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World，⭐）","4.2 IDE 的安装和配置"]},"41":{"title":"4.2.2.1 概述","titles":["第四章：C 语言入门（Hello World，⭐）","4.2 IDE 的安装和配置","4.2.2 VS Code"]},"42":{"title":"4.2.2.2 安装","titles":["第四章：C 语言入门（Hello World，⭐）","4.2 IDE 的安装和配置","4.2.2 VS Code"]},"43":{"title":"4.2.2.3 配置","titles":["第四章：C 语言入门（Hello World，⭐）","4.2 IDE 的安装和配置","4.2.2 VS Code"]},"44":{"title":"4.2.3 Microsoft Visual Studio","titles":["第四章：C 语言入门（Hello World，⭐）","4.2 IDE 的安装和配置"]},"45":{"title":"4.2.3.1 概述","titles":["第四章：C 语言入门（Hello World，⭐）","4.2 IDE 的安装和配置","4.2.3 Microsoft Visual Studio"]},"46":{"title":"4.2.3.2 安装","titles":["第四章：C 语言入门（Hello World，⭐）","4.2 IDE 的安装和配置","4.2.3 Microsoft Visual Studio"]},"47":{"title":"4.2.3.3 配置","titles":["第四章：C 语言入门（Hello World，⭐）","4.2 IDE 的安装和配置","4.2.3 Microsoft Visual Studio"]},"48":{"title":"4.3 HelloWorld","titles":["第四章：C 语言入门（Hello World，⭐）"]},"49":{"title":"4.3.1 手动版","titles":["第四章：C 语言入门（Hello World，⭐）","4.3 HelloWorld"]},"50":{"title":"4.3.2 VS Code 版","titles":["第四章：C 语言入门（Hello World，⭐）","4.3 HelloWorld"]},"51":{"title":"4.3.3 VS 版","titles":["第四章：C 语言入门（Hello World，⭐）","4.3 HelloWorld"]},"52":{"title":"4.3.4 CLion","titles":["第四章：C 语言入门（Hello World，⭐）","4.3 HelloWorld"]},"53":{"title":"第五章：注释","titles":[]},"54":{"title":"5.1 概述","titles":["第五章：注释"]},"55":{"title":"5.2 单行注释","titles":["第五章：注释"]},"56":{"title":"5.3 多行注释","titles":["第五章：注释"]},"57":{"title":"第六章：HelloWorld 的规范（⭐）","titles":[]},"58":{"title":"6.1 规范的代码风格","titles":["第六章：HelloWorld 的规范（⭐）"]},"59":{"title":"6.1.1 正确的缩进和空白","titles":["第六章：HelloWorld 的规范（⭐）","6.1 规范的代码风格"]},"60":{"title":"6.1.2 代码风格","titles":["第六章：HelloWorld 的规范（⭐）","6.1 规范的代码风格"]},"61":{"title":"6.2 代码细节剖析","titles":["第六章：HelloWorld 的规范（⭐）"]},"62":{"title":"6.2.1 main() 函数","titles":["第六章：HelloWorld 的规范（⭐）","6.2 代码细节剖析"]},"63":{"title":"6.2.2 函数体","titles":["第六章：HelloWorld 的规范（⭐）","6.2 代码细节剖析"]},"64":{"title":"6.2.3 printf() 函数","titles":["第六章：HelloWorld 的规范（⭐）","6.2 代码细节剖析"]},"65":{"title":"6.2.4 标准库和头文件","titles":["第六章：HelloWorld 的规范（⭐）","6.2 代码细节剖析"]},"66":{"title":"6.2.4.1 概述","titles":["第六章：HelloWorld 的规范（⭐）","6.2 代码细节剖析","6.2.4 标准库和头文件"]},"67":{"title":"6.2.4.2 标准库（Standard Library）","titles":["第六章：HelloWorld 的规范（⭐）","6.2 代码细节剖析","6.2.4 标准库和头文件"]},"68":{"title":"6.2.4.3 头文件（Header Files）","titles":["第六章：HelloWorld 的规范（⭐）","6.2 代码细节剖析","6.2.4 标准库和头文件"]},"69":{"title":"6.2.4.4 预处理命令","titles":["第六章：HelloWorld 的规范（⭐）","6.2 代码细节剖析","6.2.4 标准库和头文件"]},"70":{"title":"第七章：CLion 高级配置（⭐）","titles":[]},"71":{"title":"7.1 安装和配置 WSL2","titles":["第七章：CLion 高级配置（⭐）"]},"72":{"title":"7.1.1 概述","titles":["第七章：CLion 高级配置（⭐）","7.1 安装和配置 WSL2"]},"73":{"title":"7.1.2 WSL2 的安装","titles":["第七章：CLion 高级配置（⭐）","7.1 安装和配置 WSL2"]},"74":{"title":"7.1.3 配置 WSL2","titles":["第七章：CLion 高级配置（⭐）","7.1 安装和配置 WSL2"]},"75":{"title":"7.1.4 配置 WSL2","titles":["第七章：CLion 高级配置（⭐）","7.1 安装和配置 WSL2"]},"76":{"title":"7.2 切换 CLion 中的 cmake 的工具链","titles":["第七章：CLion 高级配置（⭐）"]},"77":{"title":"7.3 修改 CMakeLists.txt 文件","titles":["第七章：CLion 高级配置（⭐）"]},"78":{"title":"7.4 配置 .clang-format 文件","titles":["第七章：CLion 高级配置（⭐）"]},"79":{"title":"7.5 配置 .gitignore 文件","titles":["第七章：CLion 高级配置（⭐）"]},"80":{"title":"7.6 演示","titles":["第七章：CLion 高级配置（⭐）"]},"81":{"title":"第八章：C 语言的编译过程（⭐）","titles":[]},"82":{"title":"8.1 概述","titles":["第八章：C 语言的编译过程（⭐）"]},"83":{"title":"8.2 GCC 编译器的介绍","titles":["第八章：C 语言的编译过程（⭐）"]},"84":{"title":"8.3 通过 gcc 直接生成可执行文件","titles":["第八章：C 语言的编译过程（⭐）"]},"85":{"title":"8.4 通过 gcc 分步编译","titles":["第八章：C 语言的编译过程（⭐）"]},"86":{"title":"8.3.1 概述","titles":["第八章：C 语言的编译过程（⭐）","8.4 通过 gcc 分步编译"]},"87":{"title":"8.4.2 应用示例","titles":["第八章：C 语言的编译过程（⭐）","8.4 通过 gcc 分步编译"]},"88":{"title":"第一章：变量（⭐）","titles":[]},"89":{"title":"1.1 程序中变化的数据","titles":["第一章：变量（⭐）"]},"90":{"title":"1.2 变量","titles":["第一章：变量（⭐）"]},"91":{"title":"1.3 变量的声明和使用","titles":["第一章：变量（⭐）"]},"92":{"title":"1.4 从计算机底层看变量","titles":["第一章：变量（⭐）"]},"93":{"title":"1.4.1 内存条的内部结构","titles":["第一章：变量（⭐）","1.4 从计算机底层看变量"]},"94":{"title":"1.4.2 变量的作用","titles":["第一章：变量（⭐）","1.4 从计算机底层看变量"]},"95":{"title":"1.6 变量的重要操作","titles":["第一章：变量（⭐）"]},"96":{"title":"1.6.1 变量的输出","titles":["第一章：变量（⭐）","1.6 变量的重要操作"]},"97":{"title":"1.6.2 计算变量的大小","titles":["第一章：变量（⭐）","1.6 变量的重要操作"]},"98":{"title":"1.6.3 获取变量的地址","titles":["第一章：变量（⭐）","1.6 变量的重要操作"]},"99":{"title":"1.6.4 变量的输入","titles":["第一章：变量（⭐）","1.6 变量的重要操作"]},"100":{"title":"1.7 标识符","titles":["第一章：变量（⭐）"]},"101":{"title":"1.7.1 概述","titles":["第一章：变量（⭐）","1.7 标识符"]},"102":{"title":"1.7.2 标识符的命名规范","titles":["第一章：变量（⭐）","1.7 标识符"]},"103":{"title":"1.7.3 关键字","titles":["第一章：变量（⭐）","1.7 标识符"]},"104":{"title":"第二章：常量（⭐）","titles":[]},"105":{"title":"2.1 概述","titles":["第二章：常量（⭐）"]},"106":{"title":"2.2 常量的分类","titles":["第二章：常量（⭐）"]},"107":{"title":"2.3 使用 #define 定义常量","titles":["第二章：常量（⭐）"]},"108":{"title":"2.4 const 关键字","titles":["第二章：常量（⭐）"]},"109":{"title":"2.5 枚举常量","titles":["第二章：常量（⭐）"]},"110":{"title":"2.6 #defind 定义常量 VS const 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原码、反码和补码"]},"127":{"title":"3.4.3 反码","titles":["第三章：二进制","3.4 原码、反码和补码"]},"128":{"title":"3.4.4 补码","titles":["第三章：二进制","3.4 原码、反码和补码"]},"129":{"title":"3.4.5 总结","titles":["第三章：二进制","3.4 原码、反码和补码"]},"130":{"title":"3.5 计算机底层为什么使用补码？","titles":["第三章：二进制"]},"131":{"title":"第一章：数据类型（⭐）","titles":[]},"132":{"title":"1.1 概述","titles":["第一章：数据类型（⭐）"]},"133":{"title":"1.2 整数类型","titles":["第一章：数据类型（⭐）"]},"134":{"title":"1.2.1 概述","titles":["第一章：数据类型（⭐）","1.2 整数类型"]},"135":{"title":"1.2.2 短整型（了解）","titles":["第一章：数据类型（⭐）","1.2 整数类型"]},"136":{"title":"1.2.3 整型","titles":["第一章：数据类型（⭐）","1.2 整数类型"]},"137":{"title":"1.2.4 长整型（了解）","titles":["第一章：数据类型（⭐）","1.2 整数类型"]},"138":{"title":"1.2.5 长长整型（了解）","titles":["第一章：数据类型（⭐）","1.2 整数类型"]},"139":{"title":"1.2.6 字面量后缀","titles":["第一章：数据类型（⭐）","1.2 整数类型"]},"140":{"title":"1.2.7 精确宽度类型","titles":["第一章：数据类型（⭐）","1.2 整数类型"]},"141":{"title":"1.2.8 sizeof 运算符","titles":["第一章：数据类型（⭐）","1.2 整数类型"]},"142":{"title":"1.2.9 数值溢出","titles":["第一章：数据类型（⭐）","1.2 整数类型"]},"143":{"title":"1.3 浮点类型","titles":["第一章：数据类型（⭐）"]},"144":{"title":"1.3.1 概述","titles":["第一章：数据类型（⭐）","1.3 浮点类型"]},"145":{"title":"1.3.2 格式占位符","titles":["第一章：数据类型（⭐）","1.3 浮点类型"]},"146":{"title":"1.3.3 字面量后缀","titles":["第一章：数据类型（⭐）","1.3 浮点类型"]},"147":{"title":"1.3.4 类型占用的内存大小（存储空间）","titles":["第一章：数据类型（⭐）","1.3 浮点类型"]},"148":{"title":"1.3.5 类型的取值范围","titles":["第一章：数据类型（⭐）","1.3 浮点类型"]},"149":{"title":"1.4 字符类型","titles":["第一章：数据类型（⭐）"]},"150":{"title":"1.4.1 概述","titles":["第一章：数据类型（⭐）","1.4 字符类型"]},"151":{"title":"1.4.2 格式占位符","titles":["第一章：数据类型（⭐）","1.4 字符类型"]},"152":{"title":"1.4.3 类型占用的内存大小（存储空间）","titles":["第一章：数据类型（⭐）","1.4 字符类型"]},"153":{"title":"1.4.4 类型的取值范围","titles":["第一章：数据类型（⭐）","1.4 字符类型"]},"154":{"title":"1.4.5 字符类型的本质","titles":["第一章：数据类型（⭐）","1.4 字符类型"]},"155":{"title":"1.5 布尔类型","titles":["第一章：数据类型（⭐）"]},"156":{"title":"1.5.1 概述","titles":["第一章：数据类型（⭐）","1.5 布尔类型"]},"157":{"title":"1.5.2 早期的布尔类型","titles":["第一章：数据类型（⭐）","1.5 布尔类型"]},"158":{"title":"1.5.3 宏定义的布尔类型","titles":["第一章：数据类型（⭐）","1.5 布尔类型"]},"159":{"title":"1.5.4 C99 标准中的布尔类型","titles":["第一章：数据类型（⭐）","1.5 布尔类型"]},"160":{"title":"1.5.5 C99 标准头文件中的布尔类型（推荐）","titles":["第一章：数据类型（⭐）","1.5 布尔类型"]},"161":{"title":"1.6 数据类型转换","titles":["第一章：数据类型（⭐）"]},"162":{"title":"1.6.1 概述","titles":["第一章：数据类型（⭐）","1.6 数据类型转换"]},"163":{"title":"1.6.2 自动类型转换（隐式转换）","titles":["第一章：数据类型（⭐）","1.6 数据类型转换"]},"164":{"title":"1.6.2.1 运算过程中的自动类型转换","titles":["第一章：数据类型（⭐）","1.6 数据类型转换","1.6.2 自动类型转换（隐式转换）"]},"165":{"title":"1.6.2.2 赋值时的自动类型转换","titles":["第一章：数据类型（⭐）","1.6 数据类型转换","1.6.2 自动类型转换（隐式转换）"]},"166":{"title":"1.6.3 强制类型转换","titles":["第一章：数据类型（⭐）","1.6 数据类型转换"]},"167":{"title":"第二章：运算符（⭐）","titles":[]},"168":{"title":"2.1 概述","titles":["第二章：运算符（⭐）"]},"169":{"title":"2.2 算术运算符","titles":["第二章：运算符（⭐）"]},"170":{"title":"2.3 关系运算符（比较运算符）","titles":["第二章：运算符（⭐）"]},"171":{"title":"2.4 逻辑运算符","titles":["第二章：运算符（⭐）"]},"172":{"title":"2.5 赋值运算符","titles":["第二章：运算符（⭐）"]},"173":{"title":"2.6 位运算符（了解）","titles":["第二章：运算符（⭐）"]},"174":{"title":"2.6.1 概述","titles":["第二章：运算符（⭐）","2.6 位运算符（了解）"]},"175":{"title":"2.6.2 输出二进制位","titles":["第二章：运算符（⭐）","2.6 位运算符（了解）"]},"176":{"title":"2.6.3 按位与","titles":["第二章：运算符（⭐）","2.6 位运算符（了解）"]},"177":{"title":"2.6.4 按位或","titles":["第二章：运算符（⭐）","2.6 位运算符（了解）"]},"178":{"title":"2.6.5 按位异或","titles":["第二章：运算符（⭐）","2.6 位运算符（了解）"]},"179":{"title":"2.6.6 按位取反","titles":["第二章：运算符（⭐）","2.6 位运算符（了解）"]},"180":{"title":"2.6.7 二进制左移","titles":["第二章：运算符（⭐）","2.6 位运算符（了解）"]},"181":{"title":"2.6.8 二进制右移","titles":["第二章：运算符（⭐）","2.6 位运算符（了解）"]},"182":{"title":"2.7 三元运算符","titles":["第二章：运算符（⭐）"]},"183":{"title":"2.8 运算符优先级","titles":["第二章：运算符（⭐）"]},"184":{"title":"第三章：附录","titles":[]},"185":{"title":"3.1 字符集和字符集编码","titles":["第三章：附录"]},"186":{"title":"3.3.1 概述","titles":["第三章：附录","3.1 字符集和字符集编码"]},"187":{"title":"3.3.2 ASCII 编码","titles":["第三章：附录","3.1 字符集和字符集编码"]},"188":{"title":"3.3.3 Unicode 编码","titles":["第三章：附录","3.1 字符集和字符集编码"]},"189":{"title":"第一章：概述","titles":[]},"190":{"title":"第二章：顺序结构","titles":[]},"191":{"title":"2.1 概述","titles":["第二章：顺序结构"]},"192":{"title":"2.2 应用示例","titles":["第二章：顺序结构"]},"193":{"title":"第三章：分支结构（⭐）","titles":[]},"194":{"title":"3.1 概述","titles":["第三章：分支结构（⭐）"]},"195":{"title":"3.2 单分支结构","titles":["第三章：分支结构（⭐）"]},"196":{"title":"3.2.1 概述","titles":["第三章：分支结构（⭐）","3.2 单分支结构"]},"197":{"title":"3.2.2 应用示例","titles":["第三章：分支结构（⭐）","3.2 单分支结构"]},"198":{"title":"3.2.3 应用示例","titles":["第三章：分支结构（⭐）","3.2 单分支结构"]},"199":{"title":"3.3 双分支结构","titles":["第三章：分支结构（⭐）"]},"200":{"title":"3.3.1 概述","titles":["第三章：分支结构（⭐）","3.3 双分支结构"]},"201":{"title":"3.3.2 应用示例","titles":["第三章：分支结构（⭐）","3.3 双分支结构"]},"202":{"title":"3.3.2 应用示例","titles":["第三章：分支结构（⭐）","3.3 双分支结构"]},"203":{"title":"3.3.3 应用示例","titles":["第三章：分支结构（⭐）","3.3 双分支结构"]},"204":{"title":"3.4 多重分支结构","titles":["第三章：分支结构（⭐）"]},"205":{"title":"3.4.1 概述","titles":["第三章：分支结构（⭐）","3.4 多重分支结构"]},"206":{"title":"3.4.1 应用示例","titles":["第三章：分支结构（⭐）","3.4 多重分支结构"]},"207":{"title":"3.4.2 应用示例","titles":["第三章：分支结构（⭐）","3.4 多重分支结构"]},"208":{"title":"3.5 多重分支结构 switch","titles":["第三章：分支结构（⭐）"]},"209":{"title":"3.5.1 概述","titles":["第三章：分支结构（⭐）","3.5 多重分支结构 switch"]},"210":{"title":"3.5.2 应用示例","titles":["第三章：分支结构（⭐）","3.5 多重分支结构 switch"]},"211":{"title":"3.5.3 应用示例","titles":["第三章：分支结构（⭐）","3.5 多重分支结构 switch"]},"212":{"title":"3.5.4 switch 和 if else if 的比较","titles":["第三章：分支结构（⭐）","3.5 多重分支结构 switch"]},"213":{"title":"3.6 嵌套分支","titles":["第三章：分支结构（⭐）"]},"214":{"title":"3.6.1 概述","titles":["第三章：分支结构（⭐）","3.6 嵌套分支"]},"215":{"title":"3.6.2 应用示例","titles":["第三章：分支结构（⭐）","3.6 嵌套分支"]},"216":{"title":"第四章：随机数","titles":[]},"217":{"title":"4.1 概述","titles":["第四章：随机数"]},"218":{"title":"4.2 C 语言中随机数的产生","titles":["第四章：随机数"]},"219":{"title":"第五章：循环结构（⭐）","titles":[]},"220":{"title":"5.1 概述","titles":["第五章：循环结构（⭐）"]},"221":{"title":"5.2 for 循环","titles":["第五章：循环结构（⭐）"]},"222":{"title":"5.2.1 概述","titles":["第五章：循环结构（⭐）","5.2 for 循环"]},"223":{"title":"5.2.2 应用示例","titles":["第五章：循环结构（⭐）","5.2 for 循环"]},"224":{"title":"5.2.3 应用示例","titles":["第五章：循环结构（⭐）","5.2 for 循环"]},"225":{"title":"5.2.4 应用示例","titles":["第五章：循环结构（⭐）","5.2 for 循环"]},"226":{"title":"5.2.5 应用示例","titles":["第五章：循环结构（⭐）","5.2 for 循环"]},"227":{"title":"5.2.6 应用示例","titles":["第五章：循环结构（⭐）","5.2 for 循环"]},"228":{"title":"5.3 while 循环","titles":["第五章：循环结构（⭐）"]},"229":{"title":"5.3.1 概述","titles":["第五章：循环结构（⭐）","5.3 while 循环"]},"230":{"title":"5.3.2 应用示例","titles":["第五章：循环结构（⭐）","5.3 while 循环"]},"231":{"title":"5.3.3 应用示例","titles":["第五章：循环结构（⭐）","5.3 while 循环"]},"232":{"title":"5.3.4 应用示例","titles":["第五章：循环结构（⭐）","5.3 while 循环"]},"233":{"title":"5.4 do-while 循环","titles":["第五章：循环结构（⭐）"]},"234":{"title":"5.4.1 概述","titles":["第五章：循环结构（⭐）","5.4 do-while 循环"]},"235":{"title":"5.4.2 应用示例","titles":["第五章：循环结构（⭐）","5.4 do-while 循环"]},"236":{"title":"5.4.3 应用示例","titles":["第五章：循环结构（⭐）","5.4 do-while 循环"]},"237":{"title":"5.5 嵌套循环","titles":["第五章：循环结构（⭐）"]},"238":{"title":"5.5.1 概述","titles":["第五章：循环结构（⭐）","5.5 嵌套循环"]},"239":{"title":"5.5.2 应用示例","titles":["第五章：循环结构（⭐）","5.5 嵌套循环"]},"240":{"title":"5.5.3 应用示例","titles":["第五章：循环结构（⭐）","5.5 嵌套循环"]},"241":{"title":"5.5.4 应用示例","titles":["第五章：循环结构（⭐）","5.5 嵌套循环"]},"242":{"title":"5.5.5 应用示例","titles":["第五章：循环结构（⭐）","5.5 嵌套循环"]},"243":{"title":"5.6 无限循环","titles":["第五章：循环结构（⭐）"]},"244":{"title":"5.7 跳转控制语句","titles":["第五章：循环结构（⭐）"]},"245":{"title":"5.7.1 break","titles":["第五章：循环结构（⭐）","5.7 跳转控制语句"]},"246":{"title":"5.7.2 continue","titles":["第五章：循环结构（⭐）","5.7 跳转控制语句"]},"247":{"title":"5.7.3 return","titles":["第五章：循环结构（⭐）","5.7 跳转控制语句"]},"248":{"title":"第一章：数组的概念","titles":[]},"249":{"title":"1.1 为什么需要数组？","titles":["第一章：数组的概念"]},"250":{"title":"1.1.1 需求分析 1","titles":["第一章：数组的概念","1.1 为什么需要数组？"]},"251":{"title":"1.1.2 需求分析 2","titles":["第一章：数组的概念","1.1 为什么需要数组？"]},"252":{"title":"1.1.3 容器的概念","titles":["第一章：数组的概念","1.1 为什么需要数组？"]},"253":{"title":"1.2 什么是数组？","titles":["第一章：数组的概念"]},"254":{"title":"1.3 数组的相关概念","titles":["第一章：数组的概念"]},"255":{"title":"1.4 数组的特点","titles":["第一章：数组的概念"]},"256":{"title":"第二章：数组的操作（⭐）","titles":[]},"257":{"title":"2.1 数组的定义","titles":["第二章：数组的操作（⭐）"]},"258":{"title":"2.1.1 动态初始化","titles":["第二章：数组的操作（⭐）","2.1 数组的定义"]},"259":{"title":"2.1.2 静态初始化 1","titles":["第二章：数组的操作（⭐）","2.1 数组的定义"]},"260":{"title":"2.1.3 静态初始化 2","titles":["第二章：数组的操作（⭐）","2.1 数组的定义"]},"261":{"title":"2.2 访问数组元素","titles":["第二章：数组的操作（⭐）"]},"262":{"title":"2.3 数组越界","titles":["第二章：数组的操作（⭐）"]},"263":{"title":"2.4 计算数组的长度","titles":["第二章：数组的操作（⭐）"]},"264":{"title":"2.5 遍历数组","titles":["第二章：数组的操作（⭐）"]},"265":{"title":"2.6 一维数组的内存分析","titles":["第二章：数组的操作（⭐）"]},"266":{"title":"2.6.1 数组内存图","titles":["第二章：数组的操作（⭐）","2.6 一维数组的内存分析"]},"267":{"title":"2.6.2 数组的注意事项","titles":["第二章：数组的操作（⭐）","2.6 一维数组的内存分析"]},"268":{"title":"2.7 数组应用案例","titles":["第二章：数组的操作（⭐）"]},"269":{"title":"2.7.1 应用示例","titles":["第二章：数组的操作（⭐）","2.7 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位运算符（了解）","titles":["第二章：运算符（⭐）"]},"174":{"title":"2.6.1 概述","titles":["第二章：运算符（⭐）","2.6 位运算符（了解）"]},"175":{"title":"2.6.2 输出二进制位","titles":["第二章：运算符（⭐）","2.6 位运算符（了解）"]},"176":{"title":"2.6.3 按位与","titles":["第二章：运算符（⭐）","2.6 位运算符（了解）"]},"177":{"title":"2.6.4 按位或","titles":["第二章：运算符（⭐）","2.6 位运算符（了解）"]},"178":{"title":"2.6.5 按位异或","titles":["第二章：运算符（⭐）","2.6 位运算符（了解）"]},"179":{"title":"2.6.6 按位取反","titles":["第二章：运算符（⭐）","2.6 位运算符（了解）"]},"180":{"title":"2.6.7 二进制左移","titles":["第二章：运算符（⭐）","2.6 位运算符（了解）"]},"181":{"title":"2.6.8 二进制右移","titles":["第二章：运算符（⭐）","2.6 位运算符（了解）"]},"182":{"title":"2.7 三元运算符","titles":["第二章：运算符（⭐）"]},"183":{"title":"2.8 运算符优先级","titles":["第二章：运算符（⭐）"]},"184":{"title":"第三章：附录","titles":[]},"185":{"title":"3.1 字符集和字符集编码","titles":["第三章：附录"]},"186":{"title":"3.3.1 概述","titles":["第三章：附录","3.1 字符集和字符集编码"]},"187":{"title":"3.3.2 ASCII 编码","titles":["第三章：附录","3.1 字符集和字符集编码"]},"188":{"title":"3.3.3 Unicode 编码","titles":["第三章：附录","3.1 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Map,this._dirtCount=0,this._currentVacuum=null,this._enqueuedVacuum=null,this._enqueuedVacuumConditions=Ke,this.addFields(this._options.fields)}add(e){const{extractField:t,tokenize:s,processTerm:n,fields:r,idField:i}=this._options,o=t(e,i);if(o==null)throw new Error(`MiniSearch: document does not have ID field "${i}"`);if(this._idToShortId.has(o))throw new Error(`MiniSearch: duplicate ID ${o}`);const c=this.addDocumentId(o);this.saveStoredFields(c,e);for(const l of r){const h=t(e,l);if(h==null)continue;const f=s(h.toString(),l),v=this._fieldIds[l],b=new Set(f).size;this.addFieldLength(c,v,this._documentCount-1,b);for(const w of f){const _=n(w,l);if(Array.isArray(_))for(const y of _)this.addTerm(v,c,y);else _&&this.addTerm(v,c,_)}}}addAll(e){for(const t of e)this.add(t)}addAllAsync(e,t={}){const{chunkSize:s=10}=t,n={chunk:[],promise:Promise.resolve()},{chunk:r,promise:i}=e.reduce(({chunk:o,promise:c},l,h)=>(o.push(l),(h+1)%s===0?{chunk:[],promise:c.then(()=>new 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e)this.discard(s)}finally{this._options.autoVacuum=t}this.maybeAutoVacuum()}replace(e){const{idField:t,extractField:s}=this._options,n=s(e,t);this.discard(n),this.add(e)}vacuum(e={}){return this.conditionalVacuum(e)}conditionalVacuum(e,t){return this._currentVacuum?(this._enqueuedVacuumConditions=this._enqueuedVacuumConditions&&t,this._enqueuedVacuum!=null?this._enqueuedVacuum:(this._enqueuedVacuum=this._currentVacuum.then(()=>{const s=this._enqueuedVacuumConditions;return this._enqueuedVacuumConditions=Ke,this.performVacuuming(e,s)}),this._enqueuedVacuum)):this.vacuumConditionsMet(t)===!1?Promise.resolve():(this._currentVacuum=this.performVacuuming(e),this._currentVacuum)}performVacuuming(e,t){return Te(this,void 0,void 0,function*(){const s=this._dirtCount;if(this.vacuumConditionsMet(t)){const n=e.batchSize||We.batchSize,r=e.batchWait||We.batchWait;let i=1;for(const[o,c]of this._index){for(const[l,h]of c)for(const[f]of h)this._documentIds.has(f)||(h.size<=1?c.delete(l):h.delete(f));this._index.get(o).size===0&&this._index.delete(o),i%n===0&&(yield new Promise(l=>setTimeout(l,r))),i+=1}this._dirtCount-=s}yield null,this._currentVacuum=this._enqueuedVacuum,this._enqueuedVacuum=null})}vacuumConditionsMet(e){if(e==null)return!0;let{minDirtCount:t,minDirtFactor:s}=e;return t=t||je.minDirtCount,s=s||je.minDirtFactor,this.dirtCount>=t&&this.dirtFactor>=s}get isVacuuming(){return this._currentVacuum!=null}get dirtCount(){return this._dirtCount}get dirtFactor(){return this._dirtCount/(1+this._documentCount+this._dirtCount)}has(e){return this._idToShortId.has(e)}getStoredFields(e){const t=this._idToShortId.get(e);if(t!=null)return this._storedFields.get(t)}search(e,t={}){const s=this.executeQuery(e,t),n=[];for(const[r,{score:i,terms:o,match:c}]of s){const l=o.length||1,h={id:this._documentIds.get(r),score:i*l,terms:Object.keys(c),queryTerms:o,match:c};Object.assign(h,this._storedFields.get(r)),(t.filter==null||t.filter(h))&&n.push(h)}return e===le.wildcard&&t.boostDocument==null&&this._options.searchOptions.boostDocument==null||n.sort(ft),n}autoSuggest(e,t={}){t=Object.assign(Object.assign({},this._options.autoSuggestOptions),t);const s=new Map;for(const{score:r,terms:i}of this.search(e,t)){const o=i.join(" "),c=s.get(o);c!=null?(c.score+=r,c.count+=1):s.set(o,{score:r,terms:i,count:1})}const n=[];for(const[r,{score:i,terms:o,count:c}]of s)n.push({suggestion:r,terms:o,score:i/c});return n.sort(ft),n}get documentCount(){return this._documentCount}get termCount(){return this._index.size}static loadJSON(e,t){if(t==null)throw new Error("MiniSearch: loadJSON should be given the same options used when serializing the index");return this.loadJS(JSON.parse(e),t)}static loadJSONAsync(e,t){return Te(this,void 0,void 0,function*(){if(t==null)throw 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l=0;for(const[h,f]of s){const v=new Map;for(const b of Object.keys(f)){let w=f[b];o===1&&(w=w.ds),v.set(parseInt(b,10),yield Ee(w))}++l%1e3===0&&(yield Nt(0)),c._index.set(h,v)}return c})}static instantiateMiniSearch(e,t){const{documentCount:s,nextId:n,fieldIds:r,averageFieldLength:i,dirtCount:o,serializationVersion:c}=e;if(c!==1&&c!==2)throw new Error("MiniSearch: cannot deserialize an index created with an incompatible version");const l=new le(t);return l._documentCount=s,l._nextId=n,l._idToShortId=new Map,l._fieldIds=r,l._avgFieldLength=i,l._dirtCount=o||0,l._index=new X,l}executeQuery(e,t={}){if(e===le.wildcard)return this.executeWildcardQuery(t);if(typeof e!="string"){const v=Object.assign(Object.assign(Object.assign({},t),e),{queries:void 0}),b=e.queries.map(w=>this.executeQuery(w,v));return this.combineResults(b,v.combineWith)}const{tokenize:s,processTerm:n,searchOptions:r}=this._options,i=Object.assign(Object.assign({tokenize:s,processTerm:n},r),t),{tokenize:o,processTerm:c}=i,f=o(e).flatMap(v=>c(v)).filter(v=>!!v).map($s(i)).map(v=>this.executeQuerySpec(v,i));return this.combineResults(f,i.combineWith)}executeQuerySpec(e,t){const s=Object.assign(Object.assign({},this._options.searchOptions),t),n=(s.fields||this._options.fields).reduce((_,y)=>Object.assign(Object.assign({},_),{[y]:ze(s.boost,y)||1}),{}),{boostDocument:r,weights:i,maxFuzzy:o,bm25:c}=s,{fuzzy:l,prefix:h}=Object.assign(Object.assign({},dt.weights),i),f=this._index.get(e.term),v=this.termResults(e.term,e.term,1,e.termBoost,f,n,r,c);let b,w;if(e.prefix&&(b=this._index.atPrefix(e.term)),e.fuzzy){const _=e.fuzzy===!0?.2:e.fuzzy,y=_<1?Math.min(o,Math.round(e.term.length*_)):_;y&&(w=this._index.fuzzyGet(e.term,y))}if(b)for(const[_,y]of b){const R=_.length-e.term.length;if(!R)continue;w==null||w.delete(_);const C=h*_.length/(_.length+.3*R);this.termResults(e.term,_,C,e.termBoost,y,n,r,c,v)}if(w)for(const _ of w.keys()){const[y,R]=w.get(_);if(!R)continue;const C=l*_.length/(_.length+R);this.termResults(e.term,_,C,e.termBoost,y,n,r,c,v)}return v}executeWildcardQuery(e){const t=new Map,s=Object.assign(Object.assign({},this._options.searchOptions),e);for(const[n,r]of this._documentIds){const i=s.boostDocument?s.boostDocument(r,"",this._storedFields.get(n)):1;t.set(n,{score:i,terms:[],match:{}})}return t}combineResults(e,t=Ue){if(e.length===0)return new Map;const s=t.toLowerCase(),n=Ps[s];if(!n)throw new Error(`Invalid combination operator: ${t}`);return e.reduce(n)||new Map}toJSON(){const e=[];for(const[t,s]of this._index){const n={};for(const[r,i]of s)n[r]=Object.fromEntries(i);e.push([t,n])}return{documentCount:this._documentCount,nextId:this._nextId,documentIds:Object.fromEntries(this._documentIds),fieldIds:this._fieldIds,fieldLength:Object.fromEntries(this._fieldLength),averageFieldLength:this._avgFieldLength,storedFields:Object.fromEntries(this._storedFields),dirtCount:this._dirtCount,index:e,serializationVersion:2}}termResults(e,t,s,n,r,i,o,c,l=new Map){if(r==null)return l;for(const h of Object.keys(i)){const f=i[h],v=this._fieldIds[h],b=r.get(v);if(b==null)continue;let w=b.size;const _=this._avgFieldLength[v];for(const y of b.keys()){if(!this._documentIds.has(y)){this.removeTerm(v,y,t),w-=1;continue}const R=o?o(this._documentIds.get(y),t,this._storedFields.get(y)):1;if(!R)continue;const C=b.get(y),J=this._fieldLength.get(y)[v],H=Vs(C,w,this._documentCount,J,_,c),W=s*n*f*R*H,V=l.get(y);if(V){V.score+=W,Ws(V.terms,e);const $=ze(V.match,t);$?$.push(h):V.match[t]=[h]}else l.set(y,{score:W,terms:[e],match:{[t]:[h]}})}}return l}addTerm(e,t,s){const n=this._index.fetch(s,pt);let r=n.get(e);if(r==null)r=new Map,r.set(t,1),n.set(e,r);else{const i=r.get(t);r.set(t,(i||0)+1)}}removeTerm(e,t,s){if(!this._index.has(s)){this.warnDocumentChanged(t,e,s);return}const n=this._index.fetch(s,pt),r=n.get(e);r==null||r.get(t)==null?this.warnDocumentChanged(t,e,s):r.get(t)<=1?r.size<=1?n.delete(e):r.delete(t):r.set(t,r.get(t)-1),this._index.get(s).size===0&&this._index.delete(s)}warnDocumentChanged(e,t,s){for(const n of Object.keys(this._fieldIds))if(this._fieldIds[n]===t){this._options.logger("warn",`MiniSearch: document with ID ${this._documentIds.get(e)} has changed before removal: term "${s}" was not present in field "${n}". 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第一章：计算机组成原理 ​

1.1 计算机系统 ​

  • 计算机（Computer），俗称"电脑"，是一种能够接收和存储信息，并按照存储在其内部的程序对海量的数据进行自动、高速的处理，然后将处理结果输出的现代化智能电子设备。
  • 计算机有很多形式，如：台式电脑、笔记本电脑、智能手机、平板电脑等，还有生产环境中提供重要业务支撑的各种服务器。

  • 一个完整的计算机系统由硬件（Hardware）系统和软件（Software）系统两大部分组成，即：

1.2 冯·诺依曼体系结构 ​

  • 冯·诺依曼是一位多才多艺的科学家，他在数学、物理学、计算机科学、经济学等领域都有杰出的贡献。

  • 冯·诺依曼的主要成就：
    • 在计算机科学领域的最著名贡献是提出了冯·诺依曼体系结构（1946 年），这是现代计算机设计的基础。
    • 促进了计算机的可编程性和通用性，使得计算机能够执行各种复杂的任务。
    • 对核武器设计、自动化控制系统、人工智能等领域的发展产生了重要影响。
    • ……

IMPORTANT

冯·诺依曼体系结构是现代计算机（量子计算机除外）设计的基础。

  • 冯·诺依曼体系结构的理论要点如下：

    • ① 存储程序：程序指令和数据都存储在计算机的内存中，这使得程序可以在运行时修改。

    • ② 二进制逻辑：所有数据和指令都以二进制形式表示。

    • ③ 顺序执行：指令按照它们在内存中的顺序执行，但可以有条件地改变执行顺序。

    • ④ 五大部件：计算机由运算器、控制器、存储器、输入设备和输出设备组成。

    • ⑤ 指令结构：指令由操作码和地址码组成，操作码指示要执行的操作，地址码指示操作数的位置。

    • ⑥ 中心化控制：计算机的控制单元（CPU）负责解释和执行指令，控制数据流。

NOTE

上述的组件协同工作，构成了一个完整的计算机系统：

  • 运算器和控制器通常被集成在一起，组成中央处理器（CPU），负责数据处理和指令执行。
  • 存储器保存数据和程序，是计算机运作的基础。
  • 输入设备和输出设备负责与外界的交互，确保用户能够输入信息并接收计算机的处理结果。

1.3 各种硬件处理速度和性能优化 ​

  • 计算机的性能短板：如果 CPU 有每秒处理 1000 个服务请求的能力，各种总线的负载能力能达到 500 个， 但网卡只能接受 200个请求，而硬盘只能负担 150 个的话，那这台服务器得处理能力只能是 150 个请求/ 秒，有 85% 的处理器计算能力浪费了，在计算机系统当中，硬盘的读写速率已经成为影响系统性能进一 步提高的瓶颈。

img

  • 计算机的各个设备部件的延迟从高到低的排列，依次是机械硬盘（HDD）、固态硬盘（SSD）、内存、CPU 。

img

  • 从上图中，我们可以知道，CPU 是最快的，一个时钟周期是 0.3 ns ，内存访问需要 120 ns ，固态硬盘访问需要 50-150 us，传统的硬盘访问需要 1-10 ms，而网络访问是最慢，需要 40 ms 以上。
  • 时间的单位换算如下：
txt
1 秒 = 1000 毫秒，即 1 s = 1000 ms。
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第一章：计算机组成原理 ​
1.1 计算机系统 ​
  • 计算机（Computer），俗称"电脑"，是一种能够接收和存储信息，并按照存储在其内部的程序对海量的数据进行自动、高速的处理，然后将处理结果输出的现代化智能电子设备。
  • 计算机有很多形式，如：台式电脑、笔记本电脑、智能手机、平板电脑等，还有生产环境中提供重要业务支撑的各种服务器。
  • 一个完整的计算机系统由硬件（Hardware）系统和软件（Software）系统两大部分组成，即：
1.2 冯·诺依曼体系结构 ​
  • 冯·诺依曼是一位多才多艺的科学家，他在数学、物理学、计算机科学、经济学等领域都有杰出的贡献。
  • 冯·诺依曼的主要成就： 
    • 在计算机科学领域的最著名贡献是提出了冯·诺依曼体系结构（1946 年），这是现代计算机设计的基础。
    • 促进了计算机的可编程性和通用性，使得计算机能够执行各种复杂的任务。
    • 对核武器设计、自动化控制系统、人工智能等领域的发展产生了重要影响。
    • ……
IMPORTANT
冯·诺依曼体系结构是现代计算机（量子计算机除外）设计的基础。
  • 冯·诺依曼体系结构的理论要点如下：
    • ① 存储程序：程序指令和数据都存储在计算机的内存中，这使得程序可以在运行时修改。
    • ② 二进制逻辑：所有数据和指令都以二进制形式表示。
    • ③ 顺序执行：指令按照它们在内存中的顺序执行，但可以有条件地改变执行顺序。
    • ④ 五大部件：计算机由运算器、控制器、存储器、输入设备和输出设备组成。
    • ⑤ 指令结构：指令由操作码和地址码组成，操作码指示要执行的操作，地址码指示操作数的位置。
    • ⑥ 中心化控制：计算机的控制单元（CPU）负责解释和执行指令，控制数据流。
NOTE
上述的组件协同工作，构成了一个完整的计算机系统：
  • 运算器和控制器通常被集成在一起，组成中央处理器（CPU），负责数据处理和指令执行。
  • 存储器保存数据和程序，是计算机运作的基础。
  • 输入设备和输出设备负责与外界的交互，确保用户能够输入信息并接收计算机的处理结果。
1.3 各种硬件处理速度和性能优化 ​
  • 计算机的性能短板：如果 CPU 有每秒处理 1000 个服务请求的能力，各种总线的负载能力能达到 500 个， 但网卡只能接受 200个请求，而硬盘只能负担 150 个的话，那这台服务器得处理能力只能是 150 个请求/ 秒，有 85% 的处理器计算能力浪费了，在计算机系统当中，硬盘的读写速率已经成为影响系统性能进一 步提高的瓶颈。
img
  • 计算机的各个设备部件的延迟从高到低的排列，依次是机械硬盘（HDD）、固态硬盘（SSD）、内存、CPU 。
img
  • 从上图中，我们可以知道，CPU 是最快的，一个时钟周期是 0.3 ns ，内存访问需要 120 ns ，固态硬盘访问需要 50-150 us，传统的硬盘访问需要 1-10 ms，而网络访问是最慢，需要 40 ms 以上。
  • 时间的单位换算如下：
txt
1 秒 = 1000 毫秒，即 1 s = 1000 ms。
 1 毫秒 = 1000 微妙，即 1 ms = 1000 us 。
 1 微妙 = 1000 纳秒，即 1 us = 1000 ns。
  • 按照上图，将计算机世界的时间和人类世界的时间进行对比，即：
txt
如果 CPU 的时钟周期按照 1 秒计算，
 那么，内存访问就需要 6 分钟；
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diff --git a/assets/notes_01_c-basic_02_xdx_index.md.Cxyt4HEd.js b/assets/notes_01_c-basic_02_xdx_index.md.36L8tSmA.js
similarity index 99%
rename from assets/notes_01_c-basic_02_xdx_index.md.Cxyt4HEd.js
rename to assets/notes_01_c-basic_02_xdx_index.md.36L8tSmA.js
index d2a6a00..accfc35 100644
--- a/assets/notes_01_c-basic_02_xdx_index.md.Cxyt4HEd.js
+++ b/assets/notes_01_c-basic_02_xdx_index.md.36L8tSmA.js
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第一章：变量（⭐） ​
1.1 程序中变化的数据 ​
  • 在生活中，我们使用最多的不是固定的数据，而是会变化的数据： 
    • ① 购物车商品的数量、价格等。
    • ② 一首歌播放的时间、进度条、歌词的展示等。
    • ③ 微信聊天中消息条数、时间、语音的长度、头像、名称等。
    • ④ 游戏中技能的冷却时间、血量、蓝量、buff 时间、金币的数量等。
    • ……
  • 下图是一个购物车中变化的数据，即：
  • 那么，在实际开发中，我们就会使用变量来保存和操作这些变化的数据。
1.2 变量 ​
  • 变量的定义：变量是程序中不可或缺的组成单位，最基本的存储单元。其实，变量就是一个存储数据的临时空间，可以向其中存储不同类型的数据，如：整数、小数、字符、字符串等，并且变量中的数据在程序运行的时候可以动态改变。
NOTE
  • 变量：用来存储数据的容器。
  • 数据：可以是一个用来计算的数字，如：上文购物车中的价格等；也可以是一句话中的关键词或其它任意格式的数据。
  • 变量的特别之处就在于它存放的数据是可以改变的。
  • 我们可以将变量想象为一个容器，盒子中装的就是我们想要的数据，并且我们需要给盒子取一个特别的名称；通过这个特别的名称，我们可以给盒子添加数据或移除数据，这个特别的名称就是变量名。
NOTE
  • ① 变量是内存中的一个存储区域，该区域的数据可以在同一类型范围内不断变化。
  • ② 通过变量名，可以操作这块内存区域，向其中存储数据或获取数据以及移除数据。
  • ③ 变量的构成包含三个要素：数据类型、变量名、需要存储的数据。
  • ④ 在生活中，我们会经常说：这件衣服的价格是 100（整型） 元，这双鞋子的价格是 250.5（小数，浮点类型） 元，今天天气真好（字符串类型）之类的话；在计算机科学中，这些都是数据，并且它们是有类型，即：数据类型。（数据类型用于定义变量所能存储的数据的种类以及可以对这些数据进行的操作的一种分类，每种数据类型都有特定的属性和用途，它们决定了变量在内存中如何表示和存储，以及变量可以执行哪些操作）
1.3 变量的声明和使用 ​
  • ① 变量必须先声明，后使用。
  • ② 可以先声明变量再赋值，也可以在声明变量的同时进行赋值。
  • ③ 变量的值可以在同一类型范围内不断变化。
IMPORTANT
在实际开发中，我们通常都会在声明变量的同时，给其赋值，这被称为初始化。
  • 示例：先声明，再使用
c
#include <stdio.h>
+import{_ as s,c as i,o as a,a6 as n}from"./chunks/framework.CZKtKhAm.js";const l="/c/assets/1.CXNJqOOc.png",e="/c/assets/2.E0LS08Y5.png",t="/c/assets/3.6recRAvz.jpeg",p="/c/assets/4.DcyDw4rB.jpg",h="/c/assets/5.q20QOAIA.png",d="/c/assets/6.CmrWpBzQ.png",k="/c/assets/7.CocAjZjO.png",r="/c/assets/8.CHZSlb-7.png",c="/c/assets/9.RD2M_pYn.png",o="/c/assets/10.CmNKK_Ug.png",u="/c/assets/11.CbGZ55Dj.png",E="/c/assets/12.DpTBR420.png",b="/c/assets/13.XcPl7d9s.png",g="/c/assets/14.DL02VQMp.png",F="/c/assets/15.Dr67r_Ws.png",y="/c/assets/16.C5XiXNVN.png",m="/c/assets/17.DO8XxSV6.jpg",C="/c/assets/18.CUXrdefp.jpeg",B="/c/assets/19.uqLiL_yu.png",v="/c/assets/20.CkykpHY2.png",A="/c/assets/21.DV1YbrOP.png",D="/c/assets/22.AHNJT9TV.png",_="/c/assets/23.Bs-MOwx2.png",q="/c/assets/24.StzjmBz-.png",f="/c/assets/25.C0wVWaxD.png",x="/c/assets/26.LXJMAihe.png",P="/c/assets/27._UTCq3PD.png",O="/c/assets/28.BjQ5kBL-.png",T="/c/assets/29.COIOzcmT.png",N="/c/assets/30.Cu__mjav.png",M="/c/assets/31.BX_KzkHt.png",w="/c/assets/32.COt_QxSP.png",K=JSON.parse('{"title":"第一章：变量（⭐）","description":"","frontmatter":{},"headers":[],"relativePath":"notes/01_c-basic/02_xdx/index.md","filePath":"notes/01_c-basic/02_xdx/index.md","lastUpdated":1721202271000}'),I={name:"notes/01_c-basic/02_xdx/index.md"},U=n('
第一章：变量（⭐） ​
1.1 程序中变化的数据 ​
  • 在生活中，我们使用最多的不是固定的数据，而是会变化的数据： 
    • ① 购物车商品的数量、价格等。
    • ② 一首歌播放的时间、进度条、歌词的展示等。
    • ③ 微信聊天中消息条数、时间、语音的长度、头像、名称等。
    • ④ 游戏中技能的冷却时间、血量、蓝量、buff 时间、金币的数量等。
    • ……
  • 下图是一个购物车中变化的数据，即：
  • 那么，在实际开发中，我们就会使用变量来保存和操作这些变化的数据。
1.2 变量 ​
  • 变量的定义：变量是程序中不可或缺的组成单位，最基本的存储单元。其实，变量就是一个存储数据的临时空间，可以向其中存储不同类型的数据，如：整数、小数、字符、字符串等，并且变量中的数据在程序运行的时候可以动态改变。
NOTE
  • 变量：用来存储数据的容器。
  • 数据：可以是一个用来计算的数字，如：上文购物车中的价格等；也可以是一句话中的关键词或其它任意格式的数据。
  • 变量的特别之处就在于它存放的数据是可以改变的。
  • 我们可以将变量想象为一个容器，盒子中装的就是我们想要的数据，并且我们需要给盒子取一个特别的名称；通过这个特别的名称，我们可以给盒子添加数据或移除数据，这个特别的名称就是变量名。
NOTE
  • ① 变量是内存中的一个存储区域，该区域的数据可以在同一类型范围内不断变化。
  • ② 通过变量名，可以操作这块内存区域，向其中存储数据或获取数据以及移除数据。
  • ③ 变量的构成包含三个要素：数据类型、变量名、需要存储的数据。
  • ④ 在生活中，我们会经常说：这件衣服的价格是 100（整型） 元，这双鞋子的价格是 250.5（小数，浮点类型） 元，今天天气真好（字符串类型）之类的话；在计算机科学中，这些都是数据，并且它们是有类型，即：数据类型。（数据类型用于定义变量所能存储的数据的种类以及可以对这些数据进行的操作的一种分类，每种数据类型都有特定的属性和用途，它们决定了变量在内存中如何表示和存储，以及变量可以执行哪些操作）
1.3 变量的声明和使用 ​
  • ① 变量必须先声明，后使用。
  • ② 可以先声明变量再赋值，也可以在声明变量的同时进行赋值。
  • ③ 变量的值可以在同一类型范围内不断变化。
IMPORTANT
在实际开发中，我们通常都会在声明变量的同时，给其赋值，这被称为初始化。
  • 示例：先声明，再使用
c
#include <stdio.h>
 
 int main() {
 
diff --git a/assets/notes_01_c-basic_02_xdx_index.md.Cxyt4HEd.lean.js b/assets/notes_01_c-basic_02_xdx_index.md.36L8tSmA.lean.js
similarity index 91%
rename from assets/notes_01_c-basic_02_xdx_index.md.Cxyt4HEd.lean.js
rename to assets/notes_01_c-basic_02_xdx_index.md.36L8tSmA.lean.js
index ce04045..bb895e5 100644
--- a/assets/notes_01_c-basic_02_xdx_index.md.Cxyt4HEd.lean.js
+++ b/assets/notes_01_c-basic_02_xdx_index.md.36L8tSmA.lean.js
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diff --git a/assets/notes_01_c-basic_03_xdx_index.md.Bc0D4KAS.js b/assets/notes_01_c-basic_03_xdx_index.md.BUQ_uNMg.js
similarity index 99%
rename from assets/notes_01_c-basic_03_xdx_index.md.Bc0D4KAS.js
rename to assets/notes_01_c-basic_03_xdx_index.md.BUQ_uNMg.js
index 897d555..a23852e 100644
--- a/assets/notes_01_c-basic_03_xdx_index.md.Bc0D4KAS.js
+++ b/assets/notes_01_c-basic_03_xdx_index.md.BUQ_uNMg.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a5 as n}from"./chunks/framework.BE8if9e6.js";const l="/c/assets/1.L8V3GBrc.png",p="/c/assets/2.BkF1yWLn.png",t="/c/assets/3.CceY8r_n.png",h="/c/assets/4.DHaUgOwj.png",k="/c/assets/5.CXGaq_zh.png",e="/c/assets/6.BrZYAEEl.png",r="/c/assets/7.DpCroFHv.png",d="/c/assets/8.Cr7P0Gji.png",E="/c/assets/9.NlBmD7pA.png",c="/c/assets/10.ZiBq6Pno.png",g="/c/assets/11.DAgmsf-w.png",F="/c/assets/12.B2iC37fw.png",y="/c/assets/14.BlE3ZFud.png",u="/c/assets/15.CdvhiwcU.png",b="/c/assets/16.D74t3-Xt.png",o="/c/assets/17.DdAZIfeP.png",C="/c/assets/18.B4Zfj2jX.png",m="/c/assets/19.IfpA0D5n.png",B="/c/assets/20.CfIzYazX.png",A="/c/assets/21.eHnZcbpI.png",D="/c/assets/22.BNoKlM4o.png",v="/c/assets/23.CMVtwrqr.png",q="/c/assets/24.CN19KJG7.png",f="/c/assets/25.BIhiJHjz.png",_="/c/assets/26.A_E4n4g8.png",x="/c/assets/27.Bv4qFbwF.png",z="/c/assets/28.IKaazo2J.png",w="/c/assets/29.CGTVELeO.png",I="/c/assets/30.Bz4_lEH0.gif",P="/c/assets/31.CcDWE4nn.png",T="/c/assets/32.B7y2_JVX.gif",N="/c/assets/33.Btcc3rs2.gif",L="/c/assets/34.CR4ARW8y.png",O="/c/assets/33.Btcc3rs2.gif",S="/c/assets/36.DOX3ymYP.gif",U="/c/assets/37.Cie9_tkP.gif",M="/c/assets/38.DLjH9Ges.png",$=JSON.parse('{"title":"第一章：数据类型（⭐）","description":"","frontmatter":{},"headers":[],"relativePath":"notes/01_c-basic/03_xdx/index.md","filePath":"notes/01_c-basic/03_xdx/index.md","lastUpdated":1721697894000}'),X={name:"notes/01_c-basic/03_xdx/index.md"},R=n('
第一章：数据类型（⭐） ​
1.1 概述 ​
  • 根据变量中存储的值的不同，我们可以将变量分为两类：
    • 普通变量：变量所对应的内存中存储的是普通值。
    • 指针变量：变量所对应的内存中存储的是另一个变量的地址。
  • 如下图所示：
NOTE
普通变量和指针变量的相同点：
  • 普通变量有内存空间，指针变量也有内存空间。
  • 普通变量有内存地址，指针变量也有内存地址。
  • 普通变量所对应的内存空间中有值，指针变量所对应的内存空间中也有值。
普通变量和指针变量的不同点：
  • 普通变量所对应的内存空间存储的是普通的值，如：整数、小数、字符等；指针变量所对应的内存空间存储的是另外一个变量的地址。
  • 普通变量有普通变量的运算方式，而指针变量有指针变量的运算方式（后续讲解）。
  • 那么，在 C 语言中变量的数据类型就可以这么划分，如下所示：
NOTE
  • 根据普通变量中存储的值的类型不同，可以将普通变量类型划分为基本数据类型（整型、字符类型、浮点类型、布尔类型）和复合数据类型（数组类型、结构体类型、共用体类型、枚举类型）。
  • 根据指针变量所指向空间中存储的值的类型不同，可以将指针类型分为基本数据类型指针、复合数据类型指针、函数指针、数组指针等，例如：如果指针所指向的空间保存的是 int 类型，那么该指针就是 int 类型的指针。
1.2 整数类型 ​
1.2.1 概述 ​
  • 整数类型简称整型，用于存储整数值，如：12、20、50 等。
  • 根据所占内存空间大小的不同，可以将整数类型划分为：
  • ① 短整型：
类型存储空间（内存空间）取值范围
unsigned short （无符号短整型）2 字节0 ~ 65,535 (2^16 - 1)
[signed] short（有符号短整型，默认）2 字节-32,768 (- 2^15) ~ 32,767 (2^15 -1)
  • ② 整型：
类型存储空间（内存空间）取值范围
unsigned int（无符号整型）4 字节（通常）0 ~ 4294967295 (0 ~2^32 -1)
[signed] int（有符号整型，默认）4 字节（通常）-2147483648（- 2^31） ~ 2147483647 (2^31-1)
  • ③ 长整型：
类型存储空间（内存空间）取值范围
unsigned long（无符号长整型）4 字节（通常）0 ~2^32 -1
[signed] long（有符号长整型，默认）4 字节（通常）- 2^31 ~ 2^31-1
  • ④ 长长整型：
类型存储空间（内存空间）取值范围
unsigned long long（无符号长整型）8 字节（通常）0 ~2^64 -1
[signed] long long（有符号长整型，默认）8 字节（通常）- 2^63 ~ 2^63-1
NOTE
  • ① C 语言默认没有规定各种数据类型所占存储单元的长度，但是通常需要遵守：sizeof(short int) ≤ sizeof(int) ≤ sizeof(long int) ≤ sizeof(long long) ，具体的存储空间由编译系统自行决定；其中，sizeof 是测量类型或变量、常量长度的运算符。
  • ② short 至少 2 个字节，long 至少 4 个字节。
  • ③ 之所以这么规定，是为了可以让 C 语言长久使用，因为目前主流的 CPU 都是 64 位，但是在 C语言刚刚出现的时候，CPU 还是以 8 位和 16 位为主。如果当时就将整型定死为 8 位或 16 位，那么现在我们肯定不会再学习 C 语言了。
  • ④ 整型分为有符号 signed 和无符号 unsigned 两种，默认是 signed。
  • ⑤ 在实际开发中，最常用的整数类型就是 int 类型了，如果取值范围不够，就使用 long 或 long long 。
  • ⑥ C 语言中的格式占位符非常多，只需要大致了解即可；因为，我们在实际开发中，一般都会使用 C++ 或 Rust 以及其它的高级编程语言，如：Java 等，早已经解决了需要通过格式占位符来输入和输出变量。
1.2.2 短整型（了解） ​
  • 语法：
c
unsigned short x = 10 ; // 无符号短整型
c
short x = -10; // 有符号短整型
NOTE
  • ① 有符号表示的是正数、负数和 0 ，即有正负号。无符号表示的是 0 和正数，即正整数，没有符号。
  • ② 在 printf 中无符号短整型（unsigned short）的格式占位符是 %hu ，有符号短整型（signed short）的格式占位符是 %hd 。
  • ③ 可以通过 sizeof 运算符获取无符号短整型（unsigned short） 和 有符号短整型（signed short） 的存储空间（所占内存空间）。
  • ③ 可以通过 #include <limits.h> 来获取 无符号短整型（unsigned short） 和有符号短整型（signed short）的取值范围。
  • 示例：定义和打印短整型变量
c
#include <stdio.h>
+import{_ as s,c as i,o as a,a6 as n}from"./chunks/framework.CZKtKhAm.js";const l="/c/assets/1.L8V3GBrc.png",p="/c/assets/2.BkF1yWLn.png",t="/c/assets/3.CceY8r_n.png",h="/c/assets/4.DHaUgOwj.png",k="/c/assets/5.CXGaq_zh.png",e="/c/assets/6.BrZYAEEl.png",r="/c/assets/7.DpCroFHv.png",d="/c/assets/8.Cr7P0Gji.png",E="/c/assets/9.NlBmD7pA.png",c="/c/assets/10.ZiBq6Pno.png",g="/c/assets/11.DAgmsf-w.png",F="/c/assets/12.B2iC37fw.png",y="/c/assets/14.BlE3ZFud.png",u="/c/assets/15.CdvhiwcU.png",b="/c/assets/16.D74t3-Xt.png",o="/c/assets/17.DdAZIfeP.png",C="/c/assets/18.B4Zfj2jX.png",m="/c/assets/19.IfpA0D5n.png",B="/c/assets/20.CfIzYazX.png",A="/c/assets/21.eHnZcbpI.png",D="/c/assets/22.BNoKlM4o.png",v="/c/assets/23.CMVtwrqr.png",q="/c/assets/24.CN19KJG7.png",f="/c/assets/25.BIhiJHjz.png",_="/c/assets/26.A_E4n4g8.png",x="/c/assets/27.Bv4qFbwF.png",z="/c/assets/28.IKaazo2J.png",w="/c/assets/29.CGTVELeO.png",I="/c/assets/30.Bz4_lEH0.gif",P="/c/assets/31.CcDWE4nn.png",T="/c/assets/32.B7y2_JVX.gif",N="/c/assets/33.Btcc3rs2.gif",L="/c/assets/34.CR4ARW8y.png",O="/c/assets/33.Btcc3rs2.gif",S="/c/assets/36.DOX3ymYP.gif",U="/c/assets/37.Cie9_tkP.gif",M="/c/assets/38.DLjH9Ges.png",$=JSON.parse('{"title":"第一章：数据类型（⭐）","description":"","frontmatter":{},"headers":[],"relativePath":"notes/01_c-basic/03_xdx/index.md","filePath":"notes/01_c-basic/03_xdx/index.md","lastUpdated":1721697894000}'),X={name:"notes/01_c-basic/03_xdx/index.md"},R=n('
第一章：数据类型（⭐） ​
1.1 概述 ​
  • 根据变量中存储的值的不同，我们可以将变量分为两类：
    • 普通变量：变量所对应的内存中存储的是普通值。
    • 指针变量：变量所对应的内存中存储的是另一个变量的地址。
  • 如下图所示：
NOTE
普通变量和指针变量的相同点：
  • 普通变量有内存空间，指针变量也有内存空间。
  • 普通变量有内存地址，指针变量也有内存地址。
  • 普通变量所对应的内存空间中有值，指针变量所对应的内存空间中也有值。
普通变量和指针变量的不同点：
  • 普通变量所对应的内存空间存储的是普通的值，如：整数、小数、字符等；指针变量所对应的内存空间存储的是另外一个变量的地址。
  • 普通变量有普通变量的运算方式，而指针变量有指针变量的运算方式（后续讲解）。
  • 那么，在 C 语言中变量的数据类型就可以这么划分，如下所示：
NOTE
  • 根据普通变量中存储的值的类型不同，可以将普通变量类型划分为基本数据类型（整型、字符类型、浮点类型、布尔类型）和复合数据类型（数组类型、结构体类型、共用体类型、枚举类型）。
  • 根据指针变量所指向空间中存储的值的类型不同，可以将指针类型分为基本数据类型指针、复合数据类型指针、函数指针、数组指针等，例如：如果指针所指向的空间保存的是 int 类型，那么该指针就是 int 类型的指针。
1.2 整数类型 ​
1.2.1 概述 ​
  • 整数类型简称整型，用于存储整数值，如：12、20、50 等。
  • 根据所占内存空间大小的不同，可以将整数类型划分为：
  • ① 短整型：
类型存储空间（内存空间）取值范围
unsigned short （无符号短整型）2 字节0 ~ 65,535 (2^16 - 1)
[signed] short（有符号短整型，默认）2 字节-32,768 (- 2^15) ~ 32,767 (2^15 -1)
  • ② 整型：
类型存储空间（内存空间）取值范围
unsigned int（无符号整型）4 字节（通常）0 ~ 4294967295 (0 ~2^32 -1)
[signed] int（有符号整型，默认）4 字节（通常）-2147483648（- 2^31） ~ 2147483647 (2^31-1)
  • ③ 长整型：
类型存储空间（内存空间）取值范围
unsigned long（无符号长整型）4 字节（通常）0 ~2^32 -1
[signed] long（有符号长整型，默认）4 字节（通常）- 2^31 ~ 2^31-1
  • ④ 长长整型：
类型存储空间（内存空间）取值范围
unsigned long long（无符号长整型）8 字节（通常）0 ~2^64 -1
[signed] long long（有符号长整型，默认）8 字节（通常）- 2^63 ~ 2^63-1
NOTE
  • ① C 语言默认没有规定各种数据类型所占存储单元的长度，但是通常需要遵守：sizeof(short int) ≤ sizeof(int) ≤ sizeof(long int) ≤ sizeof(long long) ，具体的存储空间由编译系统自行决定；其中，sizeof 是测量类型或变量、常量长度的运算符。
  • ② short 至少 2 个字节，long 至少 4 个字节。
  • ③ 之所以这么规定，是为了可以让 C 语言长久使用，因为目前主流的 CPU 都是 64 位，但是在 C语言刚刚出现的时候，CPU 还是以 8 位和 16 位为主。如果当时就将整型定死为 8 位或 16 位，那么现在我们肯定不会再学习 C 语言了。
  • ④ 整型分为有符号 signed 和无符号 unsigned 两种，默认是 signed。
  • ⑤ 在实际开发中，最常用的整数类型就是 int 类型了，如果取值范围不够，就使用 long 或 long long 。
  • ⑥ C 语言中的格式占位符非常多，只需要大致了解即可；因为，我们在实际开发中，一般都会使用 C++ 或 Rust 以及其它的高级编程语言，如：Java 等，早已经解决了需要通过格式占位符来输入和输出变量。
1.2.2 短整型（了解） ​
  • 语法：
c
unsigned short x = 10 ; // 无符号短整型
c
short x = -10; // 有符号短整型
NOTE
  • ① 有符号表示的是正数、负数和 0 ，即有正负号。无符号表示的是 0 和正数，即正整数，没有符号。
  • ② 在 printf 中无符号短整型（unsigned short）的格式占位符是 %hu ，有符号短整型（signed short）的格式占位符是 %hd 。
  • ③ 可以通过 sizeof 运算符获取无符号短整型（unsigned short） 和 有符号短整型（signed short） 的存储空间（所占内存空间）。
  • ③ 可以通过 #include <limits.h> 来获取 无符号短整型（unsigned short） 和有符号短整型（signed short）的取值范围。
  • 示例：定义和打印短整型变量
c
#include <stdio.h>
 
 int main() {
 
diff --git a/assets/notes_01_c-basic_03_xdx_index.md.Bc0D4KAS.lean.js b/assets/notes_01_c-basic_03_xdx_index.md.BUQ_uNMg.lean.js
similarity index 91%
rename from assets/notes_01_c-basic_03_xdx_index.md.Bc0D4KAS.lean.js
rename to assets/notes_01_c-basic_03_xdx_index.md.BUQ_uNMg.lean.js
index 295b0a0..7192e4c 100644
--- a/assets/notes_01_c-basic_03_xdx_index.md.Bc0D4KAS.lean.js
+++ b/assets/notes_01_c-basic_03_xdx_index.md.BUQ_uNMg.lean.js
@@ -1 +1 @@
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diff --git a/assets/notes_01_c-basic_04_xdx_index.md.lfDB99hY.js b/assets/notes_01_c-basic_04_xdx_index.md.CwyFE3Gl.js
similarity index 99%
rename from assets/notes_01_c-basic_04_xdx_index.md.lfDB99hY.js
rename to assets/notes_01_c-basic_04_xdx_index.md.CwyFE3Gl.js
index 31fc909..0cb5bc6 100644
--- a/assets/notes_01_c-basic_04_xdx_index.md.lfDB99hY.js
+++ b/assets/notes_01_c-basic_04_xdx_index.md.CwyFE3Gl.js
@@ -1,4 +1,4 @@
-import{_ as l,c as a,j as s,a5 as i,o as n}from"./chunks/framework.BE8if9e6.js";const p="/c/assets/1.CTMA-Poz.jpg",h="/c/assets/2.B2g4y1OY.png",k="/c/assets/3.DEoM0p3m.png",t="/c/assets/4.DxEoA7Ht.png",e="/c/assets/5.DtY5Pf6u.png",r="/c/assets/6.CButBugT.png",E="/c/assets/7.DG_I9X5w.png",d="/c/assets/8.Cw8LCRHN.png",g="/c/assets/9.TqkSPw2X.png",c="/c/assets/10.DJkVOkw7.png",y="/c/assets/11.Bkdbe2NL.png",F="/c/assets/12.D2yeCvfw.png",H=JSON.parse('{"title":"第一章：概述","description":"","frontmatter":{},"headers":[],"relativePath":"notes/01_c-basic/04_xdx/index.md","filePath":"notes/01_c-basic/04_xdx/index.md","lastUpdated":1721701891000}'),b={name:"notes/01_c-basic/04_xdx/index.md"},u=i('
第一章：概述 ​
  • 流程控制结构是用来控制程序中各语句执行顺序的语句，并且可以将语句组合成能完成一定功能的小逻辑模块。
  • 在程序设计中规定了三种流程结构，如下所示：
    • 顺序结构：程序从上到下逐行执行，中间没有任何判断和跳转。
    • 分支结构：根据条件，有选择的执行某段代码。在 C 语言中，有 if...else 和 switch...case 两种分支语句。
    • 循环结构：根据循环条件，重复性的执行某段代码。在 C 语言中，有 for、while、do...while 三种循环结构。
  • 在生活中的洗衣工厂，就包含了上述的三种流程结构，如下所示：
第二章：顺序结构 ​
2.1 概述 ​
  • 程序从上到下逐行地执行，表达式语句都是顺序执行的，并且上一行对某个变量的修改对下一行会产生影响。
2.2 应用示例 ​
  • 示例：
c
#include <stdio.h>
+import{_ as l,c as a,j as s,a6 as i,o as n}from"./chunks/framework.CZKtKhAm.js";const p="/c/assets/1.CTMA-Poz.jpg",h="/c/assets/2.B2g4y1OY.png",k="/c/assets/3.DEoM0p3m.png",t="/c/assets/4.DxEoA7Ht.png",e="/c/assets/5.DtY5Pf6u.png",r="/c/assets/6.CButBugT.png",E="/c/assets/7.DG_I9X5w.png",d="/c/assets/8.Cw8LCRHN.png",g="/c/assets/9.TqkSPw2X.png",c="/c/assets/10.DJkVOkw7.png",y="/c/assets/11.Bkdbe2NL.png",F="/c/assets/12.D2yeCvfw.png",H=JSON.parse('{"title":"第一章：概述","description":"","frontmatter":{},"headers":[],"relativePath":"notes/01_c-basic/04_xdx/index.md","filePath":"notes/01_c-basic/04_xdx/index.md","lastUpdated":1721701891000}'),b={name:"notes/01_c-basic/04_xdx/index.md"},u=i('
第一章：概述 ​
  • 流程控制结构是用来控制程序中各语句执行顺序的语句，并且可以将语句组合成能完成一定功能的小逻辑模块。
  • 在程序设计中规定了三种流程结构，如下所示：
    • 顺序结构：程序从上到下逐行执行，中间没有任何判断和跳转。
    • 分支结构：根据条件，有选择的执行某段代码。在 C 语言中，有 if...else 和 switch...case 两种分支语句。
    • 循环结构：根据循环条件，重复性的执行某段代码。在 C 语言中，有 for、while、do...while 三种循环结构。
  • 在生活中的洗衣工厂，就包含了上述的三种流程结构，如下所示：
第二章：顺序结构 ​
2.1 概述 ​
  • 程序从上到下逐行地执行，表达式语句都是顺序执行的，并且上一行对某个变量的修改对下一行会产生影响。
2.2 应用示例 ​
  • 示例：
c
#include <stdio.h>
 
 int main() {
 
diff --git a/assets/notes_01_c-basic_04_xdx_index.md.lfDB99hY.lean.js b/assets/notes_01_c-basic_04_xdx_index.md.CwyFE3Gl.lean.js
similarity index 94%
rename from assets/notes_01_c-basic_04_xdx_index.md.lfDB99hY.lean.js
rename to assets/notes_01_c-basic_04_xdx_index.md.CwyFE3Gl.lean.js
index a493255..1990295 100644
--- a/assets/notes_01_c-basic_04_xdx_index.md.lfDB99hY.lean.js
+++ b/assets/notes_01_c-basic_04_xdx_index.md.CwyFE3Gl.lean.js
@@ -1 +1 @@
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diff --git a/assets/notes_01_c-basic_05_xdx_index.md.aZr9FRYL.js b/assets/notes_01_c-basic_05_xdx_index.md.aZr9FRYL.js
new file mode 100644
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+++ b/assets/notes_01_c-basic_05_xdx_index.md.aZr9FRYL.js
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第一章：数组的概念 ​
1.1 为什么需要数组？ ​
1.1.1 需求分析 1 ​
  • 需要统计某公司 50 个员工的工资情况，例如：计算平均工资、最高工资等。如果使用之前的知识，我们需要声明 50 个变量来分别记录每位员工的工资，即：
c
#include <stdio.h>
+
+int main(){
+    
+    double num1 = 0;
+    double num2 = 0;
+    double num3 = 0;
+    ...
+    printf("请输入第 1 个员工的工资：");
+    scanf("%lf",&num1);
+    printf("请输入第 2 个员工的工资：");
+    scanf("%lf",&num2);
+    printf("请输入第 3 个员工的工资：");
+    scanf("%lf",&num3);
+    ...   
+    return 0;
+}
  • 这样会感觉特别机械和麻烦（全是复制（Ctrl + c）和粘贴（Ctrl + v），CV 大法）；此时，我们就可以将所有的数据全部存储到一个容器（数组）中进行统一管理，并进行其它的操作，如：求最值、求平均值等，如下所示：
c
#include <stdio.h>
+
+int main(){
+    // 声明数组
+    double nums[50];
+    // 数组的长度
+    int length = sizeof(nums) / sizeof(double);
+    // 使用 for 循环向数组中添加值
+    for(int i = 0;i < length;i++){
+        printf("请输入第 &d 个员工的工资：",i);
+        scanf("%lf",&num[i]);
+    }
+    // 其它操作，如：求最值，求平均值等
+    ...        
+    return 0;
+}
1.1.2 需求分析 2 ​
  • 在现实生活中，我们会使用很多 APP 或微信小程序等，即：
  • 同样的道理，如果我们使用变量来存储每个商品信息，那么就需要非常多的变量；但是，如果我们将这些商品信息都存储到一个容器（数组）中，进行统一管理，对之后的数据处理将会非常方便。
1.1.3 容器的概念 ​
  • 生活中的容器：水杯（装水、饮料的容器）、衣柜（装衣服等物品的容器）、集装箱（装货物等物品的容器）。
  • 程序中的容器：将多个数据存储到一起，并且每个数据称为该容器中的元素。
1.2 什么是数组？ ​
  • 数组（Array）是将多个相同数据类型的数据按照一定的顺序排序的集合，并使用一个标识符命名，以及通过编号（索引，亦称为下标）的方式对这些数据进行统一管理。
1.3 数组的相关概念 ​
  • 数组名：本质上是一个标识符常量，命名需要符合标识符规则和规范。
  • 元素：同一个数组中的元素必须是相同的数据类型。
  • 索引（下标）：从 0 开始的连续数字。
  • 数组的长度：就是元素的个数。
1.4 数组的特点 ​
  • ① 创建数组的时候，会在内存中开辟一整块连续的空间，占据空间的大小，取决于数组的长度和数组中元素的类型。
  • ② 数组中的元素在内存中是依次紧密排列且有序的。
  • ③ 数组一旦初始化完成，且长度就确定的，并且数组的长度一旦确定，就不能更改。
  • ④ 我们可以直接通过索引（下标）来获取指定位置的元素，速度很快。
  • ⑤ 数组名中引用的是这块连续空间的首地址。
第二章：数组的操作（⭐） ​
2.1 数组的定义 ​
2.1.1 动态初始化 ​
  • 语法：
c
数据类型 数组名[元素个数|长度];
NOTE
  • ① 数据类型：表示的是数组中每一个元素的数据类型。
  • ② 数组名：必须符合标识符规则和规范。
  • ③ 元素个数或长度：表示的是数组中最多可以容纳多少个元素（不能是负数、也不能是 0 ）。
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 先指定元素的个数和类型，再进行初始化
+
+    // 定义数组
+    int arr[3];
+
+    // 给数组元素赋值
+    arr[0] = 10;
+    arr[1] = 20;
+    arr[2] = 30;
+
+    return 0;
+}
2.1.2 静态初始化 1 ​
  • 语法：
c
数据类型 数组名[元素个数|长度] = {元素1,元素2,...}
NOTE
  • ① 静态部分初始化：如果数组初始化的元素个数小于数组声明的长度，那么就会从数组开始位置依次赋值，不够的就补 0 。
  • ② 静态全部初始化：数组初始化的元素个数等于数组的长度。
  • 技巧：
    • 在 CLion 中可以开启聚合初始化功能，即：
    • 这样，在 CLion 中，将会显示数组初始化中的元素索引，即：
  • 示例：静态部分初识化
c
#include <stdio.h>
+
+int main() {
+
+    // 定义数组和部分初始化：
+    // 会将给定的值从数组的开始位置一个个的赋值，没有赋值的地方，用 0 填充
+    int arr[5] = {1, 2};
+
+    return 0;
+}
  • 示例：静态全部初始化
c
#include <stdio.h>
+
+int main() {
+
+    // 定义数组和全部初始化：数组初始化的元素个数等于数组的长度。
+    int arr[5] = {1, 2, 3, 4, 5};
+
+    return 0;
+}
2.1.3 静态初始化 2 ​
  • 语法：
c
数据类型 数组名[] = {元素1,元素2,...}
NOTE
没有给出数组中元素的个数，将由系统根据初始化的元素，自动推断出数组中元素的个数。
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 指定元素的类型，不指定元素个数，同时进行初始化
+    int arr[] = {1, 2, 3, 4, 5};
+
+    return 0;
+}
2.2 访问数组元素 ​
  • 语法：
c
数组名[索引|下标];
NOTE
假设数组 arr 有 n 个元素，如果使用的数组的下标 < 0 或 > n-1 ，那么将会产生数组越界访问，即超出了数组合法空间的访问；那么，数组的索引范围是 [0,arr.length - 1]。
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 先指定元素的个数和类型，再进行初始化
+
+    // 定义数组
+    int arr[3];
+
+    // 给数组元素赋值
+    arr[0] = 10;
+    arr[1] = 20;
+    arr[2] = 30;
+
+    // 访问数组元素
+    printf("arr[0] = %d\\n", arr[0]); // arr[0] = 10
+    printf("arr[1] = %d\\n", arr[1]); // arr[1] = 20
+    printf("arr[2] = %d\\n", arr[2]); // arr[2] = 30
+
+    return 0;
+}
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 定义数组和部分初始化：
+    // 会将给定的值从数组的开始位置一个个的赋值，没有赋值的地方，用 0 填充
+    int arr[5] = {1, 2};
+
+    // 访问数组元素
+    printf("arr[0] = %d\\n", arr[0]); // arr[0] = 1
+    printf("arr[1] = %d\\n", arr[1]); // arr[1] = 2
+    printf("arr[2] = %d\\n", arr[2]); // arr[2] = 0
+    printf("arr[3] = %d\\n", arr[3]); // arr[3] = 0
+    printf("arr[4] = %d\\n", arr[4]); // arr[4] = 0
+
+    return 0;
+}
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 指定元素的类型，不指定元素个数，同时进行初始化
+    int arr[] = {1, 2, 3, 4, 5};
+
+    // 访问数组元素
+    printf("arr[0] = %d\\n", arr[0]); // arr[0] = 1
+    printf("arr[1] = %d\\n", arr[1]); // arr[1] = 2
+    printf("arr[2] = %d\\n", arr[2]); // arr[2] = 3
+    printf("arr[3] = %d\\n", arr[3]); // arr[3] = 4
+    printf("arr[4] = %d\\n", arr[4]); // arr[4] = 5
+
+    return 0;
+}
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 定义数组和全部初始化：数组初始化的元素个数等于数组的长度。
+    int arr[5] = {1, 2, 3, 4, 5};
+
+    // 访问数组元素
+    printf("arr[0] = %d\\n", arr[0]); // arr[0] = 1
+    printf("arr[1] = %d\\n", arr[1]); // arr[1] = 2
+    printf("arr[2] = %d\\n", arr[2]); // arr[2] = 3
+    printf("arr[3] = %d\\n", arr[3]); // arr[3] = 4
+    printf("arr[4] = %d\\n", arr[4]); // arr[4] = 5
+
+    return 0;
+}
2.3 数组越界 ​
  • 数组下标必须在指定范围内使用，超出范围视为越界。
NOTE
  • ① C 语言是不会做数组下标越界的检查，并且编译器也不会报错；但是，编译器不报错，并不意味着程序就是正确！
  • ② 在其它高级编程语言，如：Java、JavaScript、Rust 等中，如果数组越界访问，编译器是会直接报错的！！！
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 定义数组和全部初始化：数组初始化的元素个数等于数组的长度。
+    int arr[] = {1, 2, 3, 4, 5};
+
+    // 访问数组元素
+    printf("arr[0] = %d\\n", arr[0]); // arr[0] = 1
+    printf("arr[1] = %d\\n", arr[1]); // arr[1] = 2
+    printf("arr[2] = %d\\n", arr[2]); // arr[2] = 3
+    printf("arr[3] = %d\\n", arr[3]); // arr[3] = 4
+    printf("arr[4] = %d\\n", arr[4]); // arr[4] = 5
+    printf("arr[-1] = %d\\n", arr[-1]); // 得到的是不确定的结果
+    printf("arr[5] = %d\\n", arr[5]); // 得到的是不确定的结果
+
+    return 0;
+}
2.4 计算数组的长度 ​
  • 数组长度（元素个数）是在数组定义的时候明确指定且固定的，我们不能在运行的时候直接获取数组长度；但是，我们可以通过 sizeof 运算符间接计算出数组的长度。
  • 计算步骤，如下所示： 
    • ① 使用 sizeof 运算符计算出整个数组的字节长度。
    • ② 由于数组成员是同一数据类型；那么，每个元素的字节长度一定相等，那么数组的长度 = 整个数组的字节长度 ÷ 单个元素的字节长度 。
NOTE
  • ① 在很多编程语言中，都内置了获取数组的长度的属性或方法，如：Java 中的 arr.length 或 Rust 的 arr.len()。
  • ② 但是，C 语言没有内置的获取数组长度的属性或方法，只能通过 sizeof 运算符间接来计算得到。
  • ③ 数组一旦声明或定义，其长度就固定了，不能动态变化。
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 定义数组和全部初始化：数组初始化的元素个数等于数组的长度。
+    int arr[] = {1, 2, 3, 4, 5};
+
+    // 计算数组的长度
+    size_t length = sizeof(arr) / sizeof(arr[0]);
+
+    // 遍历数组
+    for (int i = 0; i < length; i++) {
+        printf("%d \\n", arr[i]);
+    }
+
+    return 0;
+}
2.5 遍历数组 ​
  • 遍历数组是指按顺序访问数组中的每个元素，以便读取或修改它们，编程中一般使用循环结构对数组进行遍历。
  • 示例：声明一个存储有 12、2、31、24、15、36、67、108、29、51 的数组，并遍历数组所有元素
c
#include <stdio.h>
+
+int main() {
+
+    // 定义数组并初始化
+    int arr[] = {12, 2, 31, 24, 15, 36, 67, 108, 29, 51};
+
+    // 计算数组的长度
+    size_t length = sizeof(arr) / sizeof(int);
+
+    // 遍历数组
+    for (int i = 0; i < length; i++) {
+        printf("%d\\n", arr[i]);
+    }
+
+    return 0;
+}
  • 示例：声明长度为 10 的 int 类型数组，给数组元素依次赋值为 0 ~ 9 ，并遍历数组所有元素
c
#include <stdio.h>
+
+int main() {
+
+    // 定义数组
+    int arr[10];
+
+    // 计算数组的长度
+    size_t length = sizeof(arr) / sizeof(int);
+
+    // 给数组的每个元素赋值
+    for (int i = 0; i < length; i++) {
+        arr[i] = i;
+    }
+
+    // 遍历数组
+    for (int i = 0; i < length; i++) {
+        printf("%d\\n", arr[i]);
+    }
+
+    return 0;
+}
2.6 一维数组的内存分析 ​
2.6.1 数组内存图 ​
  • 假设数组是如下的定义：
c
int arr[] = {1,2,3,4,5};
  • 那么，对应的内存结构，如下所示：
NOTE
  • ① 数组名 arr 就是记录该数组的首地址，即 arr[0] 的地址。
  • ② 数组中的各个元素是连续分布的，假设 arr[0] 的地址是 0xdea7bff880，则 arr[1] 的地址 = arr[0] 的地址 + int 字节数（4） = 0xdea7bff880 + 4 = 0xdea7bff884 ，依次类推...
  • 在 C 语言中，我们可以通过 &arr 或 &arr[0] 等形式获取数组或数组元素的地址，即：
c
#include <stdio.h>
+
+int main() {
+
+    // 定义数组
+    int arr[10];
+
+    // 计算数组的长度
+    size_t length = sizeof(arr) / sizeof(int);
+
+    // 给数组的每个元素赋值
+    for (int i = 0; i < length; i++) {
+        arr[i] = i;
+    }
+
+    printf("数组的地址是 = %p\\n", arr);
+
+    // 遍历数组
+    for (int i = 0; i < length; i++) {
+        printf("数组元素 %d 的地址是 = %p\\n", arr[i], &arr[i]);
+    }
+
+    return 0;
+}
2.6.2 数组的注意事项 ​
  • C 语言规定，数组一旦声明，数组名指向的地址将不可更改。因为在声明数组的时候，编译器会自动会数组分配内存地址，这个地址和数组名是绑定的，不可更改。
WARNING
如果之后试图更改数组名对应的地址，编译器就会报错。
  • 示例：错误演示
c
int num[5]; // 声明数组
+// 使用大括号重新赋值是不允许的，必须在数组声明的时候赋值，否则编译将会报错
+num = {1,2,3,4,5} ; // 报错
  • 示例：错误演示
c
int num[] = {1,2,3,4,5};
+// 使用大括号重新赋值是不允许的，必须在数组声明的时候赋值，否则编译将会报错
+num = {2,3,4,5,6}; // 报错
  • 示例：错误演示
c
int num[5];
+
+num = NULL; // 报错，需要和 Java 区别一下，在 C 中不可以
  • 示例：错误演示
c
int a[] = {1,2,3,4,5} 
+
+int b[5] = a ; // 报错，需要和 Java 区别一下，在 C 中不可以
2.7 数组应用案例 ​
2.7.1 应用示例 ​
  • 需求：计算数组中所有元素的和以及平均数。
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 定义数组并初始化
+    int arr[] = {12, 2, 31, 24, 15, 36, 67, 108, 29, 51};
+
+    // 计算数组的长度
+    size_t length = sizeof(arr) / sizeof(int);
+
+    // 变量保存总和
+    int sum = 0;
+
+    // 遍历数组
+    for (int i = 0; i < length; i++) {
+        sum += arr[i];
+    }
+
+    double avg = (double)sum / length;
+    printf("数组的和为：%d\\n", sum); // 数组的和为：375
+    printf("数组的平均值为：%.2lf\\n", avg); //数组的平均值为：37.50
+
+    return 0;
+}
2.7.2 应用示例 ​
  • 需求：计算数组的最值（最大值和最小值）。
NOTE
思路：
  • ① 假设数组中的第一个元素是最大值或最小值，并使用变量 max 或 min 保存。
  • ② 遍历数组中的每个元素： 
    • 如果有元素比最大值还要大，就让变量 max 保存最大值。
    • 如果有元素比最小值还要小，就让变量 min 保存最小值。
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 定义数组并初始化
+    int arr[] = {12, 2, 31, 24, 15, -36, 67, 108, 29, 51};
+
+    // 计算数组的长度
+    size_t length = sizeof(arr) / sizeof(int);
+
+    // 定义最大值
+    int max = arr[0];
+    // 定义最小值
+    int min = arr[0];
+
+    // 遍历数组
+    for (int i = 0; i < length; i++) {
+        if (arr[i] >= max) {
+            max = arr[i];
+        }
+        if (arr[i] <= min) {
+            min = arr[i];
+        }
+    }
+
+    printf("数组的最大值为：%d\\n", max); // 数组的最大值为：108
+    printf("数组的最小值为：%d\\n", min); // 数组的最小值为：-36
+
+    return 0;
+}
2.7.3 应用示例 ​
  • 需求：统计数组中某个元素出现的次数，要求：使用无限循环，如果输入的数字是 0 ，就退出。
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 定义数组并初始化
+    int arr[] = {12, 2, 31, 24, 2, -36, 67, 108, 29, 51};
+
+    // 计算数组的长度
+    size_t length = sizeof(arr) / sizeof(int);
+
+    // 遍历数组
+    printf("当前数组中的元素是：");
+    for (int i = 0; i < length; i++) {
+        printf("%d ", arr[i]);
+    }
+
+    printf("\\n");
+
+    // 无限循环
+    while (true) {
+        // 统计的数字
+        int num;
+        // 统计数字出现的次数
+        int count = 0;
+        // 输入数字
+        printf("请输入要统计的数字：");
+        scanf("%d", &num);
+
+        // 0 作为结束条件
+        if (num == 0) {
+            break;
+        }
+
+        // 遍历数组，并计数
+        for (int i = 0; i < length; i++) {
+            if (arr[i] == num) {
+                count++;
+            }
+        }
+
+        printf("您输入的数字 %d 在数组中出现了 %d 次\\n", num, count);
+    }
+
+    return 0;
+}
2.7.4 应用示例 ​
  • 需求：将数组 a 中的全部元素复制到数组 b 中。
  • 示例：
c
#include <stdio.h>
+
+#define  SIZE 10
+
+int main() {
+
+    // 定义数组并初始化
+    int a[] = {12, 2, 31, 24, 15, -36, 67, 108, 29, 51};
+    int b[SIZE];
+
+    // 复制数组
+    for (int i = 0; i < SIZE; i++) {
+        b[i] = a[i];
+    }
+
+    // 打印数组 b 中的全部元素
+    for (int i = 0; i < SIZE; i++) {
+        printf("%d ", b[i]);
+    }
+
+    return 0;
+}
2.7.5 应用示例 ​
  • 需求：数组对称位置的元素互换。
NOTE
思路：假设数组一共有 10 个元素，那么：
  • a[0] 和 a[9] 互换。
  • a[1] 和 a[8] 互换。
  • ...
规律就是 a[i] <--互换--> arr[arr.length -1 -i]
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 原始数组
+    int arr[] = {12, 2, 31, 24, 15, -36, 67, 108, 29, 51};
+
+    // 计算数组的长度
+    size_t SIZE = sizeof(arr) / sizeof(arr[0]);
+    
+    // 打印原始数组中的全部元素
+    printf("原始数组：");
+    for (int i = 0; i < SIZE; i++) {
+        printf("%d ", arr[i]);
+    }
+    printf("\\n");
+
+    // 交换数组
+    for (int i = 0; i < SIZE / 2; i++) {
+        int temp          = arr[i];
+        arr[i]            = arr[SIZE - 1 - i];
+        arr[SIZE - 1 - i] = temp;
+    }
+
+    // 打印交换后的数组
+    printf("交换后数组：");
+    for (int i = 0; i < SIZE; i++) {
+        printf("%d ", arr[i]);
+    }
+    printf("\\n");
+
+    return 0;
+}
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 原始数组
+    int arr[] = {12, 2, 31, 24, 15, -36, 67, 108, 29, 51};
+
+    // 计算数组的长度
+    size_t SIZE = sizeof(arr) / sizeof(arr[0]);
+
+    // 打印原始数组中的全部元素
+    printf("原始数组：");
+    for (int i = 0; i < SIZE; i++) {
+        printf("%d ", arr[i]);
+    }
+    printf("\\n");
+
+    // 交换数组
+    for (int i = 0, j = SIZE - 1 - i; i < SIZE / 2; i++, j--) {
+        int temp = arr[i];
+        arr[i]   = arr[j];
+        arr[j]   = temp;
+    }
+
+    // 打印交换后的数组
+    printf("交换后数组：");
+    for (int i = 0; i < SIZE; i++) {
+        printf("%d ", arr[i]);
+    }
+    printf("\\n");
+
+    return 0;
+}
2.7.6 应用示例 ​
  • 需求：将数组中的最大值移动到数组的最末尾。
NOTE
思路：从数组的下标 0 开始依次遍历到 length - 1 ，如果 i 下标当前的值比 i+1 下标的值大，则交换；否则，就不交换。
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 原始数组
+    int arr[] = {12, 2, 31, -24, 15, -36, 67, 891, 29, 51};
+
+    // 计算数组的长度
+    size_t length = sizeof(arr) / sizeof(arr[0]);
+
+    // 打印原始数组中的全部元素
+    printf("原始数组：");
+    for (int i = 0; i < length; i++) {
+        printf("%d ", arr[i]);
+    }
+    printf("\\n");
+
+    // 移动最大值到数组的最后一个位置
+    for (int i = 0; i < length - 1; i++) {
+        if (arr[i] > arr[i + 1]) {
+            int temp   = arr[i];
+            arr[i]     = arr[i + 1];
+            arr[i + 1] = temp;
+        }
+    }
+
+    // 打印移动之后的数组
+    printf("移动之后的数组：");
+    for (int i = 0; i < length; i++) {
+        printf("%d ", arr[i]);
+    }
+    printf("\\n");
+
+    return 0;
+}
2.7.7 应用示例 ​
  • 需求：实现冒泡排序，即将数组的元素从小到大排列。
NOTE
思路：一层循环，能实现最大值移动到数组的最后；那么，二层循环（控制内部循环数组的长度）就能实现将数组的元素从小到大排序。
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 原始数组
+    int arr[] = {12, 2, 31, -24, 15, -36, 67, 891, 29, 51};
+
+    // 计算数组的长度
+    size_t length = sizeof(arr) / sizeof(arr[0]);
+
+    // 打印原始数组中的全部元素
+    printf("原始数组：");
+    for (int i = 0; i < length; i++) {
+        printf("%d ", arr[i]);
+    }
+    printf("\\n");
+
+    for (int j = 0; j < length - 1; j++) {
+        for (int i = 0; i < length - 1 - j; i++) {
+            if (arr[i] > arr[i + 1]) {
+                int temp = arr[i];
+                arr[i] = arr[i + 1];
+                arr[i + 1] = temp;
+            }
+        }
+    }
+
+    // 打印移动之后的数组
+    printf("移动之后的数组：");
+    for (int i = 0; i < length; i++) {
+        printf("%d ", arr[i]);
+    }
+    printf("\\n");
+
+    return 0;
+}
第三章：多维数组（⭐） ​
3.1 概述 ​
3.1.1 引入 ​
  • 我们在数学、物理和计算机科学等学科中学习过一维坐标、二维坐标以及三维坐标。
  • 其中，一维坐标通常用于描述在线段或直线上的点的位置，主要应用有：
    • 数轴：一维坐标可以用来表示数轴上的数值位置，这在基础数学和初等代数中非常常见。
    • 时间轴：时间可以看作是一维的，它可以用一维坐标表示，例如：秒、分钟、小时等。
    • 统计数据：一维坐标常用于表示单变量的数据集，如：测量身高、体重、温度等。
  • 其中，二维坐标用于描述平面上的点的位置。主要应用包括：
    • 几何学：在几何学中，二维坐标用于表示平面图形的顶点、边和面积等。
    • 地图和导航：地理坐标系统（经纬度）使用二维坐标来表示地球表面的任意位置。
    image-20240724112326592
    • 图形设计和计算机图形学：二维坐标在绘制图形、设计图案和用户界面中非常重要。
    • 物理学：二维运动和场，例如：在描述物体在平面上的运动轨迹时使用二维坐标。
  • 其中，三维坐标用于描述空间中点的位置。主要应用包括：
    • 几何学：三维坐标在空间几何中用于表示立体图形的顶点、边、面和体积。
    • 计算机图形学：三维建模和动画需要使用三维坐标来创建和操控虚拟对象。
    • 工程和建筑设计：在设计建筑物、机械部件和其他工程项目时，使用三维坐标来精确定位和规划。
    • 物理学：三维空间中的力、运动和场，例如：描述物体在空间中的位置和运动轨迹。
  • 总而言之，一维、二维和三维坐标系统在不同的领域中各有其重要的应用，从基础数学到高级科学和工程技术，它们帮助我们更好地理解和描述世界的结构和行为。
3.1.2 多维数组 ​
  • 在 C 语言中，多维数组就是数组嵌套，即：在数组中包含数组，数组中的每一个元素还是一个数组类型，如下所示：
NOTE
  • ① 如果数组中嵌套的每一个元素是一个常量值，那么该数组就是一维数组。
  • ② 如果数组中嵌套的每一个元素是一个一维数组，那么该数组就是二维数组。
  • ③ 如果数组中前台的每一个元素是一个二维数组，那么该数组就是三维数组.
  • ④ 依次类推...
  • 一维数组和多维数组的理解： 
    • 从内存角度看：一维数组或多维数组都是占用的一整块连续的内存空间。
    • 从数据操作角度看： 
      • 一维数组可以直接通过下标访问到数组中的某个元素，即：0、1、...
      • 二维数组要想访问某个元素，先要获取某个一维数组，然后在一维数组中获取对应的数据。
NOTE
  • ① C 语言中的一维数组或多维数组都是占用的一整块连续的内存空间，其它编程语言可不是这样的，如：Java 等。
  • ② 在实际开发中，最为常用的就是二维数组或三维数组了，以二维数组居多！！！
3.2 二维数组的定义 ​
3.2.1 动态初始化 ​
  • 语法：
c
数据类型 数组名[几个⼀维数组元素][每个⼀维数组中有几个具体的数据元素];
NOTE
  • ① 二维数组在实际开发中，最为常见的应用场景就是表格或矩阵了。
  • ② 几个一维数组元素 = 行数。
  • ③ 每个⼀维数组中有几个具体的数据元素 = 列数。
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 定义二维数组并初始化
+    int arr[3][4] = {{1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12}};
+
+    // 输出二维数组中的元素
+    printf("%d ", arr[0][0]);
+    printf("%d ", arr[0][1]);
+    printf("%d ", arr[0][2]);
+    printf("%d \\n", arr[0][3]);
+    printf("%d ", arr[1][0]);
+    printf("%d ", arr[1][1]);
+    printf("%d ", arr[1][2]);
+    printf("%d \\n", arr[1][3]);
+    printf("%d ", arr[2][0]);
+    printf("%d ", arr[2][1]);
+    printf("%d ", arr[2][2]);
+    printf("%d ", arr[2][3]);
+
+    return 0;
+}
3.2.2 静态初始化 1 ​
  • 语法：
c
数据类型 数组名[行数][列数] = {{元素1,元素2,...},{元素3,...},...}
NOTE
  • ① 行数 = 几个一维数组元素。
  • ② 列数 = 每个⼀维数组中有几个具体的数据元素。
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 定义二维数组
+    int arr[][4] = {{1, 2, 3, 4}, {5, 6}, {9, 10, 11, 12}};
+
+    // 输出二维数组中的元素
+    printf("%d ", arr[0][0]);
+    printf("%d ", arr[0][1]);
+    printf("%d ", arr[0][2]);
+    printf("%d \\n", arr[0][3]);
+    printf("%d ", arr[1][0]);
+    printf("%d \\n", arr[1][1]);
+    printf("%d ", arr[2][0]);
+    printf("%d ", arr[2][1]);
+    printf("%d ", arr[2][2]);
+    printf("%d ", arr[2][3]);
+
+    return 0;
+}
3.2.3 静态初始化 2 ​
  • 语法：
c
数据类型 数组名[行数][] = {{元素1,元素2,...},{元素3,...},...}
NOTE
  • ① 行数 = 几个一维数组元素 。
  • ② 可以不指定行数，必须指定列数，编译器会根据元素的个数和列的个数，自动推断出行数！！！
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 定义二维数组
+    int arr[][4] = {{1, 2, 3, 4}, {5, 6}, {9, 10, 11, 12}};
+
+    // 输出二维数组中的元素
+    printf("%d ", arr[0][0]);
+    printf("%d ", arr[0][1]);
+    printf("%d ", arr[0][2]);
+    printf("%d \\n", arr[0][3]);
+    printf("%d ", arr[1][0]);
+    printf("%d \\n", arr[1][1]);
+    printf("%d ", arr[2][0]);
+    printf("%d ", arr[2][1]);
+    printf("%d ", arr[2][2]);
+    printf("%d ", arr[2][3]);
+
+    return 0;
+}
3.3 二维数组的理解 ​
  • 如果二维数组是这么定义的，即：
c
int arr[3][4];
  • 那么，这个二维数组 arr 可以看做是 3 个一维数组组成，它们分别是 arr[0]、arr[1]、arr[2]。这 3 个一维数组都各有 4 个元素，如：一维数组 arr[0] 中的元素是 arr[0][0]、arr[0][1]、arr[0][2]、arr[0][3]，即：
3.4 二维数组的遍历 ​
  • 访问二维数组的元素，需要使用两个下标（索引），一个用于访问行（第一维），另一个用于访问列（第二维），我们通常称为行下标（行索引）或列下标（列索引）。
  • 所以，遍历二维数组，需要使用双层循环结构。
NOTE
如果一个二维数组是这么定义的，即：int arr[3][4]，那么：
  • 行的长度 = sizeof(arr) / sizeof(arr[0]) ，因为 arr 是二维数组的总的内存空间；而 arr[0] 、arr[1]、arr[2] 是二维数组中一维数组的内存空间 。
  • 列的长度 = sizeof(arr[0]) / sizeof(arr[0][0])，因为arr[0] 、arr[1]、arr[2] 是二维数组中一维数组的内存空间 ，而 arr[0][0]、arr[0][1]、... 是一维数组中元素的内存空间。
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 定义二维数组
+    int arr[][4] = {{1, 2, 3, 4}, {5, 6}, {9, 10, 11, 12}};
+
+    // 获取行列数
+    int row = sizeof(arr) / sizeof(arr[0]);
+    int col = sizeof(arr[0]) / sizeof(arr[0][0]);
+
+    // 打印二维数组元素
+    for (int i = 0; i < row; i++) {
+        for (int j = 0; j < col; j++) {
+            printf("%d ", arr[i][j]);
+        }
+        printf("\\n");
+    }
+
+    return 0;
+}
3.5 二维数组的内存分析 ​
  • 用矩阵形式（如3行4列形式）表示二维数组，是逻辑上的概念，能形象地表示出行列关系。而在内存中，各元素是连续存放的，不是二维的，是线性的。
  • C 语言中，二维数组中元素排列的顺序是按行存放的。即：先顺序存放第一行的元素，再存放第二行的元素。例如：数组a[3][4] 在内存中的存放：
3.6 二维数组的应用案例 ​
  • 需求：现在有三个班，每个班五名同学，用二维数组保存他们的成绩，并求出每个班级平均分、以及所有班级平均分，数据要求从控制台输入。
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 定义二维数组，用于保存成绩
+    double arr[3][5];
+
+    // 获取二维数组的行数和列数
+    int row = sizeof(arr) / sizeof(arr[0]);
+    int col = sizeof(arr[0]) / sizeof(arr[0][0]);
+
+    // 从控制台输入成绩
+    for (int i = 0; i < row; i++) {
+        for (int j = 0; j < col; j++) {
+            printf("请输入第%d个班级的第%d个学生的成绩：", i + 1, j + 1);
+            scanf("%lf", &arr[i][j]);
+        }
+    }
+
+    // 总分
+    double totalSum = 0;
+
+    // 遍历数组，求总分和各个班级的平均分
+    for (int i = 0; i < row; i++) {
+        double sum = 0;
+        for (int j = 0; j < col; j++) {
+            totalSum += arr[i][j];
+            sum += arr[i][j];
+        }
+        printf("第%d个班级的总分为：%.2lf\\n", i + 1, sum);
+        printf("第%d个班级的平均分为：%.2lf\\n", i + 1, sum / col);
+    }
+
+    printf("所有班级的总分为：%.2lf\\n", totalSum);
+    printf("所有班级的平均分为：%.2lf\\n", totalSum / (row * col));
+
+    return 0;
+}
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deleted file mode 100644
index 7afbbc7..0000000
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index 6f2150e..96e5f76 100644
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diff --git a/index.html b/index.html
index f0f48df..16bd163 100644
--- a/index.html
+++ b/index.html
@@ -5,14 +5,14 @@
     
     许大仙的博客 | Hi，终于等到你
     
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许大仙
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Released under the MIT License.
Copyright © 2024 许大仙

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许大仙
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Released under the MIT License.
Copyright © 2024 许大仙

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     第一章：计算机组成原理 | Hi，终于等到你
     
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许大仙
Appearance
第一章：计算机组成原理 ​
1.1 计算机系统 ​
  • 计算机（Computer），俗称"电脑"，是一种能够接收和存储信息，并按照存储在其内部的程序对海量的数据进行自动、高速的处理，然后将处理结果输出的现代化智能电子设备。
  • 计算机有很多形式，如：台式电脑、笔记本电脑、智能手机、平板电脑等，还有生产环境中提供重要业务支撑的各种服务器。
  • 一个完整的计算机系统由硬件（Hardware）系统和软件（Software）系统两大部分组成，即：
1.2 冯·诺依曼体系结构 ​
  • 冯·诺依曼是一位多才多艺的科学家，他在数学、物理学、计算机科学、经济学等领域都有杰出的贡献。
  • 冯·诺依曼的主要成就： 
    • 在计算机科学领域的最著名贡献是提出了冯·诺依曼体系结构（1946 年），这是现代计算机设计的基础。
    • 促进了计算机的可编程性和通用性，使得计算机能够执行各种复杂的任务。
    • 对核武器设计、自动化控制系统、人工智能等领域的发展产生了重要影响。
    • ……
IMPORTANT
冯·诺依曼体系结构是现代计算机（量子计算机除外）设计的基础。
  • 冯·诺依曼体系结构的理论要点如下：
    • ① 存储程序：程序指令和数据都存储在计算机的内存中，这使得程序可以在运行时修改。
    • ② 二进制逻辑：所有数据和指令都以二进制形式表示。
    • ③ 顺序执行：指令按照它们在内存中的顺序执行，但可以有条件地改变执行顺序。
    • ④ 五大部件：计算机由运算器、控制器、存储器、输入设备和输出设备组成。
    • ⑤ 指令结构：指令由操作码和地址码组成，操作码指示要执行的操作，地址码指示操作数的位置。
    • ⑥ 中心化控制：计算机的控制单元（CPU）负责解释和执行指令，控制数据流。
NOTE
上述的组件协同工作，构成了一个完整的计算机系统：
  • 运算器和控制器通常被集成在一起，组成中央处理器（CPU），负责数据处理和指令执行。
  • 存储器保存数据和程序，是计算机运作的基础。
  • 输入设备和输出设备负责与外界的交互，确保用户能够输入信息并接收计算机的处理结果。
1.3 各种硬件处理速度和性能优化 ​
  • 计算机的性能短板：如果 CPU 有每秒处理 1000 个服务请求的能力，各种总线的负载能力能达到 500 个， 但网卡只能接受 200个请求，而硬盘只能负担 150 个的话，那这台服务器得处理能力只能是 150 个请求/ 秒，有 85% 的处理器计算能力浪费了，在计算机系统当中，硬盘的读写速率已经成为影响系统性能进一 步提高的瓶颈。
img
  • 计算机的各个设备部件的延迟从高到低的排列，依次是机械硬盘（HDD）、固态硬盘（SSD）、内存、CPU 。
img
  • 从上图中，我们可以知道，CPU 是最快的，一个时钟周期是 0.3 ns ，内存访问需要 120 ns ，固态硬盘访问需要 50-150 us，传统的硬盘访问需要 1-10 ms，而网络访问是最慢，需要 40 ms 以上。
  • 时间的单位换算如下：
txt
1 秒 = 1000 毫秒，即 1 s = 1000 ms。
+    
许大仙
Appearance
第一章：计算机组成原理 ​
1.1 计算机系统 ​
  • 计算机（Computer），俗称"电脑"，是一种能够接收和存储信息，并按照存储在其内部的程序对海量的数据进行自动、高速的处理，然后将处理结果输出的现代化智能电子设备。
  • 计算机有很多形式，如：台式电脑、笔记本电脑、智能手机、平板电脑等，还有生产环境中提供重要业务支撑的各种服务器。
  • 一个完整的计算机系统由硬件（Hardware）系统和软件（Software）系统两大部分组成，即：
1.2 冯·诺依曼体系结构 ​
  • 冯·诺依曼是一位多才多艺的科学家，他在数学、物理学、计算机科学、经济学等领域都有杰出的贡献。
  • 冯·诺依曼的主要成就： 
    • 在计算机科学领域的最著名贡献是提出了冯·诺依曼体系结构（1946 年），这是现代计算机设计的基础。
    • 促进了计算机的可编程性和通用性，使得计算机能够执行各种复杂的任务。
    • 对核武器设计、自动化控制系统、人工智能等领域的发展产生了重要影响。
    • ……
IMPORTANT
冯·诺依曼体系结构是现代计算机（量子计算机除外）设计的基础。
  • 冯·诺依曼体系结构的理论要点如下：
    • ① 存储程序：程序指令和数据都存储在计算机的内存中，这使得程序可以在运行时修改。
    • ② 二进制逻辑：所有数据和指令都以二进制形式表示。
    • ③ 顺序执行：指令按照它们在内存中的顺序执行，但可以有条件地改变执行顺序。
    • ④ 五大部件：计算机由运算器、控制器、存储器、输入设备和输出设备组成。
    • ⑤ 指令结构：指令由操作码和地址码组成，操作码指示要执行的操作，地址码指示操作数的位置。
    • ⑥ 中心化控制：计算机的控制单元（CPU）负责解释和执行指令，控制数据流。
NOTE
上述的组件协同工作，构成了一个完整的计算机系统：
  • 运算器和控制器通常被集成在一起，组成中央处理器（CPU），负责数据处理和指令执行。
  • 存储器保存数据和程序，是计算机运作的基础。
  • 输入设备和输出设备负责与外界的交互，确保用户能够输入信息并接收计算机的处理结果。
1.3 各种硬件处理速度和性能优化 ​
  • 计算机的性能短板：如果 CPU 有每秒处理 1000 个服务请求的能力，各种总线的负载能力能达到 500 个， 但网卡只能接受 200个请求，而硬盘只能负担 150 个的话，那这台服务器得处理能力只能是 150 个请求/ 秒，有 85% 的处理器计算能力浪费了，在计算机系统当中，硬盘的读写速率已经成为影响系统性能进一 步提高的瓶颈。
img
  • 计算机的各个设备部件的延迟从高到低的排列，依次是机械硬盘（HDD）、固态硬盘（SSD）、内存、CPU 。
img
  • 从上图中，我们可以知道，CPU 是最快的，一个时钟周期是 0.3 ns ，内存访问需要 120 ns ，固态硬盘访问需要 50-150 us，传统的硬盘访问需要 1-10 ms，而网络访问是最慢，需要 40 ms 以上。
  • 时间的单位换算如下：
txt
1 秒 = 1000 毫秒，即 1 s = 1000 ms。
 1 毫秒 = 1000 微妙，即 1 ms = 1000 us 。
 1 微妙 = 1000 纳秒，即 1 us = 1000 ns。
  • 按照上图，将计算机世界的时间和人类世界的时间进行对比，即：
txt
如果 CPU 的时钟周期按照 1 秒计算，
 那么，内存访问就需要 6 分钟；
@@ -245,8 +245,8 @@
 SpacesInCStyleCastParentheses: false
  • CLion 中配置保存的时候自动格式化，即：
7.5 配置 .gitignore 文件 ​
  • 需要在项目中，配置 .gitignore 文件，以便在提交代码到 Git 仓库的时候，忽略某些文件或目录，如下所示：
  • .gitignore 文件的内容，如下所示：
txt
.vscode
 .idea
 cmake-build-*
-build
7.6 演示 ​
  • 我们可以在项目中，临时创建或复制一个文件，看上述配置是否生效，即：
NOTE
如果是复制并粘贴一个文件到项目中，请点击重新加载 CMake 项目！！！
第八章：C 语言的编译过程（⭐） ​
8.1 概述 ​
  • C 程序的编译过程，如下所示：
  • 过程 ① ：编写（编辑）源代码，即：编写 C 语言源程序代码，并以文件的形式存储在磁盘中。
IMPORTANT
源程序需要以 .c 作为扩展名。
  • 过程 ② ：编译，即：将 C 语言源程序转换为目标程序（或目标文件）。如果程序没有错误，没有任何提示，就会生成一个扩展名为 .obj或 .o 的二进制文件。C 语言中的每条可执行语句经过编译之后，最终都会转换为二进制的机器指令。
IMPORTANT
  • ① 其实，编译阶段包含了预处理、编译和汇编。
  • ② 预处理是编译过程的第一个阶段。在这个阶段，预处理器处理源代码中的指令（例如：#include、#define等），主要任务包括：
    • 头文件包含：将头文件的内容插入到源文件中。例如：#include <stdio.h>会被替换为stdio.h文件的内容。
    • 宏展开：替换宏定义。例如：#define PI 3.14会将代码中的PI替换为3.14。
    • 条件编译：根据条件指令（如：#ifdef、#ifndef）有选择地编译代码。
    • 删除代码中的注释，但是不会进行语法检查。
    • 预处理完成后，生成一个扩展名为.i的中间文件。
  • ③ 编译是将预处理后的源代码转换为汇编代码的过程。在这个阶段，编译器会检查代码的语法和语义，将其转换为目标机器的汇编语言，生成一个扩展名为.s的汇编文件。
  • ④ 汇编是将汇编代码转换为机器代码（也称为目标代码或目标文件）的过程。在这个阶段，汇编器将汇编指令转换为二进制机器指令，生成一个扩展名为.o或 .obj的目标文件。
  • 过程 ③ ：链接（连接），即：将编译形成的目标文件 *.obj 或 *.o和库函数以及其他目录文件链接，形成一个统一的二进制文件 *.exe。
IMPORTANT
  • 为什么需要链接库文件？
  • 因为我们的 C 程序会使用 C 程序库中的内容，如：<stdio.h> 中的 printf() 函数，这些函数不是程序员自己写的，而是 C 程序库中提供的，因此需要链接。其实，在链接过程中，还会加入启动代码，这个启动代码（和系统相关，Linux 下主要有 crt0.c、crti.c 等，它们设置堆栈后，再调用 main() 函数）负责初始化程序运行时的环境。
  • 过程 ④ ：执行，即：有了可执行的 *.exe文件，我们就可以在控制台上执行运行此 *.exe 文件。
IMPORTANT
如果修改了源代码，还需要重新编译、链接，并生成新的 *.exe文件，再执行，方能生效。
8.2 GCC 编译器的介绍 ​
  • 编辑器，如：vim 、vscode 等，是指我们用它来编写源程序的（编辑代码），而我们写的代码语句，电脑是不懂的，我们需要把它转成电脑能懂的语句，编译器就是这样的转化工具。换言之，我们用编辑器编写程序，由编译器编译后才可以运行！
  • 编译器是将易于编写、阅读和维护的高级计算机语言翻译为计算机能解读、运行的低级机器语言的程序。
  • gcc（GNU Compiler Collection，GNU 编译器套件），是由 GNU 开发的编程语言编译器。gcc 原本作为 GNU 操作系统的官方编译器，现已被大多数类 Unix 操作系统（如：Linux、BSD、Mac OS X 等）采纳为标准的编译器，gcc 同样适用于微软的 Windows 。
  • gcc 最初用于编译 C 语言，随着项目的发展， gcc 已经成为了能够编译 C、C++、Java、Ada、fortran、Object C、Object C++、Go 语言的编译器大家族。
8.3 通过 gcc 直接生成可执行文件 ​
  • 示例：进行预处理、编译、汇编和链接
shell
gcc HelloWorld.c -o HelloWorld.exe
8.4 通过 gcc 分步编译 ​
8.3.1 概述 ​
  • 预处理命令：
shell
gcc -E 源文件.c -o 源文件.i # 通常以 .i 结尾表示这个文件是一个中间状态
  • 编译（预处理和编译）命令：
shell
gcc -S 源文件.i -o 源文件.s # 在 Linux 中，通常以 .s 结尾；在 Windows 中，通常以 .asm 结尾
  • 汇编（预处理、编译和汇编）命令：
shell
gcc -c 源文件.s -o 源文件.o # 在 Linux 中，通常以 .o 结尾；在 Windows 中，通常以 .obj 结尾
  • 链接（预处理、编译、汇编和链接）命令：
shell
gcc 源文件.o -o 源文件.exe # 在 Linux 中，通常以 .out 结尾；在 Windows 中，通常以 .exe 结尾
8.4.2 应用示例 ​
  • 示例：只进行预处理
shell
gcc -E HelloWorld.c -o HelloWorld.i
  • 示例：只进行预处理和编译
shell
gcc -S HelloWorld.i -o HelloWorld.s
  • 示例：只进行预处理、编译和汇编
shell
gcc -c HelloWorld.s -o HelloWorld.o
  • 示例：进行预处理、编译、汇编和链接
shell
gcc HelloWorld.o -o HelloWorld.exe
Released under the MIT License.
Copyright © 2024 许大仙

-    
+build
7.6 演示 ​
  • 我们可以在项目中，临时创建或复制一个文件，看上述配置是否生效，即：
NOTE
如果是复制并粘贴一个文件到项目中，请点击重新加载 CMake 项目！！！
第八章：C 语言的编译过程（⭐） ​
8.1 概述 ​
  • C 程序的编译过程，如下所示：
  • 过程 ① ：编写（编辑）源代码，即：编写 C 语言源程序代码，并以文件的形式存储在磁盘中。
IMPORTANT
源程序需要以 .c 作为扩展名。
  • 过程 ② ：编译，即：将 C 语言源程序转换为目标程序（或目标文件）。如果程序没有错误，没有任何提示，就会生成一个扩展名为 .obj或 .o 的二进制文件。C 语言中的每条可执行语句经过编译之后，最终都会转换为二进制的机器指令。
IMPORTANT
  • ① 其实，编译阶段包含了预处理、编译和汇编。
  • ② 预处理是编译过程的第一个阶段。在这个阶段，预处理器处理源代码中的指令（例如：#include、#define等），主要任务包括：
    • 头文件包含：将头文件的内容插入到源文件中。例如：#include <stdio.h>会被替换为stdio.h文件的内容。
    • 宏展开：替换宏定义。例如：#define PI 3.14会将代码中的PI替换为3.14。
    • 条件编译：根据条件指令（如：#ifdef、#ifndef）有选择地编译代码。
    • 删除代码中的注释，但是不会进行语法检查。
    • 预处理完成后，生成一个扩展名为.i的中间文件。
  • ③ 编译是将预处理后的源代码转换为汇编代码的过程。在这个阶段，编译器会检查代码的语法和语义，将其转换为目标机器的汇编语言，生成一个扩展名为.s的汇编文件。
  • ④ 汇编是将汇编代码转换为机器代码（也称为目标代码或目标文件）的过程。在这个阶段，汇编器将汇编指令转换为二进制机器指令，生成一个扩展名为.o或 .obj的目标文件。
  • 过程 ③ ：链接（连接），即：将编译形成的目标文件 *.obj 或 *.o和库函数以及其他目录文件链接，形成一个统一的二进制文件 *.exe。
IMPORTANT
  • 为什么需要链接库文件？
  • 因为我们的 C 程序会使用 C 程序库中的内容，如：<stdio.h> 中的 printf() 函数，这些函数不是程序员自己写的，而是 C 程序库中提供的，因此需要链接。其实，在链接过程中，还会加入启动代码，这个启动代码（和系统相关，Linux 下主要有 crt0.c、crti.c 等，它们设置堆栈后，再调用 main() 函数）负责初始化程序运行时的环境。
  • 过程 ④ ：执行，即：有了可执行的 *.exe文件，我们就可以在控制台上执行运行此 *.exe 文件。
IMPORTANT
如果修改了源代码，还需要重新编译、链接，并生成新的 *.exe文件，再执行，方能生效。
8.2 GCC 编译器的介绍 ​
  • 编辑器，如：vim 、vscode 等，是指我们用它来编写源程序的（编辑代码），而我们写的代码语句，电脑是不懂的，我们需要把它转成电脑能懂的语句，编译器就是这样的转化工具。换言之，我们用编辑器编写程序，由编译器编译后才可以运行！
  • 编译器是将易于编写、阅读和维护的高级计算机语言翻译为计算机能解读、运行的低级机器语言的程序。
  • gcc（GNU Compiler Collection，GNU 编译器套件），是由 GNU 开发的编程语言编译器。gcc 原本作为 GNU 操作系统的官方编译器，现已被大多数类 Unix 操作系统（如：Linux、BSD、Mac OS X 等）采纳为标准的编译器，gcc 同样适用于微软的 Windows 。
  • gcc 最初用于编译 C 语言，随着项目的发展， gcc 已经成为了能够编译 C、C++、Java、Ada、fortran、Object C、Object C++、Go 语言的编译器大家族。
8.3 通过 gcc 直接生成可执行文件 ​
  • 示例：进行预处理、编译、汇编和链接
shell
gcc HelloWorld.c -o HelloWorld.exe
8.4 通过 gcc 分步编译 ​
8.3.1 概述 ​
  • 预处理命令：
shell
gcc -E 源文件.c -o 源文件.i # 通常以 .i 结尾表示这个文件是一个中间状态
  • 编译（预处理和编译）命令：
shell
gcc -S 源文件.i -o 源文件.s # 在 Linux 中，通常以 .s 结尾；在 Windows 中，通常以 .asm 结尾
  • 汇编（预处理、编译和汇编）命令：
shell
gcc -c 源文件.s -o 源文件.o # 在 Linux 中，通常以 .o 结尾；在 Windows 中，通常以 .obj 结尾
  • 链接（预处理、编译、汇编和链接）命令：
shell
gcc 源文件.o -o 源文件.exe # 在 Linux 中，通常以 .out 结尾；在 Windows 中，通常以 .exe 结尾
8.4.2 应用示例 ​
  • 示例：只进行预处理
shell
gcc -E HelloWorld.c -o HelloWorld.i
  • 示例：只进行预处理和编译
shell
gcc -S HelloWorld.i -o HelloWorld.s
  • 示例：只进行预处理、编译和汇编
shell
gcc -c HelloWorld.s -o HelloWorld.o
  • 示例：进行预处理、编译、汇编和链接
shell
gcc HelloWorld.o -o HelloWorld.exe
Released under the MIT License.
Copyright © 2024 许大仙

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     第一章：变量（⭐） | Hi，终于等到你
     
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Appearance
第一章：变量（⭐） ​
1.1 程序中变化的数据 ​
  • 在生活中，我们使用最多的不是固定的数据，而是会变化的数据： 
    • ① 购物车商品的数量、价格等。
    • ② 一首歌播放的时间、进度条、歌词的展示等。
    • ③ 微信聊天中消息条数、时间、语音的长度、头像、名称等。
    • ④ 游戏中技能的冷却时间、血量、蓝量、buff 时间、金币的数量等。
    • ……
  • 下图是一个购物车中变化的数据，即：
  • 那么，在实际开发中，我们就会使用变量来保存和操作这些变化的数据。
1.2 变量 ​
  • 变量的定义：变量是程序中不可或缺的组成单位，最基本的存储单元。其实，变量就是一个存储数据的临时空间，可以向其中存储不同类型的数据，如：整数、小数、字符、字符串等，并且变量中的数据在程序运行的时候可以动态改变。
NOTE
  • 变量：用来存储数据的容器。
  • 数据：可以是一个用来计算的数字，如：上文购物车中的价格等；也可以是一句话中的关键词或其它任意格式的数据。
  • 变量的特别之处就在于它存放的数据是可以改变的。
  • 我们可以将变量想象为一个容器，盒子中装的就是我们想要的数据，并且我们需要给盒子取一个特别的名称；通过这个特别的名称，我们可以给盒子添加数据或移除数据，这个特别的名称就是变量名。
NOTE
  • ① 变量是内存中的一个存储区域，该区域的数据可以在同一类型范围内不断变化。
  • ② 通过变量名，可以操作这块内存区域，向其中存储数据或获取数据以及移除数据。
  • ③ 变量的构成包含三个要素：数据类型、变量名、需要存储的数据。
  • ④ 在生活中，我们会经常说：这件衣服的价格是 100（整型） 元，这双鞋子的价格是 250.5（小数，浮点类型） 元，今天天气真好（字符串类型）之类的话；在计算机科学中，这些都是数据，并且它们是有类型，即：数据类型。（数据类型用于定义变量所能存储的数据的种类以及可以对这些数据进行的操作的一种分类，每种数据类型都有特定的属性和用途，它们决定了变量在内存中如何表示和存储，以及变量可以执行哪些操作）
1.3 变量的声明和使用 ​
  • ① 变量必须先声明，后使用。
  • ② 可以先声明变量再赋值，也可以在声明变量的同时进行赋值。
  • ③ 变量的值可以在同一类型范围内不断变化。
IMPORTANT
在实际开发中，我们通常都会在声明变量的同时，给其赋值，这被称为初始化。
  • 示例：先声明，再使用
c
#include <stdio.h>
+    
许大仙
Appearance
第一章：变量（⭐） ​
1.1 程序中变化的数据 ​
  • 在生活中，我们使用最多的不是固定的数据，而是会变化的数据： 
    • ① 购物车商品的数量、价格等。
    • ② 一首歌播放的时间、进度条、歌词的展示等。
    • ③ 微信聊天中消息条数、时间、语音的长度、头像、名称等。
    • ④ 游戏中技能的冷却时间、血量、蓝量、buff 时间、金币的数量等。
    • ……
  • 下图是一个购物车中变化的数据，即：
  • 那么，在实际开发中，我们就会使用变量来保存和操作这些变化的数据。
1.2 变量 ​
  • 变量的定义：变量是程序中不可或缺的组成单位，最基本的存储单元。其实，变量就是一个存储数据的临时空间，可以向其中存储不同类型的数据，如：整数、小数、字符、字符串等，并且变量中的数据在程序运行的时候可以动态改变。
NOTE
  • 变量：用来存储数据的容器。
  • 数据：可以是一个用来计算的数字，如：上文购物车中的价格等；也可以是一句话中的关键词或其它任意格式的数据。
  • 变量的特别之处就在于它存放的数据是可以改变的。
  • 我们可以将变量想象为一个容器，盒子中装的就是我们想要的数据，并且我们需要给盒子取一个特别的名称；通过这个特别的名称，我们可以给盒子添加数据或移除数据，这个特别的名称就是变量名。
NOTE
  • ① 变量是内存中的一个存储区域，该区域的数据可以在同一类型范围内不断变化。
  • ② 通过变量名，可以操作这块内存区域，向其中存储数据或获取数据以及移除数据。
  • ③ 变量的构成包含三个要素：数据类型、变量名、需要存储的数据。
  • ④ 在生活中，我们会经常说：这件衣服的价格是 100（整型） 元，这双鞋子的价格是 250.5（小数，浮点类型） 元，今天天气真好（字符串类型）之类的话；在计算机科学中，这些都是数据，并且它们是有类型，即：数据类型。（数据类型用于定义变量所能存储的数据的种类以及可以对这些数据进行的操作的一种分类，每种数据类型都有特定的属性和用途，它们决定了变量在内存中如何表示和存储，以及变量可以执行哪些操作）
1.3 变量的声明和使用 ​
  • ① 变量必须先声明，后使用。
  • ② 可以先声明变量再赋值，也可以在声明变量的同时进行赋值。
  • ③ 变量的值可以在同一类型范围内不断变化。
IMPORTANT
在实际开发中，我们通常都会在声明变量的同时，给其赋值，这被称为初始化。
  • 示例：先声明，再使用
c
#include <stdio.h>
 
 int main() {
 
@@ -255,8 +255,8 @@
     printf("%d 的十六进制（前缀）整数： %#X\n", num, num); // 100 的十六进制（前缀）整数： 0X64
 
     return 0;
-}
3.3 进制的转换 ​
3.3.1 概述 ​
  • 不同进制的转换，如下所示：
  • 在计算机中，数据是从右往左的方式排列的；其中，最右边的是低位，最左边的是高位，即：
3.3.2 二进制和十进制的转换 ​
3.3.2.1 二进制转换为十进制 ​
  • 规则：从最低位开始，将每个位上的数提取出来，乘以 2 的 （位数 - 1 ）次方，然后求和。
NOTE
  • ① 在学术界，将这种计算规则，称为位权相加法。
  • ② 八进制转换为十进制、十六进制转换为十进制和二进制转换为十进制的算法相同！！！
  • 示例：十进制转十进制
  • 示例：二进制转十进制
3.3.2.2 十进制转换二进制 ​
  • 规则：将该数不断除以 2 ，直到商为 0 为止，然后将每步得到的余数倒过来，就是对应的二进制。
NOTE
  • ① 在学术界，将这种计算规则，称为短除法或连续除2取余法。
  • ② 很好理解，只有不断地除以 2 ，就能保证最大的数字不超过 2 ，这不就是二进制（只能有 0 或 1）吗？
  • ③ 八进制转换为二进制、十六进制转换为二进制和十进制转换为二进制的算法相同！！！
  • 示例：十进制转十进制
  • 示例：十进制转二进制
3.3.3 二进制转八进制 ​
  • 规则：每 3 位二进制就是一个八进制。
  • 示例：011 101 001 -> 351
3.3.4 二进制转十六进制 ​
  • 规则：每 4 位二进制就是一个十六进制。
  • 示例：1110 1001 -> 0xE9
3.4 原码、反码和补码 ​
3.4.1 概述 ​
  • 机器数：一个数在计算机的存储形式是二进制，我们称这些二进制数为机器数。机器数可以是有符号的，用机器数的最高位来存放符号位，0 表示正数，1 表示负数。
  • 真值：因为机器数带有符号位，所以机器数的形式值不等于其真实表示的值（真值），以机器数 1000 0001 为例，其真正表示的值（首位是符号位）为 -1，而形式值却是 129 ，因此将带有符号位的机器数的真正表示的值称为机器数的真值。
3.4.2 原码 ​
  • 原码的表示与机器数真值表示的一样，即用第一位表示符号，其余位表示数值。
  • 规则： 
    • 正数的原码是它本身对应的二进制数，符号位是 0 。
    • 负数的原码是它本身绝对值对应的二进制数，但是符号位是 1 。
  • +1 的原码，使用 8 位二进数来表示，就是：
十进制数原码（8位二进制数）
+10000 0001
  • -1 的原码，使用 8 位二进数来表示，就是：
十进制数原码（8位二进制数）
-11000 0001
IMPORTANT
按照原码的规则，会出现 +0 和 -0 的情况，即：0000 0000（+0）、1000 0000（-0），显然不符合实际情况；所以，计算机底层虽然存储和计算的都是二进数，但显然不是原码。
3.4.3 反码 ​
  • 规则：
    • 正数的反码和它的原码相同。
    • 负数的反码是在其原码的基础上，符号位不变，其余各位取反。
  • +1 的反码，使用 8 位二进数来表示，就是：
十进制数原码（8位二进制数）反码（8位二进制数）
+10000 00010000 0001
  • -1 的反码，使用 8 位二进数来表示，就是：
十进制数原码（8位二进制数）反码（8位二进制数）
-11000 00011111 1110
IMPORTANT
按照反码的规则，如果是 +0，对应的原码是 0000 0000；那么，其反码还是 0000 0000 ；如果是 -0，对应的原码是 1000 0000，其反码是 1111 1111，显然不符合实际情况；所以，计算机底层虽然存储和计算的都是二进数，但显然不是反码。
3.4.4 补码 ​
  • 规则：
    • 正数的补码和它的原码相同。
    • 负数的补码是在其反码的基础上 + 1 。
  • +1 的补码，使用 8 位二进数来表示，就是：
十进制数原码（8位二进制数）反码（8位二进制数）补码（8位二进制数）
+10000 00010000 00010000 0001
  • -1 的补码，使用 8 位二进数来表示，就是：
十进制数原码（8位二进制数）反码（8位二进制数）补码（8位二进制数）
-11000 00011111 11101111 1111
  • 如果 0 ，按照 +0 的情况进行处理，即：
  • 如果 0 ，按照 -0 的情况进行处理，即：
IMPORTANT
  • ① 补码表示法解决了原码和反码存在的两种零（+0 和 -0）的问题，即：在补码表示法中，只有一个零，即 0000 0000。
  • ②补码使得加法运算和减法运算可以统一处理，通过将减法运算转换为加法运算，可以简化硬件设计，提高了运算效率。
  • ③ 计算机底层存储和计算的都是二进数的补码。
3.4.5 总结 ​
  • ① 正数的原码、反码和补码都是一样的，三码合一。
  • ② 负数的反码是在其原码的基础上，按位取反（0 变 1 ，1 变 0 ），符号位不变；负数的补码是其反码 + 1 。
  • ③ 0 的补码是 0 。
3.5 计算机底层为什么使用补码？ ​
  • 如果计算是 2 - 2 ，那么可以转换为 2 + (-2)，这样计算机内部在处理减法计算的时候，就会将其转换为加法计算的形式，以简化硬件设计和提高计算效率。
  • 最高位表示符号位，由于符号位的存在，如果使用原码来计算，就会导致计算结果不正确，即：
  • 补码的设计可以巧妙的让符号位也参与计算，并且可以得到正确的计算结果，即：
Released under the MIT License.
Copyright © 2024 许大仙

-    
+}
3.3 进制的转换 ​
3.3.1 概述 ​
  • 不同进制的转换，如下所示：
  • 在计算机中，数据是从右往左的方式排列的；其中，最右边的是低位，最左边的是高位，即：
3.3.2 二进制和十进制的转换 ​
3.3.2.1 二进制转换为十进制 ​
  • 规则：从最低位开始，将每个位上的数提取出来，乘以 2 的 （位数 - 1 ）次方，然后求和。
NOTE
  • ① 在学术界，将这种计算规则，称为位权相加法。
  • ② 八进制转换为十进制、十六进制转换为十进制和二进制转换为十进制的算法相同！！！
  • 示例：十进制转十进制
  • 示例：二进制转十进制
3.3.2.2 十进制转换二进制 ​
  • 规则：将该数不断除以 2 ，直到商为 0 为止，然后将每步得到的余数倒过来，就是对应的二进制。
NOTE
  • ① 在学术界，将这种计算规则，称为短除法或连续除2取余法。
  • ② 很好理解，只有不断地除以 2 ，就能保证最大的数字不超过 2 ，这不就是二进制（只能有 0 或 1）吗？
  • ③ 八进制转换为二进制、十六进制转换为二进制和十进制转换为二进制的算法相同！！！
  • 示例：十进制转十进制
  • 示例：十进制转二进制
3.3.3 二进制转八进制 ​
  • 规则：每 3 位二进制就是一个八进制。
  • 示例：011 101 001 -> 351
3.3.4 二进制转十六进制 ​
  • 规则：每 4 位二进制就是一个十六进制。
  • 示例：1110 1001 -> 0xE9
3.4 原码、反码和补码 ​
3.4.1 概述 ​
  • 机器数：一个数在计算机的存储形式是二进制，我们称这些二进制数为机器数。机器数可以是有符号的，用机器数的最高位来存放符号位，0 表示正数，1 表示负数。
  • 真值：因为机器数带有符号位，所以机器数的形式值不等于其真实表示的值（真值），以机器数 1000 0001 为例，其真正表示的值（首位是符号位）为 -1，而形式值却是 129 ，因此将带有符号位的机器数的真正表示的值称为机器数的真值。
3.4.2 原码 ​
  • 原码的表示与机器数真值表示的一样，即用第一位表示符号，其余位表示数值。
  • 规则： 
    • 正数的原码是它本身对应的二进制数，符号位是 0 。
    • 负数的原码是它本身绝对值对应的二进制数，但是符号位是 1 。
  • +1 的原码，使用 8 位二进数来表示，就是：
十进制数原码（8位二进制数）
+10000 0001
  • -1 的原码，使用 8 位二进数来表示，就是：
十进制数原码（8位二进制数）
-11000 0001
IMPORTANT
按照原码的规则，会出现 +0 和 -0 的情况，即：0000 0000（+0）、1000 0000（-0），显然不符合实际情况；所以，计算机底层虽然存储和计算的都是二进数，但显然不是原码。
3.4.3 反码 ​
  • 规则：
    • 正数的反码和它的原码相同。
    • 负数的反码是在其原码的基础上，符号位不变，其余各位取反。
  • +1 的反码，使用 8 位二进数来表示，就是：
十进制数原码（8位二进制数）反码（8位二进制数）
+10000 00010000 0001
  • -1 的反码，使用 8 位二进数来表示，就是：
十进制数原码（8位二进制数）反码（8位二进制数）
-11000 00011111 1110
IMPORTANT
按照反码的规则，如果是 +0，对应的原码是 0000 0000；那么，其反码还是 0000 0000 ；如果是 -0，对应的原码是 1000 0000，其反码是 1111 1111，显然不符合实际情况；所以，计算机底层虽然存储和计算的都是二进数，但显然不是反码。
3.4.4 补码 ​
  • 规则：
    • 正数的补码和它的原码相同。
    • 负数的补码是在其反码的基础上 + 1 。
  • +1 的补码，使用 8 位二进数来表示，就是：
十进制数原码（8位二进制数）反码（8位二进制数）补码（8位二进制数）
+10000 00010000 00010000 0001
  • -1 的补码，使用 8 位二进数来表示，就是：
十进制数原码（8位二进制数）反码（8位二进制数）补码（8位二进制数）
-11000 00011111 11101111 1111
  • 如果 0 ，按照 +0 的情况进行处理，即：
  • 如果 0 ，按照 -0 的情况进行处理，即：
IMPORTANT
  • ① 补码表示法解决了原码和反码存在的两种零（+0 和 -0）的问题，即：在补码表示法中，只有一个零，即 0000 0000。
  • ②补码使得加法运算和减法运算可以统一处理，通过将减法运算转换为加法运算，可以简化硬件设计，提高了运算效率。
  • ③ 计算机底层存储和计算的都是二进数的补码。
3.4.5 总结 ​
  • ① 正数的原码、反码和补码都是一样的，三码合一。
  • ② 负数的反码是在其原码的基础上，按位取反（0 变 1 ，1 变 0 ），符号位不变；负数的补码是其反码 + 1 。
  • ③ 0 的补码是 0 。
3.5 计算机底层为什么使用补码？ ​
  • 如果计算是 2 - 2 ，那么可以转换为 2 + (-2)，这样计算机内部在处理减法计算的时候，就会将其转换为加法计算的形式，以简化硬件设计和提高计算效率。
  • 最高位表示符号位，由于符号位的存在，如果使用原码来计算，就会导致计算结果不正确，即：
  • 补码的设计可以巧妙的让符号位也参与计算，并且可以得到正确的计算结果，即：
Released under the MIT License.
Copyright © 2024 许大仙

+    
     
   
 
\ No newline at end of file
diff --git a/notes/01_c-basic/03_xdx/index.html b/notes/01_c-basic/03_xdx/index.html
index c2d8bd9..e7da649 100644
--- a/notes/01_c-basic/03_xdx/index.html
+++ b/notes/01_c-basic/03_xdx/index.html
@@ -5,14 +5,14 @@
     
     第一章：数据类型（⭐） | Hi，终于等到你
     
-    
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许大仙
Appearance
第一章：数据类型（⭐） ​
1.1 概述 ​
  • 根据变量中存储的值的不同，我们可以将变量分为两类：
    • 普通变量：变量所对应的内存中存储的是普通值。
    • 指针变量：变量所对应的内存中存储的是另一个变量的地址。
  • 如下图所示：
NOTE
普通变量和指针变量的相同点：
  • 普通变量有内存空间，指针变量也有内存空间。
  • 普通变量有内存地址，指针变量也有内存地址。
  • 普通变量所对应的内存空间中有值，指针变量所对应的内存空间中也有值。
普通变量和指针变量的不同点：
  • 普通变量所对应的内存空间存储的是普通的值，如：整数、小数、字符等；指针变量所对应的内存空间存储的是另外一个变量的地址。
  • 普通变量有普通变量的运算方式，而指针变量有指针变量的运算方式（后续讲解）。
  • 那么，在 C 语言中变量的数据类型就可以这么划分，如下所示：
NOTE
  • 根据普通变量中存储的值的类型不同，可以将普通变量类型划分为基本数据类型（整型、字符类型、浮点类型、布尔类型）和复合数据类型（数组类型、结构体类型、共用体类型、枚举类型）。
  • 根据指针变量所指向空间中存储的值的类型不同，可以将指针类型分为基本数据类型指针、复合数据类型指针、函数指针、数组指针等，例如：如果指针所指向的空间保存的是 int 类型，那么该指针就是 int 类型的指针。
1.2 整数类型 ​
1.2.1 概述 ​
  • 整数类型简称整型，用于存储整数值，如：12、20、50 等。
  • 根据所占内存空间大小的不同，可以将整数类型划分为：
  • ① 短整型：
类型存储空间（内存空间）取值范围
unsigned short （无符号短整型）2 字节0 ~ 65,535 (2^16 - 1)
[signed] short（有符号短整型，默认）2 字节-32,768 (- 2^15) ~ 32,767 (2^15 -1)
  • ② 整型：
类型存储空间（内存空间）取值范围
unsigned int（无符号整型）4 字节（通常）0 ~ 4294967295 (0 ~2^32 -1)
[signed] int（有符号整型，默认）4 字节（通常）-2147483648（- 2^31） ~ 2147483647 (2^31-1)
  • ③ 长整型：
类型存储空间（内存空间）取值范围
unsigned long（无符号长整型）4 字节（通常）0 ~2^32 -1
[signed] long（有符号长整型，默认）4 字节（通常）- 2^31 ~ 2^31-1
  • ④ 长长整型：
类型存储空间（内存空间）取值范围
unsigned long long（无符号长整型）8 字节（通常）0 ~2^64 -1
[signed] long long（有符号长整型，默认）8 字节（通常）- 2^63 ~ 2^63-1
NOTE
  • ① C 语言默认没有规定各种数据类型所占存储单元的长度，但是通常需要遵守：sizeof(short int) ≤ sizeof(int) ≤ sizeof(long int) ≤ sizeof(long long) ，具体的存储空间由编译系统自行决定；其中，sizeof 是测量类型或变量、常量长度的运算符。
  • ② short 至少 2 个字节，long 至少 4 个字节。
  • ③ 之所以这么规定，是为了可以让 C 语言长久使用，因为目前主流的 CPU 都是 64 位，但是在 C语言刚刚出现的时候，CPU 还是以 8 位和 16 位为主。如果当时就将整型定死为 8 位或 16 位，那么现在我们肯定不会再学习 C 语言了。
  • ④ 整型分为有符号 signed 和无符号 unsigned 两种，默认是 signed。
  • ⑤ 在实际开发中，最常用的整数类型就是 int 类型了，如果取值范围不够，就使用 long 或 long long 。
  • ⑥ C 语言中的格式占位符非常多，只需要大致了解即可；因为，我们在实际开发中，一般都会使用 C++ 或 Rust 以及其它的高级编程语言，如：Java 等，早已经解决了需要通过格式占位符来输入和输出变量。
1.2.2 短整型（了解） ​
  • 语法：
c
unsigned short x = 10 ; // 无符号短整型
c
short x = -10; // 有符号短整型
NOTE
  • ① 有符号表示的是正数、负数和 0 ，即有正负号。无符号表示的是 0 和正数，即正整数，没有符号。
  • ② 在 printf 中无符号短整型（unsigned short）的格式占位符是 %hu ，有符号短整型（signed short）的格式占位符是 %hd 。
  • ③ 可以通过 sizeof 运算符获取无符号短整型（unsigned short） 和 有符号短整型（signed short） 的存储空间（所占内存空间）。
  • ③ 可以通过 #include <limits.h> 来获取 无符号短整型（unsigned short） 和有符号短整型（signed short）的取值范围。
  • 示例：定义和打印短整型变量
c
#include <stdio.h>
+    
许大仙
Appearance
第一章：数据类型（⭐） ​
1.1 概述 ​
  • 根据变量中存储的值的不同，我们可以将变量分为两类：
    • 普通变量：变量所对应的内存中存储的是普通值。
    • 指针变量：变量所对应的内存中存储的是另一个变量的地址。
  • 如下图所示：
NOTE
普通变量和指针变量的相同点：
  • 普通变量有内存空间，指针变量也有内存空间。
  • 普通变量有内存地址，指针变量也有内存地址。
  • 普通变量所对应的内存空间中有值，指针变量所对应的内存空间中也有值。
普通变量和指针变量的不同点：
  • 普通变量所对应的内存空间存储的是普通的值，如：整数、小数、字符等；指针变量所对应的内存空间存储的是另外一个变量的地址。
  • 普通变量有普通变量的运算方式，而指针变量有指针变量的运算方式（后续讲解）。
  • 那么，在 C 语言中变量的数据类型就可以这么划分，如下所示：
NOTE
  • 根据普通变量中存储的值的类型不同，可以将普通变量类型划分为基本数据类型（整型、字符类型、浮点类型、布尔类型）和复合数据类型（数组类型、结构体类型、共用体类型、枚举类型）。
  • 根据指针变量所指向空间中存储的值的类型不同，可以将指针类型分为基本数据类型指针、复合数据类型指针、函数指针、数组指针等，例如：如果指针所指向的空间保存的是 int 类型，那么该指针就是 int 类型的指针。
1.2 整数类型 ​
1.2.1 概述 ​
  • 整数类型简称整型，用于存储整数值，如：12、20、50 等。
  • 根据所占内存空间大小的不同，可以将整数类型划分为：
  • ① 短整型：
类型存储空间（内存空间）取值范围
unsigned short （无符号短整型）2 字节0 ~ 65,535 (2^16 - 1)
[signed] short（有符号短整型，默认）2 字节-32,768 (- 2^15) ~ 32,767 (2^15 -1)
  • ② 整型：
类型存储空间（内存空间）取值范围
unsigned int（无符号整型）4 字节（通常）0 ~ 4294967295 (0 ~2^32 -1)
[signed] int（有符号整型，默认）4 字节（通常）-2147483648（- 2^31） ~ 2147483647 (2^31-1)
  • ③ 长整型：
类型存储空间（内存空间）取值范围
unsigned long（无符号长整型）4 字节（通常）0 ~2^32 -1
[signed] long（有符号长整型，默认）4 字节（通常）- 2^31 ~ 2^31-1
  • ④ 长长整型：
类型存储空间（内存空间）取值范围
unsigned long long（无符号长整型）8 字节（通常）0 ~2^64 -1
[signed] long long（有符号长整型，默认）8 字节（通常）- 2^63 ~ 2^63-1
NOTE
  • ① C 语言默认没有规定各种数据类型所占存储单元的长度，但是通常需要遵守：sizeof(short int) ≤ sizeof(int) ≤ sizeof(long int) ≤ sizeof(long long) ，具体的存储空间由编译系统自行决定；其中，sizeof 是测量类型或变量、常量长度的运算符。
  • ② short 至少 2 个字节，long 至少 4 个字节。
  • ③ 之所以这么规定，是为了可以让 C 语言长久使用，因为目前主流的 CPU 都是 64 位，但是在 C语言刚刚出现的时候，CPU 还是以 8 位和 16 位为主。如果当时就将整型定死为 8 位或 16 位，那么现在我们肯定不会再学习 C 语言了。
  • ④ 整型分为有符号 signed 和无符号 unsigned 两种，默认是 signed。
  • ⑤ 在实际开发中，最常用的整数类型就是 int 类型了，如果取值范围不够，就使用 long 或 long long 。
  • ⑥ C 语言中的格式占位符非常多，只需要大致了解即可；因为，我们在实际开发中，一般都会使用 C++ 或 Rust 以及其它的高级编程语言，如：Java 等，早已经解决了需要通过格式占位符来输入和输出变量。
1.2.2 短整型（了解） ​
  • 语法：
c
unsigned short x = 10 ; // 无符号短整型
c
short x = -10; // 有符号短整型
NOTE
  • ① 有符号表示的是正数、负数和 0 ，即有正负号。无符号表示的是 0 和正数，即正整数，没有符号。
  • ② 在 printf 中无符号短整型（unsigned short）的格式占位符是 %hu ，有符号短整型（signed short）的格式占位符是 %hd 。
  • ③ 可以通过 sizeof 运算符获取无符号短整型（unsigned short） 和 有符号短整型（signed short） 的存储空间（所占内存空间）。
  • ③ 可以通过 #include <limits.h> 来获取 无符号短整型（unsigned short） 和有符号短整型（signed short）的取值范围。
  • 示例：定义和打印短整型变量
c
#include <stdio.h>
 
 int main() {
 
@@ -788,8 +788,8 @@
     printf("result = %d\n", result); // result = 110
 
     return 0;
-}
2.8 运算符优先级 ​
  • C 语言中运算符的优先级，如下所示：
优先级运算符名称或含义结合方向
1[]数组下标左到右
()圆括号
.成员选择（对象）
->成员选择（指针）
2-负号运算符右到左
（类型）强制类型转换
++自增运算符
--自减运算符
*取值运算符
&取地址运算符
!逻辑非运算符
~按位取反运算符
sizeof长度运算符
3/除左到右
*乘
%余数（取模）
4+加左到右
-减
5<<左移左到右
>>右移
6>大于左到右
>=大于等于
<小于
<=小于等于
7==等于左到右
!=不等于
8&按位与左到右
9^按位异或左到右
10|按位或左到右
11&&逻辑与左到右
12||逻辑或左到右
13?:条件运算符右到左
14=赋值运算符右到左
/=除后赋值
*=乘后赋值
%=取模后赋值
+=加后赋值
-=减后赋值
<<=左移后赋值
>>=右移后赋值
&=按位与后赋值
^=按位异或后赋值
|=按位或后赋值
15,逗号运算符左到右
WARNING
  • ① 不要过多的依赖运算符的优先级来控制表达式的执行顺序，这样可读性太差，尽量使用小括号来控制表达式的执行顺序。
  • ② 不要把一个表达式写得过于复杂，如果一个表达式过于复杂，则把它分成几步来完成。
  • ③ 运算符优先级不用刻意地去记忆，总体上：一元运算符 > 算术运算符 > 关系运算符 > 逻辑运算符 > 三元运算符 > 赋值运算符。
第三章：附录 ​
3.1 字符集和字符集编码 ​
3.3.1 概述 ​
  • 字符集和字符集编码（简称编码）计算机系统中处理文本数据的两个基本概念，它们密切相关但又有区别。
  • 字符集（Character Set）是一组字符的集合，其中每个字符都被分配了一个唯一的编号（通常是数字）。字符可以是字母、数字、符号、控制代码（如换行符）等。字符集定义了可以表示的字符的范围，但它并不直接定义如何将这些字符存储在计算机中。
NOTE
ASCII（美国信息交换标准代码）是最早期和最简单的字符集之一，它只包括了英文字母、数字和一些特殊字符，共 128 个字符。每个字符都分配给了一个从 0 到 127 的数字。
  • 字符集编码（Character Encoding，简称编码）是一种方案或方法，它定义了如何将字符集中的字符转换为计算机存储和传输的数据（通常是一串二进制数字）。简而言之，编码是字符到二进制数据之间的映射规则。
NOTE
ASCII编码方案定义了如何将 ASCII 字符集中的每个字符表示为 7 位的二进制数字。例如：大写字母"A"在ASCII 编码中表示为二进制的1000001，十进制的 65 。
  • 字符集和字符集编码之间的关系如下：
  • Linux 中安装帮助手册：
3.3.2 ASCII 编码 ​
  • 从冯·诺依曼体系结构中，我们知道，计算机中所有的数据和指令都是以二进制的形式表示的；所以，计算机中对于文本数据的数据也是以二进制来存储的，那么对应的流程如下：
  • 我们知道，计算机是上个世纪 60 年代在美国研制成功的，为了实现字符和二进制的转换，美国就制定了一套字符编码，即英语字符和二进制位之间的关系，即 ASCII （American Standard Code for Information Interchange）编码： 
    • ASCII 编码只包括了英文字符、数字和一些特殊字符，一共 128 个字符，并且每个字符都分配了唯一的数字，范围是 0 - 127。
    • ASCII 编码中的每个字符都使用 7 位的二进制数字表示；但是，计算机中的存储的最小单位是 1 B = 8 位，那么最高位统一规定为 0 。
NOTE
  • ① 其实，早期是没有字符集的概念的，只是后来为了解决乱码问题，而产生了字符集的概念。
  • ② 对于英文体系来说，a-zA-Z0-9以及一些特殊字符一共 128 就可以满足实际存储需求；所以，在也是为什么 ASCII 码使用 7 位二进制（2^7 = 128 ）来存储的。
  • 在操作系统中，就内置了对应的编码表，Linux 也不例外；可以使用如下的命令查看：
shell
man ascii
  • 其对应的 ASCII 编码表，如下所示：
  • 但是，随着计算机的发展，计算机开始了东征之路，由美国传播到东方：
  • 先是传播到了欧洲，欧洲在兼容 ASCII 编码的基础上，推出了 ISO8859-1 编码，即： 
    • ISO8859-1 编码包括基本的拉丁字母表、数字、标点符号，以及西欧语言中特有的一些字符，如：法语中的 è、德语中的 ü 等。
    • ISO 8859-1 为每个字符分配一个单字节（8 位）编码，意味着它可以表示最多 256 （2^8）个不同的字符（编号从 0 到 255）。
    • ISO 8859-1 的前 128 个字符与 ASCII 编码完全一致，这使得 ASCII 编码的文本可以无缝转换为 ISO 8859-1 编码。
  • 计算机继续传播到了亚洲，亚洲（双字节）各个国家分别给出了自己国家对应的字符集编码，如： 
    • 日本推出了 Shift-JIS 编码： 
      • 单字节 ASCII 范围：0 - 127。
      • 双字节范围： 
        • 第一个字节：129 - 159 和 224 - 239 。
        • 第二个字节：64 - 126 和 128 - 252 。
    • 韩国推出了 EUC-KR 编码： 
      • 单字节 ASCII 范围：0 - 127。
      • 双字节范围：从 41281 - 65278。
    • 中国推出了 GBK 编码： 
      • 单字节 ASCII 范围：0 - 127。
      • 双字节范围：33088 - 65278 。
NOTE
  • ① 通过上面日本、韩国、中国的编码十进制范围，我们可以看到，虽然这些编码系统在技术上的编码范围存在重叠（特别是在高位字节区域），但因为它们各自支持的字符集完全不同，所以实际上它们并不直接冲突。
  • ② 但是，如果一个中国人通过 GBK 编码写的文章，通过邮件发送给韩国人，因为韩国和中国在字符集编码上的高位字节有重叠部分，必然会造成歧义。
3.3.3 Unicode 编码 ​
  • 在 Unicode 之前，世界上存在着数百种不同的编码系统，每一种编码系统都是为了支持特定语言或一组语言的字符集。这些编码系统，包括：ASCII、ISO 8859 系列、GBK、Shift-JIS、EUC-KR 等，它们各自有不同的字符范围和编码方式。这种多样性虽然在局部范围内解决了字符表示的问题，但也带来了以下几个方面的挑战：
    • 编码冲突：由于不同的编码系统可以为相同的字节值分配不同的字符，因此在不同编码之间转换文本时，如果没有正确处理编码信息，就很容易产生乱码。这种编码冲突在尝试处理多种语言的文本时尤为突出。
    • 编码的复杂性：随着全球化的发展，软件和系统需要支持越来越多的语言，这就要求开发者和系统同时处理多种不同的编码系统。这不仅增加了开发和维护的复杂性，而且也增加了出错的风险。
    • 资源限制：在早期计算机技术中，内存和存储资源相对有限。不同的编码标准要求系统存储多套字符集数据，这无疑增加了对有限资源的消耗。
    • ……
  • 针对上述的种种问题，为了推行全球化，Unicode 应运而生，Unicode 的核心规则和设计原则是建立一个全球统一的字符集，使得世界上所有的文字和符号都能被唯一地识别和使用，无论使用者位于何地或使用何种语言。这套规则包括了字符的编码、表示、处理和转换机制，旨在确保不同系统和软件间能够无缝交换和处理文本数据。
    • 通用字符集 (UCS)：Unicode 为每一个字符分配一个唯一的编号（称为“码点”）。这些码点被组织在一个统一的字符集中，官方称之为 “通用字符集”（Universal Character Set，UCS）。码点通常表示为 U+ 后跟一个十六进制数，例如：U+0041 代表大写的英文字母 “A”。
    • 编码平面和区段：Unicode 码点被划分为多个 “平面（Planes）”，每个平面包含 65536（16^4）个码点。目前，Unicode定义了 17 个平面（从 0 到16），每个平面被分配了一个编号，从 “基本多文种平面（BMP）” 的 0 开始，到 16 号平面结束。这意味着 Unicode 理论上可以支持超过 110万（17*65536）个码点。
  • Unicode 仅仅只是字符集，给每个字符设置了唯一的数字编号而已，却没有给出这些数字编号实际如何存储，可以通过如下命令查看：
  • 为了在计算机系统中表示 Unicode 字符，定义了几种编码方案，这些方案包括 UTF-8、UTF-16 和 UTF-32 等。 
    • UTF-8：使用 1 - 4 个字节表示每个 Unicode 字符，兼容 ASCII，是网络上最常用的编码。
    • UTF-16：使用 2 - 4 个字节表示每个 Unicode 字符，适合于需要经常处理基本多文种平面之外字符的应用。
    • UTF-32：使用固定的 4 个字节表示每个 Unicode 字符，简化了字符处理，但增加了存储空间的需求。
  • Unicode 字符集和对应的UTF-8 字符编码之间的关系，如下所示：
Released under the MIT License.
Copyright © 2024 许大仙

-    
+}
2.8 运算符优先级 ​
  • C 语言中运算符的优先级，如下所示：
优先级运算符名称或含义结合方向
1[]数组下标左到右
()圆括号
.成员选择（对象）
->成员选择（指针）
2-负号运算符右到左
（类型）强制类型转换
++自增运算符
--自减运算符
*取值运算符
&取地址运算符
!逻辑非运算符
~按位取反运算符
sizeof长度运算符
3/除左到右
*乘
%余数（取模）
4+加左到右
-减
5<<左移左到右
>>右移
6>大于左到右
>=大于等于
<小于
<=小于等于
7==等于左到右
!=不等于
8&按位与左到右
9^按位异或左到右
10|按位或左到右
11&&逻辑与左到右
12||逻辑或左到右
13?:条件运算符右到左
14=赋值运算符右到左
/=除后赋值
*=乘后赋值
%=取模后赋值
+=加后赋值
-=减后赋值
<<=左移后赋值
>>=右移后赋值
&=按位与后赋值
^=按位异或后赋值
|=按位或后赋值
15,逗号运算符左到右
WARNING
  • ① 不要过多的依赖运算符的优先级来控制表达式的执行顺序，这样可读性太差，尽量使用小括号来控制表达式的执行顺序。
  • ② 不要把一个表达式写得过于复杂，如果一个表达式过于复杂，则把它分成几步来完成。
  • ③ 运算符优先级不用刻意地去记忆，总体上：一元运算符 > 算术运算符 > 关系运算符 > 逻辑运算符 > 三元运算符 > 赋值运算符。
第三章：附录 ​
3.1 字符集和字符集编码 ​
3.3.1 概述 ​
  • 字符集和字符集编码（简称编码）计算机系统中处理文本数据的两个基本概念，它们密切相关但又有区别。
  • 字符集（Character Set）是一组字符的集合，其中每个字符都被分配了一个唯一的编号（通常是数字）。字符可以是字母、数字、符号、控制代码（如换行符）等。字符集定义了可以表示的字符的范围，但它并不直接定义如何将这些字符存储在计算机中。
NOTE
ASCII（美国信息交换标准代码）是最早期和最简单的字符集之一，它只包括了英文字母、数字和一些特殊字符，共 128 个字符。每个字符都分配给了一个从 0 到 127 的数字。
  • 字符集编码（Character Encoding，简称编码）是一种方案或方法，它定义了如何将字符集中的字符转换为计算机存储和传输的数据（通常是一串二进制数字）。简而言之，编码是字符到二进制数据之间的映射规则。
NOTE
ASCII编码方案定义了如何将 ASCII 字符集中的每个字符表示为 7 位的二进制数字。例如：大写字母"A"在ASCII 编码中表示为二进制的1000001，十进制的 65 。
  • 字符集和字符集编码之间的关系如下：
  • Linux 中安装帮助手册：
3.3.2 ASCII 编码 ​
  • 从冯·诺依曼体系结构中，我们知道，计算机中所有的数据和指令都是以二进制的形式表示的；所以，计算机中对于文本数据的数据也是以二进制来存储的，那么对应的流程如下：
  • 我们知道，计算机是上个世纪 60 年代在美国研制成功的，为了实现字符和二进制的转换，美国就制定了一套字符编码，即英语字符和二进制位之间的关系，即 ASCII （American Standard Code for Information Interchange）编码： 
    • ASCII 编码只包括了英文字符、数字和一些特殊字符，一共 128 个字符，并且每个字符都分配了唯一的数字，范围是 0 - 127。
    • ASCII 编码中的每个字符都使用 7 位的二进制数字表示；但是，计算机中的存储的最小单位是 1 B = 8 位，那么最高位统一规定为 0 。
NOTE
  • ① 其实，早期是没有字符集的概念的，只是后来为了解决乱码问题，而产生了字符集的概念。
  • ② 对于英文体系来说，a-zA-Z0-9以及一些特殊字符一共 128 就可以满足实际存储需求；所以，在也是为什么 ASCII 码使用 7 位二进制（2^7 = 128 ）来存储的。
  • 在操作系统中，就内置了对应的编码表，Linux 也不例外；可以使用如下的命令查看：
shell
man ascii
  • 其对应的 ASCII 编码表，如下所示：
  • 但是，随着计算机的发展，计算机开始了东征之路，由美国传播到东方：
  • 先是传播到了欧洲，欧洲在兼容 ASCII 编码的基础上，推出了 ISO8859-1 编码，即： 
    • ISO8859-1 编码包括基本的拉丁字母表、数字、标点符号，以及西欧语言中特有的一些字符，如：法语中的 è、德语中的 ü 等。
    • ISO 8859-1 为每个字符分配一个单字节（8 位）编码，意味着它可以表示最多 256 （2^8）个不同的字符（编号从 0 到 255）。
    • ISO 8859-1 的前 128 个字符与 ASCII 编码完全一致，这使得 ASCII 编码的文本可以无缝转换为 ISO 8859-1 编码。
  • 计算机继续传播到了亚洲，亚洲（双字节）各个国家分别给出了自己国家对应的字符集编码，如： 
    • 日本推出了 Shift-JIS 编码： 
      • 单字节 ASCII 范围：0 - 127。
      • 双字节范围： 
        • 第一个字节：129 - 159 和 224 - 239 。
        • 第二个字节：64 - 126 和 128 - 252 。
    • 韩国推出了 EUC-KR 编码： 
      • 单字节 ASCII 范围：0 - 127。
      • 双字节范围：从 41281 - 65278。
    • 中国推出了 GBK 编码： 
      • 单字节 ASCII 范围：0 - 127。
      • 双字节范围：33088 - 65278 。
NOTE
  • ① 通过上面日本、韩国、中国的编码十进制范围，我们可以看到，虽然这些编码系统在技术上的编码范围存在重叠（特别是在高位字节区域），但因为它们各自支持的字符集完全不同，所以实际上它们并不直接冲突。
  • ② 但是，如果一个中国人通过 GBK 编码写的文章，通过邮件发送给韩国人，因为韩国和中国在字符集编码上的高位字节有重叠部分，必然会造成歧义。
3.3.3 Unicode 编码 ​
  • 在 Unicode 之前，世界上存在着数百种不同的编码系统，每一种编码系统都是为了支持特定语言或一组语言的字符集。这些编码系统，包括：ASCII、ISO 8859 系列、GBK、Shift-JIS、EUC-KR 等，它们各自有不同的字符范围和编码方式。这种多样性虽然在局部范围内解决了字符表示的问题，但也带来了以下几个方面的挑战：
    • 编码冲突：由于不同的编码系统可以为相同的字节值分配不同的字符，因此在不同编码之间转换文本时，如果没有正确处理编码信息，就很容易产生乱码。这种编码冲突在尝试处理多种语言的文本时尤为突出。
    • 编码的复杂性：随着全球化的发展，软件和系统需要支持越来越多的语言，这就要求开发者和系统同时处理多种不同的编码系统。这不仅增加了开发和维护的复杂性，而且也增加了出错的风险。
    • 资源限制：在早期计算机技术中，内存和存储资源相对有限。不同的编码标准要求系统存储多套字符集数据，这无疑增加了对有限资源的消耗。
    • ……
  • 针对上述的种种问题，为了推行全球化，Unicode 应运而生，Unicode 的核心规则和设计原则是建立一个全球统一的字符集，使得世界上所有的文字和符号都能被唯一地识别和使用，无论使用者位于何地或使用何种语言。这套规则包括了字符的编码、表示、处理和转换机制，旨在确保不同系统和软件间能够无缝交换和处理文本数据。
    • 通用字符集 (UCS)：Unicode 为每一个字符分配一个唯一的编号（称为“码点”）。这些码点被组织在一个统一的字符集中，官方称之为 “通用字符集”（Universal Character Set，UCS）。码点通常表示为 U+ 后跟一个十六进制数，例如：U+0041 代表大写的英文字母 “A”。
    • 编码平面和区段：Unicode 码点被划分为多个 “平面（Planes）”，每个平面包含 65536（16^4）个码点。目前，Unicode定义了 17 个平面（从 0 到16），每个平面被分配了一个编号，从 “基本多文种平面（BMP）” 的 0 开始，到 16 号平面结束。这意味着 Unicode 理论上可以支持超过 110万（17*65536）个码点。
  • Unicode 仅仅只是字符集，给每个字符设置了唯一的数字编号而已，却没有给出这些数字编号实际如何存储，可以通过如下命令查看：
  • 为了在计算机系统中表示 Unicode 字符，定义了几种编码方案，这些方案包括 UTF-8、UTF-16 和 UTF-32 等。 
    • UTF-8：使用 1 - 4 个字节表示每个 Unicode 字符，兼容 ASCII，是网络上最常用的编码。
    • UTF-16：使用 2 - 4 个字节表示每个 Unicode 字符，适合于需要经常处理基本多文种平面之外字符的应用。
    • UTF-32：使用固定的 4 个字节表示每个 Unicode 字符，简化了字符处理，但增加了存储空间的需求。
  • Unicode 字符集和对应的UTF-8 字符编码之间的关系，如下所示：
Released under the MIT License.
Copyright © 2024 许大仙

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第一章：概述 ​
  • 流程控制结构是用来控制程序中各语句执行顺序的语句，并且可以将语句组合成能完成一定功能的小逻辑模块。
  • 在程序设计中规定了三种流程结构，如下所示：
    • 顺序结构：程序从上到下逐行执行，中间没有任何判断和跳转。
    • 分支结构：根据条件，有选择的执行某段代码。在 C 语言中，有 if...else 和 switch...case 两种分支语句。
    • 循环结构：根据循环条件，重复性的执行某段代码。在 C 语言中，有 for、while、do...while 三种循环结构。
  • 在生活中的洗衣工厂，就包含了上述的三种流程结构，如下所示：
第二章：顺序结构 ​
2.1 概述 ​
  • 程序从上到下逐行地执行，表达式语句都是顺序执行的，并且上一行对某个变量的修改对下一行会产生影响。
2.2 应用示例 ​
  • 示例：
c
#include <stdio.h>
+    
许大仙
Appearance
第一章：概述 ​
  • 流程控制结构是用来控制程序中各语句执行顺序的语句，并且可以将语句组合成能完成一定功能的小逻辑模块。
  • 在程序设计中规定了三种流程结构，如下所示：
    • 顺序结构：程序从上到下逐行执行，中间没有任何判断和跳转。
    • 分支结构：根据条件，有选择的执行某段代码。在 C 语言中，有 if...else 和 switch...case 两种分支语句。
    • 循环结构：根据循环条件，重复性的执行某段代码。在 C 语言中，有 for、while、do...while 三种循环结构。
  • 在生活中的洗衣工厂，就包含了上述的三种流程结构，如下所示：
第二章：顺序结构 ​
2.1 概述 ​
  • 程序从上到下逐行地执行，表达式语句都是顺序执行的，并且上一行对某个变量的修改对下一行会产生影响。
2.2 应用示例 ​
  • 示例：
c
#include <stdio.h>
 
 int main() {
 
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     printf("程序结束！\n");
 
     return 0;
-}
Released under the MIT License.
Copyright © 2024 许大仙

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Released under the MIT License.
Copyright © 2024 许大仙

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第一章：数组的概念 ​
1.1 为什么需要数组？ ​
1.1.1 需求分析 1 ​
  • 需要统计某公司 50 个员工的工资情况，例如：计算平均工资、最高工资等。如果使用之前的知识，我们需要声明 50 个变量来分别记录每位员工的工资，即：
c
#include <stdio.h>
+
+int main(){
+    
+    double num1 = 0;
+    double num2 = 0;
+    double num3 = 0;
+    ...
+    printf("请输入第 1 个员工的工资：");
+    scanf("%lf",&num1);
+    printf("请输入第 2 个员工的工资：");
+    scanf("%lf",&num2);
+    printf("请输入第 3 个员工的工资：");
+    scanf("%lf",&num3);
+    ...   
+    return 0;
+}
  • 这样会感觉特别机械和麻烦（全是复制（Ctrl + c）和粘贴（Ctrl + v），CV 大法）；此时，我们就可以将所有的数据全部存储到一个容器（数组）中进行统一管理，并进行其它的操作，如：求最值、求平均值等，如下所示：
c
#include <stdio.h>
+
+int main(){
+    // 声明数组
+    double nums[50];
+    // 数组的长度
+    int length = sizeof(nums) / sizeof(double);
+    // 使用 for 循环向数组中添加值
+    for(int i = 0;i < length;i++){
+        printf("请输入第 &d 个员工的工资：",i);
+        scanf("%lf",&num[i]);
+    }
+    // 其它操作，如：求最值，求平均值等
+    ...        
+    return 0;
+}
1.1.2 需求分析 2 ​
  • 在现实生活中，我们会使用很多 APP 或微信小程序等，即：
  • 同样的道理，如果我们使用变量来存储每个商品信息，那么就需要非常多的变量；但是，如果我们将这些商品信息都存储到一个容器（数组）中，进行统一管理，对之后的数据处理将会非常方便。
1.1.3 容器的概念 ​
  • 生活中的容器：水杯（装水、饮料的容器）、衣柜（装衣服等物品的容器）、集装箱（装货物等物品的容器）。
  • 程序中的容器：将多个数据存储到一起，并且每个数据称为该容器中的元素。
1.2 什么是数组？ ​
  • 数组（Array）是将多个相同数据类型的数据按照一定的顺序排序的集合，并使用一个标识符命名，以及通过编号（索引，亦称为下标）的方式对这些数据进行统一管理。
1.3 数组的相关概念 ​
  • 数组名：本质上是一个标识符常量，命名需要符合标识符规则和规范。
  • 元素：同一个数组中的元素必须是相同的数据类型。
  • 索引（下标）：从 0 开始的连续数字。
  • 数组的长度：就是元素的个数。
1.4 数组的特点 ​
  • ① 创建数组的时候，会在内存中开辟一整块连续的空间，占据空间的大小，取决于数组的长度和数组中元素的类型。
  • ② 数组中的元素在内存中是依次紧密排列且有序的。
  • ③ 数组一旦初始化完成，且长度就确定的，并且数组的长度一旦确定，就不能更改。
  • ④ 我们可以直接通过索引（下标）来获取指定位置的元素，速度很快。
  • ⑤ 数组名中引用的是这块连续空间的首地址。
第二章：数组的操作（⭐） ​
2.1 数组的定义 ​
2.1.1 动态初始化 ​
  • 语法：
c
数据类型 数组名[元素个数|长度];
NOTE
  • ① 数据类型：表示的是数组中每一个元素的数据类型。
  • ② 数组名：必须符合标识符规则和规范。
  • ③ 元素个数或长度：表示的是数组中最多可以容纳多少个元素（不能是负数、也不能是 0 ）。
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 先指定元素的个数和类型，再进行初始化
+
+    // 定义数组
+    int arr[3];
+
+    // 给数组元素赋值
+    arr[0] = 10;
+    arr[1] = 20;
+    arr[2] = 30;
+
+    return 0;
+}
2.1.2 静态初始化 1 ​
  • 语法：
c
数据类型 数组名[元素个数|长度] = {元素1,元素2,...}
NOTE
  • ① 静态部分初始化：如果数组初始化的元素个数小于数组声明的长度，那么就会从数组开始位置依次赋值，不够的就补 0 。
  • ② 静态全部初始化：数组初始化的元素个数等于数组的长度。
  • 技巧：
    • 在 CLion 中可以开启聚合初始化功能，即：
    • 这样，在 CLion 中，将会显示数组初始化中的元素索引，即：
  • 示例：静态部分初识化
c
#include <stdio.h>
+
+int main() {
+
+    // 定义数组和部分初始化：
+    // 会将给定的值从数组的开始位置一个个的赋值，没有赋值的地方，用 0 填充
+    int arr[5] = {1, 2};
+
+    return 0;
+}
  • 示例：静态全部初始化
c
#include <stdio.h>
+
+int main() {
+
+    // 定义数组和全部初始化：数组初始化的元素个数等于数组的长度。
+    int arr[5] = {1, 2, 3, 4, 5};
+
+    return 0;
+}
2.1.3 静态初始化 2 ​
  • 语法：
c
数据类型 数组名[] = {元素1,元素2,...}
NOTE
没有给出数组中元素的个数，将由系统根据初始化的元素，自动推断出数组中元素的个数。
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 指定元素的类型，不指定元素个数，同时进行初始化
+    int arr[] = {1, 2, 3, 4, 5};
+
+    return 0;
+}
2.2 访问数组元素 ​
  • 语法：
c
数组名[索引|下标];
NOTE
假设数组 arr 有 n 个元素，如果使用的数组的下标 < 0 或 > n-1 ，那么将会产生数组越界访问，即超出了数组合法空间的访问；那么，数组的索引范围是 [0,arr.length - 1]。
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 先指定元素的个数和类型，再进行初始化
+
+    // 定义数组
+    int arr[3];
+
+    // 给数组元素赋值
+    arr[0] = 10;
+    arr[1] = 20;
+    arr[2] = 30;
+
+    // 访问数组元素
+    printf("arr[0] = %d\n", arr[0]); // arr[0] = 10
+    printf("arr[1] = %d\n", arr[1]); // arr[1] = 20
+    printf("arr[2] = %d\n", arr[2]); // arr[2] = 30
+
+    return 0;
+}
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 定义数组和部分初始化：
+    // 会将给定的值从数组的开始位置一个个的赋值，没有赋值的地方，用 0 填充
+    int arr[5] = {1, 2};
+
+    // 访问数组元素
+    printf("arr[0] = %d\n", arr[0]); // arr[0] = 1
+    printf("arr[1] = %d\n", arr[1]); // arr[1] = 2
+    printf("arr[2] = %d\n", arr[2]); // arr[2] = 0
+    printf("arr[3] = %d\n", arr[3]); // arr[3] = 0
+    printf("arr[4] = %d\n", arr[4]); // arr[4] = 0
+
+    return 0;
+}
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 指定元素的类型，不指定元素个数，同时进行初始化
+    int arr[] = {1, 2, 3, 4, 5};
+
+    // 访问数组元素
+    printf("arr[0] = %d\n", arr[0]); // arr[0] = 1
+    printf("arr[1] = %d\n", arr[1]); // arr[1] = 2
+    printf("arr[2] = %d\n", arr[2]); // arr[2] = 3
+    printf("arr[3] = %d\n", arr[3]); // arr[3] = 4
+    printf("arr[4] = %d\n", arr[4]); // arr[4] = 5
+
+    return 0;
+}
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 定义数组和全部初始化：数组初始化的元素个数等于数组的长度。
+    int arr[5] = {1, 2, 3, 4, 5};
+
+    // 访问数组元素
+    printf("arr[0] = %d\n", arr[0]); // arr[0] = 1
+    printf("arr[1] = %d\n", arr[1]); // arr[1] = 2
+    printf("arr[2] = %d\n", arr[2]); // arr[2] = 3
+    printf("arr[3] = %d\n", arr[3]); // arr[3] = 4
+    printf("arr[4] = %d\n", arr[4]); // arr[4] = 5
+
+    return 0;
+}
2.3 数组越界 ​
  • 数组下标必须在指定范围内使用，超出范围视为越界。
NOTE
  • ① C 语言是不会做数组下标越界的检查，并且编译器也不会报错；但是，编译器不报错，并不意味着程序就是正确！
  • ② 在其它高级编程语言，如：Java、JavaScript、Rust 等中，如果数组越界访问，编译器是会直接报错的！！！
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 定义数组和全部初始化：数组初始化的元素个数等于数组的长度。
+    int arr[] = {1, 2, 3, 4, 5};
+
+    // 访问数组元素
+    printf("arr[0] = %d\n", arr[0]); // arr[0] = 1
+    printf("arr[1] = %d\n", arr[1]); // arr[1] = 2
+    printf("arr[2] = %d\n", arr[2]); // arr[2] = 3
+    printf("arr[3] = %d\n", arr[3]); // arr[3] = 4
+    printf("arr[4] = %d\n", arr[4]); // arr[4] = 5
+    printf("arr[-1] = %d\n", arr[-1]); // 得到的是不确定的结果
+    printf("arr[5] = %d\n", arr[5]); // 得到的是不确定的结果
+
+    return 0;
+}
2.4 计算数组的长度 ​
  • 数组长度（元素个数）是在数组定义的时候明确指定且固定的，我们不能在运行的时候直接获取数组长度；但是，我们可以通过 sizeof 运算符间接计算出数组的长度。
  • 计算步骤，如下所示： 
    • ① 使用 sizeof 运算符计算出整个数组的字节长度。
    • ② 由于数组成员是同一数据类型；那么，每个元素的字节长度一定相等，那么数组的长度 = 整个数组的字节长度 ÷ 单个元素的字节长度 。
NOTE
  • ① 在很多编程语言中，都内置了获取数组的长度的属性或方法，如：Java 中的 arr.length 或 Rust 的 arr.len()。
  • ② 但是，C 语言没有内置的获取数组长度的属性或方法，只能通过 sizeof 运算符间接来计算得到。
  • ③ 数组一旦声明或定义，其长度就固定了，不能动态变化。
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 定义数组和全部初始化：数组初始化的元素个数等于数组的长度。
+    int arr[] = {1, 2, 3, 4, 5};
+
+    // 计算数组的长度
+    size_t length = sizeof(arr) / sizeof(arr[0]);
+
+    // 遍历数组
+    for (int i = 0; i < length; i++) {
+        printf("%d \n", arr[i]);
+    }
+
+    return 0;
+}
2.5 遍历数组 ​
  • 遍历数组是指按顺序访问数组中的每个元素，以便读取或修改它们，编程中一般使用循环结构对数组进行遍历。
  • 示例：声明一个存储有 12、2、31、24、15、36、67、108、29、51 的数组，并遍历数组所有元素
c
#include <stdio.h>
+
+int main() {
+
+    // 定义数组并初始化
+    int arr[] = {12, 2, 31, 24, 15, 36, 67, 108, 29, 51};
+
+    // 计算数组的长度
+    size_t length = sizeof(arr) / sizeof(int);
+
+    // 遍历数组
+    for (int i = 0; i < length; i++) {
+        printf("%d\n", arr[i]);
+    }
+
+    return 0;
+}
  • 示例：声明长度为 10 的 int 类型数组，给数组元素依次赋值为 0 ~ 9 ，并遍历数组所有元素
c
#include <stdio.h>
+
+int main() {
+
+    // 定义数组
+    int arr[10];
+
+    // 计算数组的长度
+    size_t length = sizeof(arr) / sizeof(int);
+
+    // 给数组的每个元素赋值
+    for (int i = 0; i < length; i++) {
+        arr[i] = i;
+    }
+
+    // 遍历数组
+    for (int i = 0; i < length; i++) {
+        printf("%d\n", arr[i]);
+    }
+
+    return 0;
+}
2.6 一维数组的内存分析 ​
2.6.1 数组内存图 ​
  • 假设数组是如下的定义：
c
int arr[] = {1,2,3,4,5};
  • 那么，对应的内存结构，如下所示：
NOTE
  • ① 数组名 arr 就是记录该数组的首地址，即 arr[0] 的地址。
  • ② 数组中的各个元素是连续分布的，假设 arr[0] 的地址是 0xdea7bff880，则 arr[1] 的地址 = arr[0] 的地址 + int 字节数（4） = 0xdea7bff880 + 4 = 0xdea7bff884 ，依次类推...
  • 在 C 语言中，我们可以通过 &arr 或 &arr[0] 等形式获取数组或数组元素的地址，即：
c
#include <stdio.h>
+
+int main() {
+
+    // 定义数组
+    int arr[10];
+
+    // 计算数组的长度
+    size_t length = sizeof(arr) / sizeof(int);
+
+    // 给数组的每个元素赋值
+    for (int i = 0; i < length; i++) {
+        arr[i] = i;
+    }
+
+    printf("数组的地址是 = %p\n", arr);
+
+    // 遍历数组
+    for (int i = 0; i < length; i++) {
+        printf("数组元素 %d 的地址是 = %p\n", arr[i], &arr[i]);
+    }
+
+    return 0;
+}
2.6.2 数组的注意事项 ​
  • C 语言规定，数组一旦声明，数组名指向的地址将不可更改。因为在声明数组的时候，编译器会自动会数组分配内存地址，这个地址和数组名是绑定的，不可更改。
WARNING
如果之后试图更改数组名对应的地址，编译器就会报错。
  • 示例：错误演示
c
int num[5]; // 声明数组
+// 使用大括号重新赋值是不允许的，必须在数组声明的时候赋值，否则编译将会报错
+num = {1,2,3,4,5} ; // 报错
  • 示例：错误演示
c
int num[] = {1,2,3,4,5};
+// 使用大括号重新赋值是不允许的，必须在数组声明的时候赋值，否则编译将会报错
+num = {2,3,4,5,6}; // 报错
  • 示例：错误演示
c
int num[5];
+
+num = NULL; // 报错，需要和 Java 区别一下，在 C 中不可以
  • 示例：错误演示
c
int a[] = {1,2,3,4,5} 
+
+int b[5] = a ; // 报错，需要和 Java 区别一下，在 C 中不可以
2.7 数组应用案例 ​
2.7.1 应用示例 ​
  • 需求：计算数组中所有元素的和以及平均数。
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 定义数组并初始化
+    int arr[] = {12, 2, 31, 24, 15, 36, 67, 108, 29, 51};
+
+    // 计算数组的长度
+    size_t length = sizeof(arr) / sizeof(int);
+
+    // 变量保存总和
+    int sum = 0;
+
+    // 遍历数组
+    for (int i = 0; i < length; i++) {
+        sum += arr[i];
+    }
+
+    double avg = (double)sum / length;
+    printf("数组的和为：%d\n", sum); // 数组的和为：375
+    printf("数组的平均值为：%.2lf\n", avg); //数组的平均值为：37.50
+
+    return 0;
+}
2.7.2 应用示例 ​
  • 需求：计算数组的最值（最大值和最小值）。
NOTE
思路：
  • ① 假设数组中的第一个元素是最大值或最小值，并使用变量 max 或 min 保存。
  • ② 遍历数组中的每个元素： 
    • 如果有元素比最大值还要大，就让变量 max 保存最大值。
    • 如果有元素比最小值还要小，就让变量 min 保存最小值。
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 定义数组并初始化
+    int arr[] = {12, 2, 31, 24, 15, -36, 67, 108, 29, 51};
+
+    // 计算数组的长度
+    size_t length = sizeof(arr) / sizeof(int);
+
+    // 定义最大值
+    int max = arr[0];
+    // 定义最小值
+    int min = arr[0];
+
+    // 遍历数组
+    for (int i = 0; i < length; i++) {
+        if (arr[i] >= max) {
+            max = arr[i];
+        }
+        if (arr[i] <= min) {
+            min = arr[i];
+        }
+    }
+
+    printf("数组的最大值为：%d\n", max); // 数组的最大值为：108
+    printf("数组的最小值为：%d\n", min); // 数组的最小值为：-36
+
+    return 0;
+}
2.7.3 应用示例 ​
  • 需求：统计数组中某个元素出现的次数，要求：使用无限循环，如果输入的数字是 0 ，就退出。
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 定义数组并初始化
+    int arr[] = {12, 2, 31, 24, 2, -36, 67, 108, 29, 51};
+
+    // 计算数组的长度
+    size_t length = sizeof(arr) / sizeof(int);
+
+    // 遍历数组
+    printf("当前数组中的元素是：");
+    for (int i = 0; i < length; i++) {
+        printf("%d ", arr[i]);
+    }
+
+    printf("\n");
+
+    // 无限循环
+    while (true) {
+        // 统计的数字
+        int num;
+        // 统计数字出现的次数
+        int count = 0;
+        // 输入数字
+        printf("请输入要统计的数字：");
+        scanf("%d", &num);
+
+        // 0 作为结束条件
+        if (num == 0) {
+            break;
+        }
+
+        // 遍历数组，并计数
+        for (int i = 0; i < length; i++) {
+            if (arr[i] == num) {
+                count++;
+            }
+        }
+
+        printf("您输入的数字 %d 在数组中出现了 %d 次\n", num, count);
+    }
+
+    return 0;
+}
2.7.4 应用示例 ​
  • 需求：将数组 a 中的全部元素复制到数组 b 中。
  • 示例：
c
#include <stdio.h>
+
+#define  SIZE 10
+
+int main() {
+
+    // 定义数组并初始化
+    int a[] = {12, 2, 31, 24, 15, -36, 67, 108, 29, 51};
+    int b[SIZE];
+
+    // 复制数组
+    for (int i = 0; i < SIZE; i++) {
+        b[i] = a[i];
+    }
+
+    // 打印数组 b 中的全部元素
+    for (int i = 0; i < SIZE; i++) {
+        printf("%d ", b[i]);
+    }
+
+    return 0;
+}
2.7.5 应用示例 ​
  • 需求：数组对称位置的元素互换。
NOTE
思路：假设数组一共有 10 个元素，那么：
  • a[0] 和 a[9] 互换。
  • a[1] 和 a[8] 互换。
  • ...
规律就是 a[i] <--互换--> arr[arr.length -1 -i]
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 原始数组
+    int arr[] = {12, 2, 31, 24, 15, -36, 67, 108, 29, 51};
+
+    // 计算数组的长度
+    size_t SIZE = sizeof(arr) / sizeof(arr[0]);
+    
+    // 打印原始数组中的全部元素
+    printf("原始数组：");
+    for (int i = 0; i < SIZE; i++) {
+        printf("%d ", arr[i]);
+    }
+    printf("\n");
+
+    // 交换数组
+    for (int i = 0; i < SIZE / 2; i++) {
+        int temp          = arr[i];
+        arr[i]            = arr[SIZE - 1 - i];
+        arr[SIZE - 1 - i] = temp;
+    }
+
+    // 打印交换后的数组
+    printf("交换后数组：");
+    for (int i = 0; i < SIZE; i++) {
+        printf("%d ", arr[i]);
+    }
+    printf("\n");
+
+    return 0;
+}
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 原始数组
+    int arr[] = {12, 2, 31, 24, 15, -36, 67, 108, 29, 51};
+
+    // 计算数组的长度
+    size_t SIZE = sizeof(arr) / sizeof(arr[0]);
+
+    // 打印原始数组中的全部元素
+    printf("原始数组：");
+    for (int i = 0; i < SIZE; i++) {
+        printf("%d ", arr[i]);
+    }
+    printf("\n");
+
+    // 交换数组
+    for (int i = 0, j = SIZE - 1 - i; i < SIZE / 2; i++, j--) {
+        int temp = arr[i];
+        arr[i]   = arr[j];
+        arr[j]   = temp;
+    }
+
+    // 打印交换后的数组
+    printf("交换后数组：");
+    for (int i = 0; i < SIZE; i++) {
+        printf("%d ", arr[i]);
+    }
+    printf("\n");
+
+    return 0;
+}
2.7.6 应用示例 ​
  • 需求：将数组中的最大值移动到数组的最末尾。
NOTE
思路：从数组的下标 0 开始依次遍历到 length - 1 ，如果 i 下标当前的值比 i+1 下标的值大，则交换；否则，就不交换。
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 原始数组
+    int arr[] = {12, 2, 31, -24, 15, -36, 67, 891, 29, 51};
+
+    // 计算数组的长度
+    size_t length = sizeof(arr) / sizeof(arr[0]);
+
+    // 打印原始数组中的全部元素
+    printf("原始数组：");
+    for (int i = 0; i < length; i++) {
+        printf("%d ", arr[i]);
+    }
+    printf("\n");
+
+    // 移动最大值到数组的最后一个位置
+    for (int i = 0; i < length - 1; i++) {
+        if (arr[i] > arr[i + 1]) {
+            int temp   = arr[i];
+            arr[i]     = arr[i + 1];
+            arr[i + 1] = temp;
+        }
+    }
+
+    // 打印移动之后的数组
+    printf("移动之后的数组：");
+    for (int i = 0; i < length; i++) {
+        printf("%d ", arr[i]);
+    }
+    printf("\n");
+
+    return 0;
+}
2.7.7 应用示例 ​
  • 需求：实现冒泡排序，即将数组的元素从小到大排列。
NOTE
思路：一层循环，能实现最大值移动到数组的最后；那么，二层循环（控制内部循环数组的长度）就能实现将数组的元素从小到大排序。
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 原始数组
+    int arr[] = {12, 2, 31, -24, 15, -36, 67, 891, 29, 51};
+
+    // 计算数组的长度
+    size_t length = sizeof(arr) / sizeof(arr[0]);
+
+    // 打印原始数组中的全部元素
+    printf("原始数组：");
+    for (int i = 0; i < length; i++) {
+        printf("%d ", arr[i]);
+    }
+    printf("\n");
+
+    for (int j = 0; j < length - 1; j++) {
+        for (int i = 0; i < length - 1 - j; i++) {
+            if (arr[i] > arr[i + 1]) {
+                int temp = arr[i];
+                arr[i] = arr[i + 1];
+                arr[i + 1] = temp;
+            }
+        }
+    }
+
+    // 打印移动之后的数组
+    printf("移动之后的数组：");
+    for (int i = 0; i < length; i++) {
+        printf("%d ", arr[i]);
+    }
+    printf("\n");
+
+    return 0;
+}
第三章：多维数组（⭐） ​
3.1 概述 ​
3.1.1 引入 ​
  • 我们在数学、物理和计算机科学等学科中学习过一维坐标、二维坐标以及三维坐标。
  • 其中，一维坐标通常用于描述在线段或直线上的点的位置，主要应用有：
    • 数轴：一维坐标可以用来表示数轴上的数值位置，这在基础数学和初等代数中非常常见。
    • 时间轴：时间可以看作是一维的，它可以用一维坐标表示，例如：秒、分钟、小时等。
    • 统计数据：一维坐标常用于表示单变量的数据集，如：测量身高、体重、温度等。
  • 其中，二维坐标用于描述平面上的点的位置。主要应用包括：
    • 几何学：在几何学中，二维坐标用于表示平面图形的顶点、边和面积等。
    • 地图和导航：地理坐标系统（经纬度）使用二维坐标来表示地球表面的任意位置。
    image-20240724112326592
    • 图形设计和计算机图形学：二维坐标在绘制图形、设计图案和用户界面中非常重要。
    • 物理学：二维运动和场，例如：在描述物体在平面上的运动轨迹时使用二维坐标。
  • 其中，三维坐标用于描述空间中点的位置。主要应用包括：
    • 几何学：三维坐标在空间几何中用于表示立体图形的顶点、边、面和体积。
    • 计算机图形学：三维建模和动画需要使用三维坐标来创建和操控虚拟对象。
    • 工程和建筑设计：在设计建筑物、机械部件和其他工程项目时，使用三维坐标来精确定位和规划。
    • 物理学：三维空间中的力、运动和场，例如：描述物体在空间中的位置和运动轨迹。
  • 总而言之，一维、二维和三维坐标系统在不同的领域中各有其重要的应用，从基础数学到高级科学和工程技术，它们帮助我们更好地理解和描述世界的结构和行为。
3.1.2 多维数组 ​
  • 在 C 语言中，多维数组就是数组嵌套，即：在数组中包含数组，数组中的每一个元素还是一个数组类型，如下所示：
NOTE
  • ① 如果数组中嵌套的每一个元素是一个常量值，那么该数组就是一维数组。
  • ② 如果数组中嵌套的每一个元素是一个一维数组，那么该数组就是二维数组。
  • ③ 如果数组中前台的每一个元素是一个二维数组，那么该数组就是三维数组.
  • ④ 依次类推...
  • 一维数组和多维数组的理解： 
    • 从内存角度看：一维数组或多维数组都是占用的一整块连续的内存空间。
    • 从数据操作角度看： 
      • 一维数组可以直接通过下标访问到数组中的某个元素，即：0、1、...
      • 二维数组要想访问某个元素，先要获取某个一维数组，然后在一维数组中获取对应的数据。
NOTE
  • ① C 语言中的一维数组或多维数组都是占用的一整块连续的内存空间，其它编程语言可不是这样的，如：Java 等。
  • ② 在实际开发中，最为常用的就是二维数组或三维数组了，以二维数组居多！！！
3.2 二维数组的定义 ​
3.2.1 动态初始化 ​
  • 语法：
c
数据类型 数组名[几个⼀维数组元素][每个⼀维数组中有几个具体的数据元素];
NOTE
  • ① 二维数组在实际开发中，最为常见的应用场景就是表格或矩阵了。
  • ② 几个一维数组元素 = 行数。
  • ③ 每个⼀维数组中有几个具体的数据元素 = 列数。
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 定义二维数组并初始化
+    int arr[3][4] = {{1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12}};
+
+    // 输出二维数组中的元素
+    printf("%d ", arr[0][0]);
+    printf("%d ", arr[0][1]);
+    printf("%d ", arr[0][2]);
+    printf("%d \n", arr[0][3]);
+    printf("%d ", arr[1][0]);
+    printf("%d ", arr[1][1]);
+    printf("%d ", arr[1][2]);
+    printf("%d \n", arr[1][3]);
+    printf("%d ", arr[2][0]);
+    printf("%d ", arr[2][1]);
+    printf("%d ", arr[2][2]);
+    printf("%d ", arr[2][3]);
+
+    return 0;
+}
3.2.2 静态初始化 1 ​
  • 语法：
c
数据类型 数组名[行数][列数] = {{元素1,元素2,...},{元素3,...},...}
NOTE
  • ① 行数 = 几个一维数组元素。
  • ② 列数 = 每个⼀维数组中有几个具体的数据元素。
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 定义二维数组
+    int arr[][4] = {{1, 2, 3, 4}, {5, 6}, {9, 10, 11, 12}};
+
+    // 输出二维数组中的元素
+    printf("%d ", arr[0][0]);
+    printf("%d ", arr[0][1]);
+    printf("%d ", arr[0][2]);
+    printf("%d \n", arr[0][3]);
+    printf("%d ", arr[1][0]);
+    printf("%d \n", arr[1][1]);
+    printf("%d ", arr[2][0]);
+    printf("%d ", arr[2][1]);
+    printf("%d ", arr[2][2]);
+    printf("%d ", arr[2][3]);
+
+    return 0;
+}
3.2.3 静态初始化 2 ​
  • 语法：
c
数据类型 数组名[行数][] = {{元素1,元素2,...},{元素3,...},...}
NOTE
  • ① 行数 = 几个一维数组元素 。
  • ② 可以不指定行数，必须指定列数，编译器会根据元素的个数和列的个数，自动推断出行数！！！
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 定义二维数组
+    int arr[][4] = {{1, 2, 3, 4}, {5, 6}, {9, 10, 11, 12}};
+
+    // 输出二维数组中的元素
+    printf("%d ", arr[0][0]);
+    printf("%d ", arr[0][1]);
+    printf("%d ", arr[0][2]);
+    printf("%d \n", arr[0][3]);
+    printf("%d ", arr[1][0]);
+    printf("%d \n", arr[1][1]);
+    printf("%d ", arr[2][0]);
+    printf("%d ", arr[2][1]);
+    printf("%d ", arr[2][2]);
+    printf("%d ", arr[2][3]);
+
+    return 0;
+}
3.3 二维数组的理解 ​
  • 如果二维数组是这么定义的，即：
c
int arr[3][4];
  • 那么，这个二维数组 arr 可以看做是 3 个一维数组组成，它们分别是 arr[0]、arr[1]、arr[2]。这 3 个一维数组都各有 4 个元素，如：一维数组 arr[0] 中的元素是 arr[0][0]、arr[0][1]、arr[0][2]、arr[0][3]，即：
3.4 二维数组的遍历 ​
  • 访问二维数组的元素，需要使用两个下标（索引），一个用于访问行（第一维），另一个用于访问列（第二维），我们通常称为行下标（行索引）或列下标（列索引）。
  • 所以，遍历二维数组，需要使用双层循环结构。
NOTE
如果一个二维数组是这么定义的，即：int arr[3][4]，那么：
  • 行的长度 = sizeof(arr) / sizeof(arr[0]) ，因为 arr 是二维数组的总的内存空间；而 arr[0] 、arr[1]、arr[2] 是二维数组中一维数组的内存空间 。
  • 列的长度 = sizeof(arr[0]) / sizeof(arr[0][0])，因为arr[0] 、arr[1]、arr[2] 是二维数组中一维数组的内存空间 ，而 arr[0][0]、arr[0][1]、... 是一维数组中元素的内存空间。
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 定义二维数组
+    int arr[][4] = {{1, 2, 3, 4}, {5, 6}, {9, 10, 11, 12}};
+
+    // 获取行列数
+    int row = sizeof(arr) / sizeof(arr[0]);
+    int col = sizeof(arr[0]) / sizeof(arr[0][0]);
+
+    // 打印二维数组元素
+    for (int i = 0; i < row; i++) {
+        for (int j = 0; j < col; j++) {
+            printf("%d ", arr[i][j]);
+        }
+        printf("\n");
+    }
+
+    return 0;
+}
3.5 二维数组的内存分析 ​
  • 用矩阵形式（如3行4列形式）表示二维数组，是逻辑上的概念，能形象地表示出行列关系。而在内存中，各元素是连续存放的，不是二维的，是线性的。
  • C 语言中，二维数组中元素排列的顺序是按行存放的。即：先顺序存放第一行的元素，再存放第二行的元素。例如：数组a[3][4] 在内存中的存放：
3.6 二维数组的应用案例 ​
  • 需求：现在有三个班，每个班五名同学，用二维数组保存他们的成绩，并求出每个班级平均分、以及所有班级平均分，数据要求从控制台输入。
  • 示例：
c
#include <stdio.h>
+
+int main() {
+
+    // 定义二维数组，用于保存成绩
+    double arr[3][5];
+
+    // 获取二维数组的行数和列数
+    int row = sizeof(arr) / sizeof(arr[0]);
+    int col = sizeof(arr[0]) / sizeof(arr[0][0]);
+
+    // 从控制台输入成绩
+    for (int i = 0; i < row; i++) {
+        for (int j = 0; j < col; j++) {
+            printf("请输入第%d个班级的第%d个学生的成绩：", i + 1, j + 1);
+            scanf("%lf", &arr[i][j]);
+        }
+    }
+
+    // 总分
+    double totalSum = 0;
+
+    // 遍历数组，求总分和各个班级的平均分
+    for (int i = 0; i < row; i++) {
+        double sum = 0;
+        for (int j = 0; j < col; j++) {
+            totalSum += arr[i][j];
+            sum += arr[i][j];
+        }
+        printf("第%d个班级的总分为：%.2lf\n", i + 1, sum);
+        printf("第%d个班级的平均分为：%.2lf\n", i + 1, sum / col);
+    }
+
+    printf("所有班级的总分为：%.2lf\n", totalSum);
+    printf("所有班级的平均分为：%.2lf\n", totalSum / (row * col));
+
+    return 0;
+}
Released under the MIT License.
Copyright © 2024 许大仙

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c/c++ 学科 ​
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