|
|
---
|
|
|
comments: true
|
|
|
---
|
|
|
|
|
|
# 栈
|
|
|
|
|
|
「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。
|
|
|
|
|
|
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」。
|
|
|
|
|
|
|
|
|
|
|
|
<p align="center"> Fig. 栈的先入后出特性 </p>
|
|
|
|
|
|
## 栈常用操作
|
|
|
|
|
|
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。
|
|
|
|
|
|
<p align="center"> Table. 栈的常用操作 </p>
|
|
|
|
|
|
<div class="center-table" markdown>
|
|
|
|
|
|
| 方法 | 描述 |
|
|
|
| --------- | ---------------------- |
|
|
|
| push() | 元素入栈（添加至栈顶） |
|
|
|
| pop() | 栈顶元素出栈 |
|
|
|
| peek() | 访问栈顶元素 |
|
|
|
| size() | 获取栈的长度 |
|
|
|
| isEmpty() | 判断栈是否为空 |
|
|
|
|
|
|
</div>
|
|
|
|
|
|
我们可以直接使用编程语言实现好的栈类。
|
|
|
|
|
|
=== "Java"
|
|
|
|
|
|
```java title="stack.java"
|
|
|
/* 初始化栈 */
|
|
|
// 在 Java 中，推荐将 LinkedList 当作栈来使用
|
|
|
LinkedList<Integer> stack = new LinkedList<>();
|
|
|
|
|
|
/* 元素入栈 */
|
|
|
stack.addLast(1);
|
|
|
stack.addLast(3);
|
|
|
stack.addLast(2);
|
|
|
stack.addLast(5);
|
|
|
stack.addLast(4);
|
|
|
|
|
|
/* 访问栈顶元素 */
|
|
|
int peek = stack.peekLast();
|
|
|
|
|
|
/* 元素出栈 */
|
|
|
int pop = stack.removeLast();
|
|
|
|
|
|
/* 获取栈的长度 */
|
|
|
int size = stack.size();
|
|
|
|
|
|
/* 判断是否为空 */
|
|
|
boolean isEmpty = stack.isEmpty();
|
|
|
```
|
|
|
|
|
|
=== "C++"
|
|
|
|
|
|
```cpp title="stack.cpp"
|
|
|
/* 初始化栈 */
|
|
|
stack<int> stack;
|
|
|
|
|
|
/* 元素入栈 */
|
|
|
stack.push(1);
|
|
|
stack.push(3);
|
|
|
stack.push(2);
|
|
|
stack.push(5);
|
|
|
stack.push(4);
|
|
|
|
|
|
/* 访问栈顶元素 */
|
|
|
int top = stack.top();
|
|
|
|
|
|
/* 元素出栈 */
|
|
|
stack.pop();
|
|
|
|
|
|
/* 获取栈的长度 */
|
|
|
int size = stack.size();
|
|
|
|
|
|
/* 判断是否为空 */
|
|
|
bool empty = stack.empty();
|
|
|
```
|
|
|
|
|
|
=== "Python"
|
|
|
|
|
|
```python title="stack.py"
|
|
|
""" 初始化栈 """
|
|
|
# Python 没有内置的栈类，可以把 List 当作栈来使用
|
|
|
stack = []
|
|
|
|
|
|
""" 元素入栈 """
|
|
|
stack.append(1)
|
|
|
stack.append(3)
|
|
|
stack.append(2)
|
|
|
stack.append(5)
|
|
|
stack.append(4)
|
|
|
|
|
|
""" 访问栈顶元素 """
|
|
|
peek = stack[-1]
|
|
|
|
|
|
""" 元素出栈 """
|
|
|
pop = stack.pop()
|
|
|
|
|
|
""" 获取栈的长度 """
|
|
|
size = len(stack)
|
|
|
|
|
|
""" 判断是否为空 """
|
|
|
is_empty = len(stack) == 0
|
|
|
```
|
|
|
|
|
|
=== "Go"
|
|
|
|
|
|
```go title="stack.go"
|
|
|
|
|
|
```
|
|
|
|
|
|
=== "JavaScript"
|
|
|
|
|
|
```js title="stack.js"
|
|
|
|
|
|
```
|
|
|
|
|
|
=== "TypeScript"
|
|
|
|
|
|
```typescript title="stack.ts"
|
|
|
|
|
|
```
|
|
|
|
|
|
=== "C"
|
|
|
|
|
|
```c title="stack.c"
|
|
|
|
|
|
```
|
|
|
|
|
|
=== "C#"
|
|
|
|
|
|
```csharp title="stack.cs"
|
|
|
|
|
|
```
|
|
|
|
|
|
## 栈的实现
|
|
|
|
|
|
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。
|
|
|
|
|
|
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。
|
|
|
|
|
|
### 基于链表的实现
|
|
|
|
|
|
使用「链表」实现栈时，将链表的尾结点看作栈顶即可。
|
|
|
|
|
|
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。
|
|
|
|
|
|
=== "Java"
|
|
|
|
|
|
```java title="linkedlist_stack.java"
|
|
|
/* 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 boolean 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 IndexOutOfBoundsException();
|
|
|
return stackPeek.val;
|
|
|
}
|
|
|
}
|
|
|
```
|
|
|
|
|
|
=== "C++"
|
|
|
|
|
|
```cpp title="linkedlist_stack.cpp"
|
|
|
/* 基于链表实现的栈 */
|
|
|
class LinkedListStack {
|
|
|
private:
|
|
|
ListNode* stackTop; // 将头结点作为栈顶
|
|
|
int stkSize; // 栈的长度
|
|
|
|
|
|
public:
|
|
|
LinkedListStack() {
|
|
|
stackTop = nullptr;
|
|
|
stkSize = 0;
|
|
|
}
|
|
|
/* 获取栈的长度 */
|
|
|
int size() {
|
|
|
return stkSize;
|
|
|
}
|
|
|
/* 判断栈是否为空 */
|
|
|
bool empty() {
|
|
|
return size() == 0;
|
|
|
}
|
|
|
/* 入栈 */
|
|
|
void push(int num) {
|
|
|
ListNode* node = new ListNode(num);
|
|
|
node->next = stackTop;
|
|
|
stackTop = node;
|
|
|
stkSize++;
|
|
|
}
|
|
|
/* 出栈 */
|
|
|
int pop() {
|
|
|
int num = top();
|
|
|
stackTop = stackTop->next;
|
|
|
stkSize--;
|
|
|
return num;
|
|
|
}
|
|
|
/* 访问栈顶元素 */
|
|
|
int top() {
|
|
|
if (size() == 0)
|
|
|
throw out_of_range("栈为空");
|
|
|
return stackTop->val;
|
|
|
}
|
|
|
};
|
|
|
```
|
|
|
|
|
|
=== "Python"
|
|
|
|
|
|
```python title="linkedlist_stack.py"
|
|
|
""" 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):
|
|
|
num = self.peek()
|
|
|
self.__peek = self.__peek.next
|
|
|
self.__size -= 1
|
|
|
return num
|
|
|
|
|
|
""" 访问栈顶元素 """
|
|
|
def peek(self):
|
|
|
# 判空处理
|
|
|
if not self.__peek: return None
|
|
|
return self.__peek.val
|
|
|
```
|
|
|
|
|
|
=== "Go"
|
|
|
|
|
|
```go title="linkedlist_stack.go"
|
|
|
|
|
|
```
|
|
|
|
|
|
=== "JavaScript"
|
|
|
|
|
|
```js title="linkedlist_stack.js"
|
|
|
|
|
|
```
|
|
|
|
|
|
=== "TypeScript"
|
|
|
|
|
|
```typescript title="linkedlist_stack.ts"
|
|
|
|
|
|
```
|
|
|
|
|
|
=== "C"
|
|
|
|
|
|
```c title="linkedlist_stack.c"
|
|
|
|
|
|
```
|
|
|
|
|
|
=== "C#"
|
|
|
|
|
|
```csharp title="linkedlist_stack.cs"
|
|
|
|
|
|
```
|
|
|
|
|
|
### 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 {
|
|
|
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() {
|
|
|
return stack.remove(size() - 1);
|
|
|
}
|
|
|
/* 访问栈顶元素 */
|
|
|
public int peek() {
|
|
|
return stack.get(size() - 1);
|
|
|
}
|
|
|
/* 访问索引 index 处元素 */
|
|
|
public int get(int index) {
|
|
|
return stack.get(index);
|
|
|
}
|
|
|
}
|
|
|
```
|
|
|
|
|
|
=== "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 */
|
|
|
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];
|
|
|
}
|
|
|
};
|
|
|
```
|
|
|
|
|
|
=== "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):
|
|
|
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]
|
|
|
```
|
|
|
|
|
|
=== "Go"
|
|
|
|
|
|
```go title="array_stack.go"
|
|
|
|
|
|
```
|
|
|
|
|
|
=== "JavaScript"
|
|
|
|
|
|
```js title="array_stack.js"
|
|
|
|
|
|
```
|
|
|
|
|
|
=== "TypeScript"
|
|
|
|
|
|
```typescript title="array_stack.ts"
|
|
|
|
|
|
```
|
|
|
|
|
|
=== "C"
|
|
|
|
|
|
```c title="array_stack.c"
|
|
|
|
|
|
```
|
|
|
|
|
|
=== "C#"
|
|
|
|
|
|
```csharp title="array_stack.cs"
|
|
|
|
|
|
```
|
|
|
|
|
|
!!! 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。
|
|
|
- **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。
|
