|
class ArrayDeque {
|
|
|
private int[] nums; // 用于存储双向队列元素的数组
|
|
|
private int front; // 队首指针，指向队首元素
|
|
|
private int queSize; // 双向队列长度
|
|
|
|
|
|
/* 构造方法 */
|
|
|
public ArrayDeque(int capacity) {
|
|
|
this.nums = new int[capacity];
|
|
|
front = queSize = 0;
|
|
|
}
|
|
|
|
|
|
/* 获取双向队列的容量 */
|
|
|
public int capacity() {
|
|
|
return nums.length;
|
|
|
}
|
|
|
|
|
|
/* 获取双向队列的长度 */
|
|
|
public int size() {
|
|
|
return queSize;
|
|
|
}
|
|
|
|
|
|
/* 判断双向队列是否为空 */
|
|
|
public boolean isEmpty() {
|
|
|
return queSize == 0;
|
|
|
}
|
|
|
|
|
|
/* 计算环形数组索引 */
|
|
|
private int index(int i) {
|
|
|
// 通过取余操作实现数组首尾相连
|
|
|
// 当 i 越过数组尾部后，回到头部
|
|
|
// 当 i 越过数组头部后，回到尾部
|
|
|
return (i + capacity()) % capacity();
|
|
|
}
|
|
|
|
|
|
/* 队首入队 */
|
|
|
public void pushFirst(int num) {
|
|
|
if (queSize == capacity()) {
|
|
|
System.out.println("双向队列已满");
|
|
|
return;
|
|
|
}
|
|
|
// 队首指针向左移动一位
|
|
|
// 通过取余操作，实现 front 越过数组头部后回到尾部
|
|
|
front = index(front - 1);
|
|
|
// 将 num 添加至队首
|
|
|
nums[front] = num;
|
|
|
queSize++;
|
|
|
}
|
|
|
|
|
|
/* 队尾入队 */
|
|
|
public void pushLast(int num) {
|
|
|
if (queSize == capacity()) {
|
|
|
System.out.println("双向队列已满");
|
|
|
return;
|
|
|
}
|
|
|
// 计算尾指针，指向队尾索引 + 1
|
|
|
int rear = index(front + queSize);
|
|
|
// 将 num 添加至队尾
|
|
|
nums[rear] = num;
|
|
|
queSize++;
|
|
|
}
|
|
|
|
|
|
/* 队首出队 */
|
|
|
public int popFirst() {
|
|
|
int num = peekFirst();
|
|
|
// 队首指针向后移动一位
|
|
|
front = index(front + 1);
|
|
|
queSize--;
|
|
|
return num;
|
|
|
}
|
|
|
|
|
|
/* 队尾出队 */
|
|
|
public int popLast() {
|
|
|
int num = peekLast();
|
|
|
queSize--;
|
|
|
return num;
|
|
|
}
|
|
|
|
|
|
/* 访问队首元素 */
|
|
|
public int peekFirst() {
|
|
|
if (isEmpty())
|
|
|
throw new EmptyStackException();
|
|
|
return nums[front];
|
|
|
}
|
|
|
|
|
|
/* 访问队尾元素 */
|
|
|
public int peekLast() {
|
|
|
if (isEmpty())
|
|
|
throw new EmptyStackException();
|
|
|
// 计算尾元素索引
|
|
|
int last = index(front + queSize - 1);
|
|
|
return nums[last];
|
|
|
}
|
|
|
|
|
|
/* 返回数组用于打印 */
|
|
|
public int[] toArray() {
|
|
|
// 仅转换有效长度范围内的列表元素
|
|
|
int[] res = new int[queSize];
|
|
|
for (int i = 0, j = front; i < queSize; i++, j++) {
|
|
|
res[i] = nums[index(j)];
|
|
|
}
|
|
|
return res;
|
|
|
}
|
|
|
}
|
|
|
```
|
|
|
|
|
|
=== "C++"
|
|
|
|
|
|
```cpp title="array_deque.cpp"
|
|
|
/* 基于环形数组实现的双向队列 */
|
|
|
class ArrayDeque {
|
|
|
private:
|
|
|
vector<int> nums; // 用于存储双向队列元素的数组
|
|
|
int front; // 队首指针，指向队首元素
|
|
|
int queSize; // 双向队列长度
|
|
|
|
|
|
public:
|
|
|
/* 构造方法 */
|
|
|
ArrayDeque(int capacity) {
|
|
|
nums.resize(capacity);
|
|
|
front = queSize = 0;
|
|
|
}
|
|
|
|
|
|
/* 获取双向队列的容量 */
|
|
|
int capacity() {
|
|
|
return nums.size();
|
|
|
}
|
|
|
|
|
|
/* 获取双向队列的长度 */
|
|
|
int size() {
|
|
|
return queSize;
|
|
|
}
|
|
|
|
|
|
/* 判断双向队列是否为空 */
|
|
|
bool isEmpty() {
|
|
|
return queSize == 0;
|
|
|
}
|
|
|
|
|
|
/* 计算环形数组索引 */
|
|
|
int index(int i) {
|
|
|
// 通过取余操作实现数组首尾相连
|
|
|
// 当 i 越过数组尾部后，回到头部
|
|
|
// 当 i 越过数组头部后，回到尾部
|
|
|
return (i + capacity()) % capacity();
|
|
|
}
|
|
|
|
|
|
/* 队首入队 */
|
|
|
void pushFirst(int num) {
|
|
|
if (queSize == capacity()) {
|
|
|
cout << "双向队列已满" << endl;
|
|
|
return;
|
|
|
}
|
|
|
// 队首指针向左移动一位
|
|
|
// 通过取余操作，实现 front 越过数组头部后回到尾部
|
|
|
front = index(front - 1);
|
|
|
// 将 num 添加至队首
|
|
|
nums[front] = num;
|
|
|
queSize++;
|
|
|
}
|
|
|
|
|
|
/* 队尾入队 */
|
|
|
void pushLast(int num) {
|
|
|
if (queSize == capacity()) {
|
|
|
cout << "双向队列已满" << endl;
|
|
|
return;
|
|
|
}
|
|
|
// 计算尾指针，指向队尾索引 + 1
|
|
|
int rear = index(front + queSize);
|
|
|
// 将 num 添加至队尾
|
|
|
nums[rear] = num;
|
|
|
queSize++;
|
|
|
}
|
|
|
|
|
|
/* 队首出队 */
|
|
|
int popFirst() {
|
|
|
int num = peekFirst();
|
|
|
// 队首指针向后移动一位
|
|
|
front = index(front + 1);
|
|
|
queSize--;
|
|
|
return num;
|
|
|
}
|
|
|
|
|
|
/* 队尾出队 */
|
|
|
int popLast() {
|
|
|
int num = peekLast();
|
|
|
queSize--;
|
|
|
return num;
|
|
|
}
|
|
|
|
|
|
/* 访问队首元素 */
|
|
|
int peekFirst() {
|
|
|
if (isEmpty())
|
|
|
throw out_of_range("双向队列为空");
|
|
|
return nums[front];
|
|
|
}
|
|
|
|
|
|
/* 访问队尾元素 */
|
|
|
int peekLast() {
|
|
|
if (isEmpty())
|
|
|
throw out_of_range("双向队列为空");
|
|
|
// 计算尾元素索引
|
|
|
int last = index(front + queSize - 1);
|
|
|
return nums[last];
|
|
|
}
|
|
|
|
|
|
/* 返回数组用于打印 */
|
|
|
vector<int> toVector() {
|
|
|
// 仅转换有效长度范围内的列表元素
|
|
|
vector<int> res(queSize);
|
|
|
for (int i = 0, j = front; i < queSize; i++, j++) {
|
|
|
res[i] = nums[index(j)];
|
|
|
}
|
|
|
return res;
|
|
|
}
|
|
|
};
|
|
|
```
|
|
|
|
|
|
=== "Python"
|
|
|
|
|
|
```python title="array_deque.py"
|
|
|
class ArrayDeque:
|
|
|
"""基于环形数组实现的双向队列"""
|
|
|
|
|
|
def __init__(self, capacity: int) -> None:
|
|
|
"""构造方法"""
|
|
|
self.__nums: list[int] = [0] * capacity
|
|
|
self.__front: int = 0
|
|
|
self.__size: int = 0
|
|
|
|
|
|
def capacity(self) -> int:
|
|
|
"""获取双向队列的容量"""
|
|
|
return len(self.__nums)
|
|
|
|
|
|
def size(self) -> int:
|
|
|
"""获取双向队列的长度"""
|
|
|
return self.__size
|
|
|
|
|
|
def is_empty(self) -> bool:
|
|
|
"""判断双向队列是否为空"""
|
|
|
return self.__size == 0
|
|
|
|
|
|
def index(self, i: int) -> int:
|
|
|
"""计算环形数组索引"""
|
|
|
# 通过取余操作实现数组首尾相连
|
|
|
# 当 i 越过数组尾部后，回到头部
|
|
|
# 当 i 越过数组头部后，回到尾部
|
|
|
return (i + self.capacity()) % self.capacity()
|
|
|
|
|
|
def push_first(self, num: int) -> None:
|
|
|
"""队首入队"""
|
|
|
if self.__size == self.capacity():
|
|
|
print("双向队列已满")
|
|
|
return
|
|
|
# 队首指针向左移动一位
|
|
|
# 通过取余操作，实现 front 越过数组头部后回到尾部
|
|
|
self.__front = self.index(self.__front - 1)
|
|
|
# 将 num 添加至队首
|
|
|
self.__nums[self.__front] = num
|
|
|
self.__size += 1
|
|
|
|
|
|
def push_last(self, num: int) -> None:
|
|
|
"""队尾入队"""
|
|
|
if self.__size == self.capacity():
|
|
|
print("双向队列已满")
|
|
|
return
|
|
|
# 计算尾指针，指向队尾索引 + 1
|
|
|
rear = self.index(self.__front + self.__size)
|
|
|
# 将 num 添加至队尾
|
|
|
self.__nums[rear] = num
|
|
|
self.__size += 1
|
|
|
|
|
|
def pop_first(self) -> int:
|
|
|
"""队首出队"""
|
|
|
num = self.peek_first()
|
|
|
# 队首指针向后移动一位
|
|
|
self.__front = self.index(self.__front + 1)
|
|
|
self.__size -= 1
|
|
|
return num
|
|
|
|
|
|
def pop_last(self) -> int:
|
|
|
"""队尾出队"""
|
|
|
num = self.peek_last()
|
|
|
self.__size -= 1
|
|
|
return num
|
|
|
|
|
|
def peek_first(self) -> int:
|
|
|
"""访问队首元素"""
|
|
|
assert not self.is_empty(), "双向队列为空"
|
|
|
return self.__nums[self.__front]
|
|
|
|
|
|
def peek_last(self) -> int:
|
|
|
"""访问队尾元素"""
|
|
|
assert not self.is_empty(), "双向队列为空"
|
|
|
# 计算尾元素索引
|
|
|
last = self.index(self.__front + self.__size - 1)
|
|
|
return self.__nums[last]
|
|
|
|
|
|
def to_array(self) -> list[int]:
|
|
|
"""返回数组用于打印"""
|
|
|
# 仅转换有效长度范围内的列表元素
|
|
|
res = []
|
|
|
for i in range(self.__size):
|
|
|
res.append(self.__nums[self.index(self.__front + i)])
|
|
|
return res
|
|
|
```
|
|
|
|
|
|
=== "Go"
|
|
|
|
|
|
```go title="array_deque.go"
|
|
|
/* 基于环形数组实现的双向队列 */
|
|
|
type arrayDeque struct {
|
|
|
nums []int // 用于存储双向队列元素的数组
|
|
|
front int // 队首指针，指向队首元素
|
|
|
queSize int // 双向队列长度
|
|
|
queCapacity int // 队列容量（即最大容纳元素数量）
|
|
|
}
|
|
|
|
|
|
/* 初始化队列 */
|
|
|
func newArrayDeque(queCapacity int) *arrayDeque {
|
|
|
return &arrayDeque{
|
|
|
nums: make([]int, queCapacity),
|
|
|
queCapacity: queCapacity,
|
|
|
front: 0,
|
|
|
queSize: 0,
|
|
|
}
|
|
|
}
|
|
|
|
|
|
/* 获取双向队列的长度 */
|
|
|
func (q *arrayDeque) size() int {
|
|
|
return q.queSize
|
|
|
}
|
|
|
|
|
|
/* 判断双向队列是否为空 */
|
|
|
func (q *arrayDeque) isEmpty() bool {
|
|
|
return q.queSize == 0
|
|
|
}
|
|
|
|
|
|
/* 计算环形数组索引 */
|
|
|
func (q *arrayDeque) index(i int) int {
|
|
|
// 通过取余操作实现数组首尾相连
|
|
|
// 当 i 越过数组尾部后，回到头部
|
|
|
// 当 i 越过数组头部后，回到尾部
|
|
|
return (i + q.queCapacity) % q.queCapacity
|
|
|
}
|
|
|
|
|
|
/* 队首入队 */
|
|
|
func (q *arrayDeque) pushFirst(num int) {
|
|
|
if q.queSize == q.queCapacity {
|
|
|
fmt.Println("双向队列已满")
|
|
|
return
|
|
|
}
|
|
|
// 队首指针向左移动一位
|
|
|
// 通过取余操作，实现 front 越过数组头部后回到尾部
|
|
|
q.front = q.index(q.front - 1)
|
|
|
// 将 num 添加至队首
|
|
|
q.nums[q.front] = num
|
|
|
q.queSize++
|
|
|
}
|
|
|
|
|
|
/* 队尾入队 */
|
|
|
func (q *arrayDeque) pushLast(num int) {
|
|
|
if q.queSize == q.queCapacity {
|
|
|
fmt.Println("双向队列已满")
|
|
|
return
|
|
|
}
|
|
|
// 计算尾指针，指向队尾索引 + 1
|
|
|
rear := q.index(q.front + q.queSize)
|
|
|
// 将 num 添加至队首
|
|
|
q.nums[rear] = num
|
|
|
q.queSize++
|
|
|
}
|
|
|
|
|
|
/* 队首出队 */
|
|
|
func (q *arrayDeque) popFirst() any {
|
|
|
num := q.peekFirst()
|
|
|
// 队首指针向后移动一位
|
|
|
q.front = q.index(q.front + 1)
|
|
|
q.queSize--
|
|
|
return num
|
|
|
}
|
|
|
|
|
|
/* 队尾出队 */
|
|
|
func (q *arrayDeque) popLast() any {
|
|
|
num := q.peekLast()
|
|
|
q.queSize--
|
|
|
return num
|
|
|
}
|
|
|
|
|
|
/* 访问队首元素 */
|
|
|
func (q *arrayDeque) peekFirst() any {
|
|
|
if q.isEmpty() {
|
|
|
return nil
|
|
|
}
|
|
|
return q.nums[q.front]
|
|
|
}
|
|
|
|
|
|
/* 访问队尾元素 */
|
|
|
func (q *arrayDeque) peekLast() any {
|
|
|
if q.isEmpty() {
|
|
|
return nil
|
|
|
}
|
|
|
// 计算尾元素索引
|
|
|
last := q.index(q.front + q.queSize - 1)
|
|
|
return q.nums[last]
|
|
|
}
|
|
|
|
|
|
/* 获取 Slice 用于打印 */
|
|
|
func (q *arrayDeque) toSlice() []int {
|
|
|
// 仅转换有效长度范围内的列表元素
|
|
|
res := make([]int, q.queSize)
|
|
|
for i, j := 0, q.front; i < q.queSize; i++ {
|
|
|
res[i] = q.nums[q.index(j)]
|
|
|
j++
|
|
|
}
|
|
|
return res
|
|
|
}
|
|
|
```
|
|
|
|
|
|
=== "JavaScript"
|
|
|
|
|
|
```javascript title="array_deque.js"
|
|
|
/* 基于环形数组实现的双向队列 */
|
|
|
class ArrayDeque {
|
|
|
#nums; // 用于存储双向队列元素的数组
|
|
|
#front; // 队首指针，指向队首元素
|
|
|
#queSize; // 双向队列长度
|
|
|
|
|
|
/* 构造方法 */
|
|
|
constructor(capacity) {
|
|
|
this.#nums = new Array(capacity);
|
|
|
this.#front = 0;
|
|
|
this.#queSize = 0;
|
|
|
}
|
|
|
|
|
|
/* 获取双向队列的容量 */
|
|
|
capacity() {
|
|
|
return this.#nums.length;
|
|
|
}
|
|
|
|
|
|
/* 获取双向队列的长度 */
|
|
|
size() {
|
|
|
return this.#queSize;
|
|
|
}
|
|
|
|
|
|
/* 判断双向队列是否为空 */
|
|
|
isEmpty() {
|
|
|
return this.#queSize === 0;
|
|
|
}
|
|
|
|
|
|
/* 计算环形数组索引 */
|
|
|
index(i) {
|
|
|
// 通过取余操作实现数组首尾相连
|
|
|
// 当 i 越过数组尾部后，回到头部
|
|
|
// 当 i 越过数组头部后，回到尾部
|
|
|
return (i + this.capacity()) % this.capacity();
|
|
|
}
|
|
|
|
|
|
/* 队首入队 */
|
|
|
pushFirst(num) {
|
|
|
if (this.#queSize === this.capacity()) {
|
|
|
console.log("双向队列已满");
|
|
|
return;
|
|
|
}
|
|
|
// 队首指针向左移动一位
|
|
|
// 通过取余操作，实现 front 越过数组头部后回到尾部
|
|
|
this.#front = this.index(this.#front - 1);
|
|
|
// 将 num 添加至队首
|
|
|
this.#nums[this.#front] = num;
|
|
|
this.#queSize++;
|
|
|
}
|
|
|
|
|
|
/* 队尾入队 */
|
|
|
pushLast(num) {
|
|
|
if (this.#queSize === this.capacity()) {
|
|
|
console.log("双向队列已满");
|
|
|
return;
|
|
|
}
|
|
|
// 计算尾指针，指向队尾索引 + 1
|
|
|
const rear = this.index(this.#front + this.#queSize);
|
|
|
// 将 num 添加至队尾
|
|
|
this.#nums[rear] = num;
|
|
|
this.#queSize++;
|
|
|
}
|
|
|
|
|
|
/* 队首出队 */
|
|
|
popFirst() {
|
|
|
const num = this.peekFirst();
|
|
|
// 队首指针向后移动一位
|
|
|
this.#front = this.index(this.#front + 1);
|
|
|
this.#queSize--;
|
|
|
return num;
|
|
|
}
|
|
|
|
|
|
/* 队尾出队 */
|
|
|
popLast() {
|
|
|
const num = this.peekLast();
|
|
|
this.#queSize--;
|
|
|
return num;
|
|
|
}
|
|
|
|
|
|
/* 访问队首元素 */
|
|
|
peekFirst() {
|
|
|
if (this.isEmpty())
|
|
|
throw new Error("The Deque Is Empty.");
|
|
|
return this.#nums[this.#front];
|
|
|
}
|
|
|
|
|
|
/* 访问队尾元素 */
|
|
|
peekLast() {
|
|
|
if (this.isEmpty())
|
|
|
throw new Error("The Deque Is Empty.");
|
|
|
// 计算尾元素索引
|
|
|
const last = this.index(this.#front + this.#queSize - 1);
|
|
|
return this.#nums[last];
|
|
|
}
|
|
|
|
|
|
/* 返回数组用于打印 */
|
|
|
toArray() {
|
|
|
// 仅转换有效长度范围内的列表元素
|
|
|
const res = [];
|
|
|
for (let i = 0, j = this.#front; i < this.#queSize; i++, j++) {
|
|
|
res[i] = this.#nums[this.index(j)];
|
|
|
}
|
|
|
return res;
|
|
|
}
|
|
|
}
|
|
|
```
|
|
|
|
|
|
=== "TypeScript"
|
|
|
|
|
|
```typescript title="array_deque.ts"
|
|
|
/* 基于环形数组实现的双向队列 */
|
|
|
class ArrayDeque {
|
|
|
private nums: number[]; // 用于存储双向队列元素的数组
|
|
|
private front: number; // 队首指针，指向队首元素
|
|
|
private queSize: number; // 双向队列长度
|
|
|
|
|
|
/* 构造方法 */
|
|
|
constructor(capacity: number) {
|
|
|
this.nums = new Array(capacity);
|
|
|
this.front = 0;
|
|
|
this.queSize = 0;
|
|
|
}
|
|
|
|
|
|
/* 获取双向队列的容量 */
|
|
|
capacity(): number {
|
|
|
return this.nums.length;
|
|
|
}
|
|
|
|
|
|
/* 获取双向队列的长度 */
|
|
|
size(): number {
|
|
|
return this.queSize;
|
|
|
}
|
|
|
|
|
|
/* 判断双向队列是否为空 */
|
|
|
isEmpty(): boolean {
|
|
|
return this.queSize === 0;
|
|
|
}
|
|
|
|
|
|
/* 计算环形数组索引 */
|
|
|
index(i: number): number {
|
|
|
// 通过取余操作实现数组首尾相连
|
|
|
// 当 i 越过数组尾部后，回到头部
|
|
|
// 当 i 越过数组头部后，回到尾部
|
|
|
return (i + this.capacity()) % this.capacity();
|
|
|
}
|
|
|
|
|
|
/* 队首入队 */
|
|
|
pushFirst(num: number): void {
|
|
|
if (this.queSize === this.capacity()) {
|
|
|
console.log("双向队列已满");
|
|
|
return;
|
|
|
}
|
|
|
// 队首指针向左移动一位
|
|
|
// 通过取余操作，实现 front 越过数组头部后回到尾部
|
|
|
this.front = this.index(this.front - 1);
|
|
|
// 将 num 添加至队首
|
|
|
this.nums[this.front] = num;
|
|
|
this.queSize++;
|
|
|
}
|
|
|
|
|
|
/* 队尾入队 */
|
|
|
pushLast(num: number): void {
|
|
|
if (this.queSize === this.capacity()) {
|
|
|
console.log("双向队列已满");
|
|
|
return;
|
|
|
}
|
|
|
// 计算尾指针，指向队尾索引 + 1
|
|
|
const rear: number = this.index(this.front + this.queSize);
|
|
|
// 将 num 添加至队尾
|
|
|
this.nums[rear] = num;
|
|
|
this.queSize++;
|
|
|
}
|
|
|
|
|
|
/* 队首出队 */
|
|
|
popFirst(): number {
|
|
|
const num: number = this.peekFirst();
|
|
|
// 队首指针向后移动一位
|
|
|
this.front = this.index(this.front + 1);
|
|
|
this.queSize--;
|
|
|
return num;
|
|
|
}
|
|
|
|
|
|
/* 队尾出队 */
|
|
|
popLast(): number {
|
|
|
const num: number = this.peekLast();
|
|
|
this.queSize--;
|
|
|
return num;
|
|
|
}
|
|
|
|
|
|
/* 访问队首元素 */
|
|
|
peekFirst(): number {
|
|
|
if (this.isEmpty())
|
|
|
throw new Error("The Deque Is Empty.");
|
|
|
return this.nums[this.front];
|
|
|
}
|
|
|
|
|
|
/* 访问队尾元素 */
|
|
|
peekLast(): number {
|
|
|
if (this.isEmpty())
|
|
|
throw new Error("The Deque Is Empty.");
|
|
|
// 计算尾元素索引
|
|
|
const last = this.index(this.front + this.queSize - 1);
|
|
|
return this.nums[last];
|
|
|
}
|
|
|
|
|
|
/* 返回数组用于打印 */
|
|
|
toArray(): number[] {
|
|
|
// 仅转换有效长度范围内的列表元素
|
|
|
const res: number[] = [];
|
|
|
for (let i = 0, j = this.front; i < this.queSize; i++, j++) {
|
|
|
res[i] = this.nums[this.index(j)];
|
|
|
}
|
|
|
return res;
|
|
|
}
|
|
|
}
|
|
|
```
|
|
|
|
|
|
=== "C"
|
|
|
|
|
|
```c title="array_deque.c"
|
|
|
[class]{ArrayDeque}-[func]{}
|
|
|
```
|
|
|
|
|
|
=== "C#"
|
|
|
|
|
|
```csharp title="array_deque.cs"
|
|
|
[class]{ArrayDeque}-[func]{}
|
|
|
```
|
|
|
|
|
|
=== "Swift"
|
|
|
|
|
|
```swift title="array_deque.swift"
|
|
|
/* 基于环形数组实现的双向队列 */
|
|
|
class ArrayDeque {
|
|
|
private var nums: [Int] // 用于存储双向队列元素的数组
|
|
|
private var front: Int // 队首指针，指向队首元素
|
|
|
private var queSize: Int // 双向队列长度
|
|
|
|
|
|
/* 构造方法 */
|
|
|
init(capacity: Int) {
|
|
|
nums = Array(repeating: 0, count: capacity)
|
|
|
front = 0
|
|
|
queSize = 0
|
|
|
}
|
|
|
|
|
|
/* 获取双向队列的容量 */
|
|
|
func capacity() -> Int {
|
|
|
nums.count
|
|
|
}
|
|
|
|
|
|
/* 获取双向队列的长度 */
|
|
|
func size() -> Int {
|
|
|
queSize
|
|
|
}
|
|
|
|
|
|
/* 判断双向队列是否为空 */
|
|
|
func isEmpty() -> Bool {
|
|
|
size() == 0
|
|
|
}
|
|
|
|
|
|
/* 计算环形数组索引 */
|
|
|
private func index(i: Int) -> Int {
|
|
|
// 通过取余操作实现数组首尾相连
|
|
|
// 当 i 越过数组尾部后，回到头部
|
|
|
// 当 i 越过数组头部后，回到尾部
|
|
|
(i + capacity()) % capacity()
|
|
|
}
|
|
|
|
|
|
/* 队首入队 */
|
|
|
func pushFirst(num: Int) {
|
|
|
if size() == capacity() {
|
|
|
print("双向队列已满")
|
|
|
return
|
|
|
}
|
|
|
// 队首指针向左移动一位
|
|
|
// 通过取余操作，实现 front 越过数组头部后回到尾部
|
|
|
front = index(i: front - 1)
|
|
|
// 将 num 添加至队首
|
|
|
nums[front] = num
|
|
|
queSize += 1
|
|
|
}
|
|
|
|
|
|
/* 队尾入队 */
|
|
|
func pushLast(num: Int) {
|
|
|
if size() == capacity() {
|
|
|
print("双向队列已满")
|
|
|
return
|
|
|
}
|
|
|
// 计算尾指针，指向队尾索引 + 1
|
|
|
let rear = index(i: front + size())
|
|
|
// 将 num 添加至队尾
|
|
|
nums[rear] = num
|
|
|
queSize += 1
|
|
|
}
|
|
|
|
|
|
/* 队首出队 */
|
|
|
func popFirst() -> Int {
|
|
|
let num = peekFirst()
|
|
|
// 队首指针向后移动一位
|
|
|
front = index(i: front + 1)
|
|
|
queSize -= 1
|
|
|
return num
|
|
|
}
|
|
|
|
|
|
/* 队尾出队 */
|
|
|
func popLast() -> Int {
|
|
|
let num = peekLast()
|
|
|
queSize -= 1
|
|
|
return num
|
|
|
}
|
|
|
|
|
|
/* 访问队首元素 */
|
|
|
func peekFirst() -> Int {
|
|
|
if isEmpty() {
|
|
|
fatalError("双向队列为空")
|
|
|
}
|
|
|
return nums[front]
|
|
|
}
|
|
|
|
|
|
/* 访问队尾元素 */
|
|
|
func peekLast() -> Int {
|
|
|
if isEmpty() {
|
|
|
fatalError("双向队列为空")
|
|
|
}
|
|
|
// 计算尾元素索引
|
|
|
let last = index(i: front + size() - 1)
|
|
|
return nums[last]
|
|
|
}
|
|
|
|
|
|
/* 返回数组用于打印 */
|
|
|
func toArray() -> [Int] {
|
|
|
// 仅转换有效长度范围内的列表元素
|
|
|
var res = Array(repeating: 0, count: size())
|
|
|
for (i, j) in sequence(first: (0, front), next: { $0 < self.size() - 1 ? ($0 + 1, $1 + 1) : nil }) {
|
|
|
res[i] = nums[index(i: j)]
|
|
|
}
|
|
|
return res
|
|
|
}
|
|
|
}
|
|
|
```
|
|
|
|
|
|
=== "Zig"
|
|
|
|
|
|
```zig title="array_deque.zig"
|
|
|
[class]{ArrayDeque}-[func]{}
|
|
|
```
|
|
|
|
|
|
## 5.3.3. 双向队列应用
|
|
|
|
|
|
双向队列兼具栈与队列的逻辑，**因此它可以实现这两者的所有应用场景，同时提供更高的自由度**。
|
|
|
|
|
|
我们知道，软件的“撤销”功能通常使用栈来实现：系统将每次更改操作 `push` 到栈中，然后通过 `pop` 实现撤销。然而，考虑到系统资源的限制，软件通常会限制撤销的步数（例如仅允许保存 $50$ 步）。当栈的长度超过 $50$ 时，软件需要在栈底（即队首）执行删除操作。**但栈无法实现该功能，此时就需要使用双向队列来替代栈**。请注意，“撤销”的核心逻辑仍然遵循栈的先入后出原则，只是双向队列能够更加灵活地实现一些额外逻辑。
|
