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---
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comments: true
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---
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# 栈
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「栈 Stack」是一种遵循「先入后出 first in, last out」数据操作规则的线性数据结构。我们可以将栈类比为放在桌面上的一摞盘子，如果需要拿出底部的盘子，则需要先将上面的盘子依次取出。
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“盘子”是一种形象比喻，我们将盘子替换为任意一种元素（例如整数、字符、对象等），就得到了栈数据结构。
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我们将这一摞元素的顶部称为「栈顶」，将底部称为「栈底」，将把元素添加到栈顶的操作称为「入栈」，将删除栈顶元素的操作称为「出栈」。
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<p align="center"> Fig. 栈的先入后出特性 </p>
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## 栈常用操作
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栈的常用操作见下表（方法命名以 Java 为例）。
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<p align="center"> Table. 栈的常用操作 </p>
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<div class="center-table" markdown>
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| 方法 | 描述 | 时间复杂度 |
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| --------- | ---------------------- | ---------- |
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| push() | 元素入栈（添加至栈顶） | $O(1)$ |
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| pop() | 栈顶元素出栈 | $O(1)$ |
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| peek() | 访问栈顶元素 | $O(1)$ |
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| size() | 获取栈的长度 | $O(1)$ |
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| isEmpty() | 判断栈是否为空 | $O(1)$ |
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</div>
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我们可以直接使用编程语言实现好的栈类。
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=== "Java"
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```java title="stack.java"
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/* 初始化栈 */
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// 在 Java 中，推荐将 LinkedList 当作栈来使用
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LinkedList<Integer> stack = new LinkedList<>();
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/* 元素入栈 */
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stack.addLast(1);
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stack.addLast(3);
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stack.addLast(2);
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stack.addLast(5);
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stack.addLast(4);
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/* 访问栈顶元素 */
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int peek = stack.peekLast();
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/* 元素出栈 */
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int pop = stack.removeLast();
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/* 获取栈的长度 */
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int size = stack.size();
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/* 判断是否为空 */
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boolean isEmpty = stack.isEmpty();
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```
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=== "C++"
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```cpp title="stack.cpp"
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/* 初始化栈 */
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stack<int> stack;
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/* 元素入栈 */
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stack.push(1);
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stack.push(3);
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stack.push(2);
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stack.push(5);
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stack.push(4);
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/* 访问栈顶元素 */
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int top = stack.top();
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/* 元素出栈 */
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stack.pop();
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/* 获取栈的长度 */
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int size = stack.size();
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/* 判断是否为空 */
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bool empty = stack.empty();
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```
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=== "Python"
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```python title="stack.py"
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""" 初始化栈 """
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# Python 没有内置的栈类，可以把 List 当作栈来使用
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stack = []
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""" 元素入栈 """
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stack.append(1)
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stack.append(3)
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stack.append(2)
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stack.append(5)
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stack.append(4)
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""" 访问栈顶元素 """
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peek = stack[-1]
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""" 元素出栈 """
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pop = stack.pop()
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""" 获取栈的长度 """
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size = len(stack)
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""" 判断是否为空 """
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is_empty = len(stack) == 0
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```
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=== "Go"
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```go title="stack_test.go"
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/* 初始化栈 */
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// 在 Go 中，推荐将 Slice 当作栈来使用
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var stack []int
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/* 元素入栈 */
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stack = append(stack, 1)
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stack = append(stack, 3)
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stack = append(stack, 2)
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stack = append(stack, 5)
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stack = append(stack, 4)
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/* 访问栈顶元素 */
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peek := stack[len(stack)-1]
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/* 元素出栈 */
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pop := stack[len(stack)-1]
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stack = stack[:len(stack)-1]
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/* 获取栈的长度 */
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size := len(stack)
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/* 判断是否为空 */
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isEmpty := len(stack) == 0
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```
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=== "JavaScript"
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```js title="stack.js"
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/* 初始化栈 */
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// Javascript 没有内置的栈类，可以把 Array 当作栈来使用
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const stack = [];
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/* 元素入栈 */
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stack.push(1);
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stack.push(3);
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stack.push(2);
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stack.push(5);
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stack.push(4);
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/* 访问栈顶元素 */
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const peek = stack[stack.length-1];
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/* 元素出栈 */
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const pop = stack.pop();
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/* 获取栈的长度 */
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const size = stack.length;
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/* 判断是否为空 */
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const is_empty = stack.length === 0;
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```
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=== "TypeScript"
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```typescript title="stack.ts"
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/* 初始化栈 */
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// Typescript 没有内置的栈类，可以把 Array 当作栈来使用
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const stack: number[] = [];
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/* 元素入栈 */
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stack.push(1);
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stack.push(3);
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stack.push(2);
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stack.push(5);
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stack.push(4);
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/* 访问栈顶元素 */
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const peek = stack[stack.length - 1];
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/* 元素出栈 */
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const pop = stack.pop();
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/* 获取栈的长度 */
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const size = stack.length;
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/* 判断是否为空 */
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const is_empty = stack.length === 0;
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```
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=== "C"
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```c title="stack.c"
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```
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=== "C#"
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```csharp title="stack.cs"
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/* 初始化栈 */
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Stack<int> stack = new ();
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/* 元素入栈 */
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stack.Push(1);
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stack.Push(3);
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stack.Push(2);
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stack.Push(5);
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stack.Push(4);
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/* 访问栈顶元素 */
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int peek = stack.Peek();
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/* 元素出栈 */
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int pop = stack.Pop();
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/* 获取栈的长度 */
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int size = stack.Count();
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/* 判断是否为空 */
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bool isEmpty = stack.Count()==0;
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```
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=== "Swift"
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```swift title="stack.swift"
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/* 初始化栈 */
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// Swift 没有内置的栈类，可以把 Array 当作栈来使用
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var stack: [Int] = []
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/* 元素入栈 */
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stack.append(1)
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stack.append(3)
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stack.append(2)
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stack.append(5)
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stack.append(4)
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/* 访问栈顶元素 */
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let peek = stack.last!
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/* 元素出栈 */
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let pop = stack.removeLast()
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/* 获取栈的长度 */
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let size = stack.count
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/* 判断是否为空 */
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let isEmpty = stack.isEmpty
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```
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## 栈的实现
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为了更加清晰地了解栈的运行机制，接下来我们来自己动手实现一个栈类。
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栈规定元素是先入后出的，因此我们只能在栈顶添加或删除元素。然而，数组或链表都可以在任意位置添加删除元素，因此 **栈可被看作是一种受约束的数组或链表**。换言之，我们可以“屏蔽”数组或链表的部分无关操作，使之对外的表现逻辑符合栈的规定即可。
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### 基于链表的实现
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使用「链表」实现栈时，将链表的头结点看作栈顶，尾结点看作栈底。
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对于入栈操作，将元素插入到链表头部即可，这种结点添加方式被称为“头插法”。而对于出栈操作，则将头结点从链表中删除即可。
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受益于链表的离散存储方式，栈的扩容更加灵活，删除元素的内存也会被系统自动回收；缺点是无法像数组一样高效地随机访问，并且由于链表结点需存储指针，导致单个元素占用空间更大。
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=== "Java"
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```java title="linkedlist_stack.java"
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/* 基于链表实现的栈 */
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class LinkedListStack {
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private ListNode stackPeek; // 将头结点作为栈顶
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private int stkSize = 0; // 栈的长度
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public LinkedListStack() {
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stackPeek = null;
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}
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/* 获取栈的长度 */
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public int size() {
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return stkSize;
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}
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/* 判断栈是否为空 */
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public boolean isEmpty() {
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return size() == 0;
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}
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/* 入栈 */
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public void push(int num) {
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ListNode node = new ListNode(num);
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node.next = stackPeek;
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stackPeek = node;
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stkSize++;
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}
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/* 出栈 */
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public int pop() {
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int num = peek();
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stackPeek = stackPeek.next;
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stkSize--;
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return num;
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}
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/* 访问栈顶元素 */
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public int peek() {
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if (size() == 0)
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throw new EmptyStackException();
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return stackPeek.val;
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}
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}
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```
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=== "C++"
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```cpp title="linkedlist_stack.cpp"
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/* 基于链表实现的栈 */
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class LinkedListStack {
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private:
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ListNode* stackTop; // 将头结点作为栈顶
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int stkSize; // 栈的长度
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public:
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LinkedListStack() {
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stackTop = nullptr;
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stkSize = 0;
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}
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~LinkedListStack() {
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freeMemoryLinkedList(stackTop);
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}
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/* 获取栈的长度 */
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int size() {
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return stkSize;
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}
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/* 判断栈是否为空 */
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bool empty() {
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return size() == 0;
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}
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/* 入栈 */
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void push(int num) {
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ListNode* node = new ListNode(num);
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node->next = stackTop;
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stackTop = node;
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stkSize++;
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}
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/* 出栈 */
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void pop() {
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int num = top();
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ListNode *tmp = stackTop;
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stackTop = stackTop->next;
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// 释放内存
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delete tmp;
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stkSize--;
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}
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/* 访问栈顶元素 */
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int top() {
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if (size() == 0)
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throw out_of_range("栈为空");
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return stackTop->val;
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}
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};
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```
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=== "Python"
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```python title="linkedlist_stack.py"
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""" 基于链表实现的栈 """
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class LinkedListStack:
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def __init__(self):
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self.__peek = None
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self.__size = 0
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""" 获取栈的长度 """
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def size(self):
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return self.__size
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""" 判断栈是否为空 """
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def is_empty(self):
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return not self.__peek
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""" 入栈 """
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def push(self, val):
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node = ListNode(val)
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node.next = self.__peek
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self.__peek = node
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self.__size += 1
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""" 出栈 """
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def pop(self):
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num = self.peek()
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self.__peek = self.__peek.next
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self.__size -= 1
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return num
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""" 访问栈顶元素 """
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def peek(self):
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# 判空处理
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if not self.__peek: return None
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return self.__peek.val
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```
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=== "Go"
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```go title="linkedlist_stack.go"
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/* 基于链表实现的栈 */
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type linkedListStack struct {
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// 使用内置包 list 来实现栈
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data *list.List
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}
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// newLinkedListStack 初始化链表
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func newLinkedListStack() *linkedListStack {
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return &linkedListStack{
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data: list.New(),
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}
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}
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// push 入栈
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func (s *linkedListStack) push(value int) {
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s.data.PushBack(value)
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}
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// pop 出栈
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func (s *linkedListStack) pop() any {
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if s.isEmpty() {
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return nil
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}
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e := s.data.Back()
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s.data.Remove(e)
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return e.Value
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}
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// peek 访问栈顶元素
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func (s *linkedListStack) peek() any {
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if s.isEmpty() {
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return nil
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}
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e := s.data.Back()
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return e.Value
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}
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// size 获取栈的长度
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func (s *linkedListStack) size() int {
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return s.data.Len()
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}
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// isEmpty 判断栈是否为空
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func (s *linkedListStack) isEmpty() bool {
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return s.data.Len() == 0
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}
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```
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=== "JavaScript"
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```js title="linkedlist_stack.js"
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/* 基于链表实现的栈 */
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class LinkedListStack {
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#stackPeek; // 将头结点作为栈顶
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#stkSize = 0; // 栈的长度
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|
constructor() {
|
|
|
this.#stackPeek = null;
|
|
|
}
|
|
|
|
|
|
/* 获取栈的长度 */
|
|
|
get size() {
|
|
|
return this.#stkSize;
|
|
|
}
|
|
|
|
|
|
/* 判断栈是否为空 */
|
|
|
isEmpty() {
|
|
|
return this.size == 0;
|
|
|
}
|
|
|
|
|
|
/* 入栈 */
|
|
|
push(num) {
|
|
|
const node = new ListNode(num);
|
|
|
node.next = this.#stackPeek;
|
|
|
this.#stackPeek = node;
|
|
|
this.#stkSize++;
|
|
|
}
|
|
|
|
|
|
/* 出栈 */
|
|
|
pop() {
|
|
|
const num = this.peek();
|
|
|
if (!this.#stackPeek) {
|
|
|
throw new Error("栈为空！");
|
|
|
}
|
|
|
this.#stackPeek = this.#stackPeek.next;
|
|
|
this.#stkSize--;
|
|
|
return num;
|
|
|
}
|
|
|
|
|
|
/* 访问栈顶元素 */
|
|
|
peek() {
|
|
|
if (!this.#stackPeek) {
|
|
|
throw new Error("栈为空！");
|
|
|
}
|
|
|
return this.#stackPeek.val;
|
|
|
}
|
|
|
|
|
|
/* 将链表转化为 Array 并返回 */
|
|
|
toArray() {
|
|
|
let node = this.#stackPeek;
|
|
|
const res = new Array(this.size);
|
|
|
for (let i = res.length - 1; i >= 0; i--) {
|
|
|
res[i] = node.val;
|
|
|
node = node.next;
|
|
|
}
|
|
|
return res;
|
|
|
}
|
|
|
}
|
|
|
```
|
|
|
|
|
|
=== "TypeScript"
|
|
|
|
|
|
```typescript title="linkedlist_stack.ts"
|
|
|
/* 基于链表实现的栈 */
|
|
|
class LinkedListStack {
|
|
|
private stackPeek: ListNode | null; // 将头结点作为栈顶
|
|
|
private stkSize: number = 0; // 栈的长度
|
|
|
|
|
|
constructor() {
|
|
|
this.stackPeek = null;
|
|
|
}
|
|
|
|
|
|
/* 获取栈的长度 */
|
|
|
get size(): number {
|
|
|
return this.stkSize;
|
|
|
}
|
|
|
|
|
|
/* 判断栈是否为空 */
|
|
|
isEmpty(): boolean {
|
|
|
return this.size == 0;
|
|
|
}
|
|
|
|
|
|
/* 入栈 */
|
|
|
push(num: number): void {
|
|
|
const node = new ListNode(num);
|
|
|
node.next = this.stackPeek;
|
|
|
this.stackPeek = node;
|
|
|
this.stkSize++;
|
|
|
}
|
|
|
|
|
|
/* 出栈 */
|
|
|
pop(): number {
|
|
|
const num = this.peek();
|
|
|
if (!this.stackPeek) {
|
|
|
throw new Error("栈为空！");
|
|
|
}
|
|
|
this.stackPeek = this.stackPeek.next;
|
|
|
this.stkSize--;
|
|
|
return num;
|
|
|
}
|
|
|
|
|
|
/* 访问栈顶元素 */
|
|
|
peek(): number {
|
|
|
if (!this.stackPeek) {
|
|
|
throw new Error("栈为空！");
|
|
|
}
|
|
|
return this.stackPeek.val;
|
|
|
}
|
|
|
|
|
|
/* 将链表转化为 Array 并返回 */
|
|
|
toArray(): number[] {
|
|
|
let node = this.stackPeek;
|
|
|
const res = new Array<number>(this.size);
|
|
|
for (let i = res.length - 1; i >= 0; i--) {
|
|
|
res[i] = node!.val;
|
|
|
node = node!.next;
|
|
|
}
|
|
|
return res;
|
|
|
}
|
|
|
}
|
|
|
```
|
|
|
|
|
|
=== "C"
|
|
|
|
|
|
```c title="linkedlist_stack.c"
|
|
|
|
|
|
```
|
|
|
|
|
|
=== "C#"
|
|
|
|
|
|
```csharp title="linkedlist_stack.cs"
|
|
|
/* 基于链表实现的栈 */
|
|
|
class LinkedListStack
|
|
|
{
|
|
|
private ListNode stackPeek; // 将头结点作为栈顶
|
|
|
private int stkSize = 0; // 栈的长度
|
|
|
public LinkedListStack()
|
|
|
{
|
|
|
stackPeek = null;
|
|
|
}
|
|
|
/* 获取栈的长度 */
|
|
|
public int size()
|
|
|
{
|
|
|
return stkSize;
|
|
|
}
|
|
|
/* 判断栈是否为空 */
|
|
|
public bool isEmpty()
|
|
|
{
|
|
|
return size() == 0;
|
|
|
}
|
|
|
/* 入栈 */
|
|
|
public void push(int num)
|
|
|
{
|
|
|
ListNode node = new ListNode(num);
|
|
|
node.next = stackPeek;
|
|
|
stackPeek = node;
|
|
|
stkSize++;
|
|
|
}
|
|
|
/* 出栈 */
|
|
|
public int pop()
|
|
|
{
|
|
|
int num = peek();
|
|
|
stackPeek = stackPeek?.next;
|
|
|
stkSize--;
|
|
|
return num;
|
|
|
}
|
|
|
/* 访问栈顶元素 */
|
|
|
public int peek()
|
|
|
{
|
|
|
if (size() == 0)
|
|
|
throw new Exception();
|
|
|
return stackPeek.val;
|
|
|
}
|
|
|
}
|
|
|
```
|
|
|
|
|
|
=== "Swift"
|
|
|
|
|
|
```swift title="linkedlist_stack.swift"
|
|
|
/* 基于链表实现的栈 */
|
|
|
class LinkedListStack {
|
|
|
private var _peek: ListNode? // 将头结点作为栈顶
|
|
|
private var _size = 0 // 栈的长度
|
|
|
|
|
|
init() {}
|
|
|
|
|
|
/* 获取栈的长度 */
|
|
|
func size() -> Int {
|
|
|
_size
|
|
|
}
|
|
|
|
|
|
/* 判断栈是否为空 */
|
|
|
func isEmpty() -> Bool {
|
|
|
size() == 0
|
|
|
}
|
|
|
|
|
|
/* 入栈 */
|
|
|
func push(num: Int) {
|
|
|
let node = ListNode(x: num)
|
|
|
node.next = _peek
|
|
|
_peek = node
|
|
|
_size += 1
|
|
|
}
|
|
|
|
|
|
/* 出栈 */
|
|
|
@discardableResult
|
|
|
func pop() -> Int {
|
|
|
let num = peek()
|
|
|
_peek = _peek?.next
|
|
|
_size -= 1
|
|
|
return num
|
|
|
}
|
|
|
|
|
|
/* 访问栈顶元素 */
|
|
|
func peek() -> Int {
|
|
|
if isEmpty() {
|
|
|
fatalError("栈为空")
|
|
|
}
|
|
|
return _peek!.val
|
|
|
}
|
|
|
}
|
|
|
```
|
|
|
|
|
|
### 基于数组的实现
|
|
|
|
|
|
使用「数组」实现栈时，将数组的尾部当作栈顶，这样可以保证入栈与出栈操作的时间复杂度都为 $O(1)$ 。准确地说，由于入栈的元素可能是源源不断的，我们需要使用可以动态扩容的「列表」。
|
|
|
|
|
|
基于数组实现的栈，优点是支持随机访问，缺点是会造成一定的空间浪费，因为列表的容量始终 $\geq$ 元素数量。
|
|
|
|
|
|
=== "Java"
|
|
|
|
|
|
```java title="array_stack.java"
|
|
|
/* 基于数组实现的栈 */
|
|
|
class ArrayStack {
|
|
|
private ArrayList<Integer> stack;
|
|
|
public ArrayStack() {
|
|
|
// 初始化列表（动态数组）
|
|
|
stack = new ArrayList<>();
|
|
|
}
|
|
|
/* 获取栈的长度 */
|
|
|
public int size() {
|
|
|
return stack.size();
|
|
|
}
|
|
|
/* 判断栈是否为空 */
|
|
|
public boolean isEmpty() {
|
|
|
return size() == 0;
|
|
|
}
|
|
|
/* 入栈 */
|
|
|
public void push(int num) {
|
|
|
stack.add(num);
|
|
|
}
|
|
|
/* 出栈 */
|
|
|
public int pop() {
|
|
|
if (isEmpty())
|
|
|
throw new EmptyStackException();
|
|
|
return stack.remove(size() - 1);
|
|
|
}
|
|
|
/* 访问栈顶元素 */
|
|
|
public int peek() {
|
|
|
if (isEmpty())
|
|
|
throw new EmptyStackException();
|
|
|
return stack.get(size() - 1);
|
|
|
}
|
|
|
}
|
|
|
```
|
|
|
|
|
|
=== "C++"
|
|
|
|
|
|
```cpp title="array_stack.cpp"
|
|
|
/* 基于数组实现的栈 */
|
|
|
class ArrayStack {
|
|
|
private:
|
|
|
vector<int> stack;
|
|
|
|
|
|
public:
|
|
|
/* 获取栈的长度 */
|
|
|
int size() {
|
|
|
return stack.size();
|
|
|
}
|
|
|
/* 判断栈是否为空 */
|
|
|
bool empty() {
|
|
|
return stack.empty();
|
|
|
}
|
|
|
/* 入栈 */
|
|
|
void push(int num) {
|
|
|
stack.push_back(num);
|
|
|
}
|
|
|
/* 出栈 */
|
|
|
void pop() {
|
|
|
int oldTop = top();
|
|
|
stack.pop_back();
|
|
|
}
|
|
|
/* 访问栈顶元素 */
|
|
|
int top() {
|
|
|
if(empty())
|
|
|
throw out_of_range("栈为空");
|
|
|
return stack.back();
|
|
|
}
|
|
|
};
|
|
|
```
|
|
|
|
|
|
=== "Python"
|
|
|
|
|
|
```python title="array_stack.py"
|
|
|
""" 基于数组实现的栈 """
|
|
|
class ArrayStack:
|
|
|
def __init__(self):
|
|
|
self.__stack = []
|
|
|
|
|
|
""" 获取栈的长度 """
|
|
|
def size(self):
|
|
|
return len(self.__stack)
|
|
|
|
|
|
""" 判断栈是否为空 """
|
|
|
def is_empty(self):
|
|
|
return self.__stack == []
|
|
|
|
|
|
""" 入栈 """
|
|
|
def push(self, item):
|
|
|
self.__stack.append(item)
|
|
|
|
|
|
""" 出栈 """
|
|
|
def pop(self):
|
|
|
assert not self.is_empty(), "栈为空"
|
|
|
return self.__stack.pop()
|
|
|
|
|
|
""" 访问栈顶元素 """
|
|
|
def peek(self):
|
|
|
assert not self.is_empty(), "栈为空"
|
|
|
return self.__stack[-1]
|
|
|
```
|
|
|
|
|
|
=== "Go"
|
|
|
|
|
|
```go title="array_stack.go"
|
|
|
/* 基于数组实现的栈 */
|
|
|
type arrayStack struct {
|
|
|
data []int // 数据
|
|
|
}
|
|
|
|
|
|
func newArrayStack() *arrayStack {
|
|
|
return &arrayStack{
|
|
|
// 设置栈的长度为 0，容量为 16
|
|
|
data: make([]int, 0, 16),
|
|
|
}
|
|
|
}
|
|
|
|
|
|
// size 栈的长度
|
|
|
func (s *arrayStack) size() int {
|
|
|
return len(s.data)
|
|
|
}
|
|
|
|
|
|
// isEmpty 栈是否为空
|
|
|
func (s *arrayStack) isEmpty() bool {
|
|
|
return s.size() == 0
|
|
|
}
|
|
|
|
|
|
// push 入栈
|
|
|
func (s *arrayStack) push(v int) {
|
|
|
// 切片会自动扩容
|
|
|
s.data = append(s.data, v)
|
|
|
}
|
|
|
|
|
|
// pop 出栈
|
|
|
func (s *arrayStack) pop() any {
|
|
|
// 弹出栈前，先判断是否为空
|
|
|
if s.isEmpty() {
|
|
|
return nil
|
|
|
}
|
|
|
val := s.peek()
|
|
|
s.data = s.data[:len(s.data)-1]
|
|
|
return val
|
|
|
}
|
|
|
|
|
|
// peek 获取栈顶元素
|
|
|
func (s *arrayStack) peek() any {
|
|
|
if s.isEmpty() {
|
|
|
return nil
|
|
|
}
|
|
|
val := s.data[len(s.data)-1]
|
|
|
return val
|
|
|
}
|
|
|
```
|
|
|
|
|
|
=== "JavaScript"
|
|
|
|
|
|
```js title="array_stack.js"
|
|
|
/* 基于数组实现的栈 */
|
|
|
class ArrayStack {
|
|
|
stack;
|
|
|
constructor() {
|
|
|
this.stack = [];
|
|
|
}
|
|
|
/* 获取栈的长度 */
|
|
|
get size() {
|
|
|
return this.stack.length;
|
|
|
}
|
|
|
/* 判断栈是否为空 */
|
|
|
empty() {
|
|
|
return this.stack.length === 0;
|
|
|
}
|
|
|
/* 入栈 */
|
|
|
push(num) {
|
|
|
this.stack.push(num);
|
|
|
}
|
|
|
/* 出栈 */
|
|
|
pop() {
|
|
|
if (this.empty())
|
|
|
throw new Error("栈为空");
|
|
|
return this.stack.pop();
|
|
|
}
|
|
|
/* 访问栈顶元素 */
|
|
|
top() {
|
|
|
if (this.empty())
|
|
|
throw new Error("栈为空");
|
|
|
return this.stack[this.stack.length - 1];
|
|
|
}
|
|
|
};
|
|
|
```
|
|
|
|
|
|
=== "TypeScript"
|
|
|
|
|
|
```typescript title="array_stack.ts"
|
|
|
/* 基于数组实现的栈 */
|
|
|
class ArrayStack {
|
|
|
private stack: number[];
|
|
|
constructor() {
|
|
|
this.stack = [];
|
|
|
}
|
|
|
/* 获取栈的长度 */
|
|
|
get size(): number {
|
|
|
return this.stack.length;
|
|
|
}
|
|
|
/* 判断栈是否为空 */
|
|
|
empty(): boolean {
|
|
|
return this.stack.length === 0;
|
|
|
}
|
|
|
/* 入栈 */
|
|
|
push(num: number): void {
|
|
|
this.stack.push(num);
|
|
|
}
|
|
|
/* 出栈 */
|
|
|
pop(): number | undefined {
|
|
|
if (this.empty())
|
|
|
throw new Error('栈为空');
|
|
|
return this.stack.pop();
|
|
|
}
|
|
|
/* 访问栈顶元素 */
|
|
|
top(): number | undefined {
|
|
|
if (this.empty())
|
|
|
throw new Error('栈为空');
|
|
|
return this.stack[this.stack.length - 1];
|
|
|
}
|
|
|
};
|
|
|
```
|
|
|
|
|
|
=== "C"
|
|
|
|
|
|
```c title="array_stack.c"
|
|
|
|
|
|
```
|
|
|
|
|
|
=== "C#"
|
|
|
|
|
|
```csharp title="array_stack.cs"
|
|
|
/* 基于数组实现的栈 */
|
|
|
class ArrayStack
|
|
|
{
|
|
|
private List<int> stack;
|
|
|
public ArrayStack()
|
|
|
{
|
|
|
// 初始化列表（动态数组）
|
|
|
stack = new();
|
|
|
}
|
|
|
/* 获取栈的长度 */
|
|
|
public int size()
|
|
|
{
|
|
|
return stack.Count();
|
|
|
}
|
|
|
/* 判断栈是否为空 */
|
|
|
public bool isEmpty()
|
|
|
{
|
|
|
return size() == 0;
|
|
|
}
|
|
|
/* 入栈 */
|
|
|
public void push(int num)
|
|
|
{
|
|
|
stack.Add(num);
|
|
|
}
|
|
|
/* 出栈 */
|
|
|
public int pop()
|
|
|
{
|
|
|
if (isEmpty())
|
|
|
throw new Exception();
|
|
|
var val = peek();
|
|
|
stack.RemoveAt(size() - 1);
|
|
|
return val;
|
|
|
}
|
|
|
/* 访问栈顶元素 */
|
|
|
public int peek()
|
|
|
{
|
|
|
if (isEmpty())
|
|
|
throw new Exception();
|
|
|
return stack[size() - 1];
|
|
|
}
|
|
|
}
|
|
|
```
|
|
|
|
|
|
=== "Swift"
|
|
|
|
|
|
```swift title="array_stack.swift"
|
|
|
/* 基于数组实现的栈 */
|
|
|
class ArrayStack {
|
|
|
private var stack: [Int]
|
|
|
|
|
|
init() {
|
|
|
// 初始化列表（动态数组）
|
|
|
stack = []
|
|
|
}
|
|
|
|
|
|
/* 获取栈的长度 */
|
|
|
func size() -> Int {
|
|
|
stack.count
|
|
|
}
|
|
|
|
|
|
/* 判断栈是否为空 */
|
|
|
func isEmpty() -> Bool {
|
|
|
stack.isEmpty
|
|
|
}
|
|
|
|
|
|
/* 入栈 */
|
|
|
func push(num: Int) {
|
|
|
stack.append(num)
|
|
|
}
|
|
|
|
|
|
/* 出栈 */
|
|
|
@discardableResult
|
|
|
func pop() -> Int {
|
|
|
if isEmpty() {
|
|
|
fatalError("栈为空")
|
|
|
}
|
|
|
return stack.removeLast()
|
|
|
}
|
|
|
|
|
|
/* 访问栈顶元素 */
|
|
|
func peek() -> Int {
|
|
|
if isEmpty() {
|
|
|
fatalError("栈为空")
|
|
|
}
|
|
|
return stack.last!
|
|
|
}
|
|
|
}
|
|
|
```
|
|
|
|
|
|
!!! tip
|
|
|
|
|
|
某些语言并未专门提供栈类，但我们可以直接把该语言的「数组」或「链表」看作栈来使用，并通过“脑补”来屏蔽无关操作，而无需像上述代码去特意包装一层。
|
|
|
|
|
|
## 栈典型应用
|
|
|
|
|
|
- **浏览器中的后退与前进、软件中的撤销与反撤销**。每当我们打开新的网页，浏览器就将上一个网页执行入栈，这样我们就可以通过「后退」操作来回到上一页面，后退操作实际上是在执行出栈。如果要同时支持后退和前进，那么则需要两个栈来配合实现。
|
|
|
- **程序内存管理**。每当调用函数时，系统就会在栈顶添加一个栈帧，用来记录函数的上下文信息。在递归函数中，向下递推会不断执行入栈，向上回溯阶段时出栈。
|
