2022-11-22 17:47:26 +08:00
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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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我们将顶部盘子称为「栈顶」,底部盘子称为「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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![stack_operations](stack.assets/stack_operations.png)
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2022-11-23 15:50:59 +08:00
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<p align="center"> Fig. 栈的先入后出特性 </p>
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2022-11-22 17:47:26 +08:00
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## 栈常用操作
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栈的常用操作见下表,方法名需根据编程语言设定来具体确定。
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2022-11-23 15:50:59 +08:00
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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 |
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| --------- | ---------------------- |
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| push() | 元素入栈(添加至栈顶) |
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| pop() | 栈顶元素出栈 |
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| peek() | 访问栈顶元素 |
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| size() | 获取栈的长度 |
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| isEmpty() | 判断栈是否为空 |
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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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2022-11-30 03:46:53 +08:00
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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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2022-12-03 01:31:29 +08:00
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=== "Go"
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```go title="stack.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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2022-12-03 20:25:24 +08:00
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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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2022-12-03 23:00:13 +08:00
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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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2022-12-03 23:00:13 +08:00
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/* 访问栈顶元素 */
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peek = stack[stack.length-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 = stack.length;
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/* 判断是否为空 */
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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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2022-12-03 23:00:13 +08:00
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/* 访问栈顶元素 */
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peek = stack[stack.length-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 = stack.length;
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/* 判断是否为空 */
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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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```
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2022-11-22 17:47:26 +08:00
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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,将链表的尾结点看作栈顶即可。
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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 IndexOutOfBoundsException();
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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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/* 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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int pop() {
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int num = top();
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stackTop = stackTop->next;
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stkSize--;
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|
|
return num;
|
|
|
|
|
}
|
|
|
|
|
/* 访问栈顶元素 */
|
|
|
|
|
int top() {
|
|
|
|
|
if (size() == 0)
|
|
|
|
|
throw out_of_range("栈为空");
|
|
|
|
|
return stackTop->val;
|
|
|
|
|
}
|
|
|
|
|
};
|
2022-11-22 17:47:26 +08:00
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "Python"
|
|
|
|
|
|
|
|
|
|
```python title="linkedlist_stack.py"
|
2022-11-30 02:27:26 +08:00
|
|
|
|
""" 基于链表实现的栈 """
|
|
|
|
|
class LinkedListStack:
|
|
|
|
|
def __init__(self):
|
|
|
|
|
self.__peek = None
|
|
|
|
|
self.__size = 0
|
|
|
|
|
|
|
|
|
|
""" 获取栈的长度 """
|
|
|
|
|
def size(self):
|
|
|
|
|
return self.__size
|
|
|
|
|
|
|
|
|
|
""" 判断栈是否为空 """
|
|
|
|
|
def is_empty(self):
|
|
|
|
|
return not self.__peek
|
|
|
|
|
|
|
|
|
|
""" 入栈 """
|
|
|
|
|
def push(self, val):
|
|
|
|
|
node = ListNode(val)
|
|
|
|
|
node.next = self.__peek
|
|
|
|
|
self.__peek = node
|
|
|
|
|
self.__size += 1
|
|
|
|
|
|
|
|
|
|
""" 出栈 """
|
|
|
|
|
def pop(self):
|
2022-11-30 03:46:53 +08:00
|
|
|
|
num = self.peek()
|
2022-11-30 02:27:26 +08:00
|
|
|
|
self.__peek = self.__peek.next
|
|
|
|
|
self.__size -= 1
|
2022-11-30 03:46:53 +08:00
|
|
|
|
return num
|
2022-11-30 02:27:26 +08:00
|
|
|
|
|
|
|
|
|
""" 访问栈顶元素 """
|
|
|
|
|
def peek(self):
|
|
|
|
|
# 判空处理
|
|
|
|
|
if not self.__peek: return None
|
|
|
|
|
return self.__peek.val
|
2022-11-22 17:47:26 +08:00
|
|
|
|
```
|
|
|
|
|
|
2022-12-03 01:31:29 +08:00
|
|
|
|
=== "Go"
|
|
|
|
|
|
|
|
|
|
```go title="linkedlist_stack.go"
|
2022-12-03 20:25:24 +08:00
|
|
|
|
/* 基于链表实现的栈 */
|
|
|
|
|
type LinkedListStack struct {
|
|
|
|
|
// 使用内置包 list 来实现栈
|
|
|
|
|
data *list.List
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// NewLinkedListStack 初始化链表
|
|
|
|
|
func NewLinkedListStack() *LinkedListStack {
|
|
|
|
|
return &LinkedListStack{
|
|
|
|
|
data: list.New(),
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// Push 入栈
|
|
|
|
|
func (s *LinkedListStack) Push(value int) {
|
|
|
|
|
s.data.PushBack(value)
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// Pop 出栈
|
|
|
|
|
func (s *LinkedListStack) Pop() any {
|
|
|
|
|
if s.IsEmpty() {
|
|
|
|
|
return nil
|
|
|
|
|
}
|
|
|
|
|
e := s.data.Back()
|
|
|
|
|
s.data.Remove(e)
|
|
|
|
|
return e.Value
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// Peek 访问栈顶元素
|
|
|
|
|
func (s *LinkedListStack) Peek() any {
|
|
|
|
|
if s.IsEmpty() {
|
|
|
|
|
return nil
|
|
|
|
|
}
|
|
|
|
|
e := s.data.Back()
|
|
|
|
|
return e.Value
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// Size 获取栈的长度
|
|
|
|
|
func (s *LinkedListStack) Size() int {
|
|
|
|
|
return s.data.Len()
|
|
|
|
|
}
|
2022-12-03 01:31:29 +08:00
|
|
|
|
|
2022-12-03 20:25:24 +08:00
|
|
|
|
// IsEmpty 判断栈是否为空
|
|
|
|
|
func (s *LinkedListStack) IsEmpty() bool {
|
|
|
|
|
return s.data.Len() == 0
|
|
|
|
|
}
|
2022-12-03 01:31:29 +08:00
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "JavaScript"
|
|
|
|
|
|
|
|
|
|
```js title="linkedlist_stack.js"
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "TypeScript"
|
|
|
|
|
|
|
|
|
|
```typescript title="linkedlist_stack.ts"
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "C"
|
|
|
|
|
|
|
|
|
|
```c title="linkedlist_stack.c"
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "C#"
|
|
|
|
|
|
|
|
|
|
```csharp title="linkedlist_stack.cs"
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
2022-11-22 17:47:26 +08:00
|
|
|
|
### 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。准确地说,我们需要使用「列表」,因为入栈的元素可能是源源不断的,因此使用动态数组可以方便扩容。
|
|
|
|
|
|
|
|
|
|
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 {
|
2022-11-30 02:27:26 +08:00
|
|
|
|
private ArrayList<Integer> stack;
|
2022-11-22 17:47:26 +08:00
|
|
|
|
public ArrayStack() {
|
|
|
|
|
// 初始化列表(动态数组)
|
2022-11-30 02:27:26 +08:00
|
|
|
|
stack = new ArrayList<>();
|
2022-11-22 17:47:26 +08:00
|
|
|
|
}
|
|
|
|
|
/* 获取栈的长度 */
|
|
|
|
|
public int size() {
|
2022-11-30 02:27:26 +08:00
|
|
|
|
return stack.size();
|
2022-11-22 17:47:26 +08:00
|
|
|
|
}
|
|
|
|
|
/* 判断栈是否为空 */
|
|
|
|
|
public boolean isEmpty() {
|
|
|
|
|
return size() == 0;
|
|
|
|
|
}
|
|
|
|
|
/* 入栈 */
|
|
|
|
|
public void push(int num) {
|
2022-11-30 02:27:26 +08:00
|
|
|
|
stack.add(num);
|
2022-11-22 17:47:26 +08:00
|
|
|
|
}
|
|
|
|
|
/* 出栈 */
|
|
|
|
|
public int pop() {
|
2022-11-30 02:27:26 +08:00
|
|
|
|
return stack.remove(size() - 1);
|
2022-11-22 17:47:26 +08:00
|
|
|
|
}
|
|
|
|
|
/* 访问栈顶元素 */
|
|
|
|
|
public int peek() {
|
2022-11-30 02:27:26 +08:00
|
|
|
|
return stack.get(size() - 1);
|
2022-11-22 17:47:26 +08:00
|
|
|
|
}
|
|
|
|
|
/* 访问索引 index 处元素 */
|
|
|
|
|
public int get(int index) {
|
2022-11-30 02:27:26 +08:00
|
|
|
|
return stack.get(index);
|
2022-11-22 17:47:26 +08:00
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "C++"
|
|
|
|
|
|
|
|
|
|
```cpp title="array_stack.cpp"
|
2022-11-30 02:27:26 +08:00
|
|
|
|
/* 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 */
|
|
|
|
|
int pop() {
|
|
|
|
|
int oldTop = stack.back();
|
|
|
|
|
stack.pop_back();
|
|
|
|
|
return oldTop;
|
|
|
|
|
}
|
|
|
|
|
/* 访问栈顶元素 */
|
|
|
|
|
int top() {
|
|
|
|
|
return stack.back();
|
|
|
|
|
}
|
|
|
|
|
/* 访问索引 index 处元素 */
|
|
|
|
|
int get(int index) {
|
|
|
|
|
return stack[index];
|
|
|
|
|
}
|
|
|
|
|
};
|
2022-11-22 17:47:26 +08:00
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "Python"
|
|
|
|
|
|
|
|
|
|
```python title="array_stack.py"
|
2022-11-30 02:27:26 +08:00
|
|
|
|
""" 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):
|
|
|
|
|
return self.__stack.pop()
|
|
|
|
|
|
|
|
|
|
""" 访问栈顶元素 """
|
|
|
|
|
def peek(self):
|
|
|
|
|
return self.__stack[-1]
|
|
|
|
|
|
|
|
|
|
""" 访问索引 index 处元素 """
|
|
|
|
|
def get(self, index):
|
|
|
|
|
return self.__stack[index]
|
2022-11-22 17:47:26 +08:00
|
|
|
|
```
|
|
|
|
|
|
2022-12-03 01:31:29 +08:00
|
|
|
|
=== "Go"
|
|
|
|
|
|
|
|
|
|
```go title="array_stack.go"
|
2022-12-03 20:25:24 +08:00
|
|
|
|
/* 基于数组实现的栈 */
|
|
|
|
|
type ArrayStack struct {
|
|
|
|
|
data []int // 数据
|
|
|
|
|
}
|
2022-12-03 01:31:29 +08:00
|
|
|
|
|
2022-12-03 20:25:24 +08:00
|
|
|
|
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
|
|
|
|
|
}
|
2022-12-03 01:31:29 +08:00
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "JavaScript"
|
|
|
|
|
|
|
|
|
|
```js title="array_stack.js"
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "TypeScript"
|
|
|
|
|
|
|
|
|
|
```typescript title="array_stack.ts"
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "C"
|
|
|
|
|
|
|
|
|
|
```c title="array_stack.c"
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "C#"
|
|
|
|
|
|
|
|
|
|
```csharp title="array_stack.cs"
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
2022-11-22 17:47:26 +08:00
|
|
|
|
!!! tip
|
|
|
|
|
|
|
|
|
|
实际编程中,我们一般直接将 `ArrayList` 或 `LinkedList` 当作「栈」来使用。我们仅需通过脑补来屏蔽无关操作,而不用专门去包装它。
|
|
|
|
|
|
|
|
|
|
## 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,浏览器就讲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。
|
2022-11-29 10:15:45 +08:00
|
|
|
|
- **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。
|