刘心向学（16）数据结构：栈的定义及其应用

摘要：在计算机科学中，栈（Stack）是一种常见的数据结构，遵循“后进先出”（LIFO, Last In First Out）的原则。栈的操作主要集中在一端进行，包括插入（入栈）和删除（出栈）。这种简单而高效的特性使得栈在许多场景中得到了广泛应用。本文将介绍栈的基本

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一、思维导图（Mind map）

二、引言（Introduction）

在计算机科学中，栈（Stack）是一种常见的数据结构，遵循“后进先出”（LIFO, Last In First Out）的原则。栈的操作主要集中在一端进行，包括插入（入栈）和删除（出栈）。这种简单而高效的特性使得栈在许多场景中得到了广泛应用。本文将介绍栈的基本概念、其优势以及如何在C/C++中实现，并通过几个实际例子来展示它的强大功能。

In computer science, a stack is a common data structure that follows the "Last In First Out" (LIFO) principle, where operations mainly focus on one end, including insertion (push) and deletion (pop). This simple and efficient characteristic makes stacks widely used in many scenarios. This article will introduce the basic concepts of stacks, their advantages, and how to implement them in C/C++, along with several practical examples to demonstrate their powerful Functionality.

三、什么是栈？（What is a stack?）

栈是一种线性数据结构，所有的操作（如插入和删除）都发生在栈顶。栈的基本操作包括：

A stack is a linear data structure in which all operations, such as insertions and deletions, occur at one end called the top of the stack. The basic operations of a stack include:

Push（入栈）：将一个元素添加到栈顶。

Push: Adds an element to the top of the stack.

Pop（出栈）：从栈顶移除一个元素。

Pop: Removes an element from the top of the stack.

Top（或Peek）：返回栈顶元素但不移除它。

Top (or Peek): Returns the top element of the stack without removing it.

isEmpty：检查栈是否为空。

isEmpty: Checks whether the stack is empty.

栈的存储可以基于数组或链表实现。使用数组时，栈的大小通常是固定的；而使用链表时，栈的大小可以动态调整。

The storage for a stack can be implemented using either an array or a linked list. When using an array, the size of the stack is typically fixed. In contrast, when using a linked list, the size of the stack can dynamically adjust.

四、栈的优势（Advantages of a Stack）

简单高效：栈的操作时间复杂度为O(1)，适合需要快速访问和修改数据的场景。

Simple and Efficient:Stack operations have a time complexity of O(1), making them suitable for scenarios that require fast data access and modification.

节省内存：由于只在一端操作，栈可以有效利用内存空间。

Memory Saving:Since all operations occur at one end, stacks can effectively utilize memory space.

Wide Applicability:Stacks are fundamental tools in many algorithms and program designs.

函数调用管理：在程序运行过程中，函数调用的参数、返回地址等信息通常存储在栈中。

Function Call Management: During program execution, information such as function call parameters and return addresses is typically stored in a stack.

表达式求值与转换：栈可以用来解析和计算数学表达式，例如将中缀表达式转换为后缀表达式。

Expression Evaluation and Conversion: Stacks can be used to parse and evaluate mathematical expressions, such as converting infix expressions to postfix expressions.

括号匹配：栈可以用于检测括号是否正确匹配。

Bracket Matching: Stacks can be used to detect whether brackets are properly matched.

回溯算法：栈是实现回溯算法的核心工具之一。

Backtracking Algorithms: Stacks are one of the key tools for implementing backtracking algorithms.

Below is a simple example of implementing a stack using an array:

此代码片段实现了一个简单的栈，并展示了如何进行入栈、出栈和获取栈顶元素的操作。

This code snippet implements a simple stack and demonstrates how to perform push, pop, and get the top element operations.

此代码片段实现了括号匹配的功能，通过栈来判断给定表达式中的括号是否正确配对。

This code snippet implements the functionality of bracket matching, using a stack to determine whether the brackets in a given expression are correctly paired.

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参考资料：通义千问

参考文献：Cormen, T. H., Leiserson, C. E., Rivest, R. L., & Stein, C. (2009). Introduction to Algorithms (3rd ed.). MIT Press.