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a/docs/.vitepress/sidebar/index.ts b/docs/.vitepress/sidebar/index.ts index 4f274b2..6722248 100644 --- a/docs/.vitepress/sidebar/index.ts +++ b/docs/.vitepress/sidebar/index.ts @@ -10,15 +10,17 @@ export const sidebar: DefaultTheme.Sidebar = { { text: '编程基础二', link: `/notes/01_c-basic/01_${commonDirectoryName}/` }, { text: 'C 语言入门一', link: `/notes/01_c-basic/02_${commonDirectoryName}/` }, { text: 'C 语言入门二', link: `/notes/01_c-basic/03_${commonDirectoryName}/` }, - { text: '变量和进制', link: `/notes/01_c-basic/04_${commonDirectoryName}/` }, - { text: '数据类型和运算符', link: `/notes/01_c-basic/05_${commonDirectoryName}/` }, - { text: 'C 语言中的字符集', link: `/notes/01_c-basic/06_${commonDirectoryName}/` }, - { text: '格式化输入输出', link: `/notes/01_c-basic/07_${commonDirectoryName}/` }, - { text: '虚拟地址空间', link: `/notes/01_c-basic/08_${commonDirectoryName}/` }, - { text: '流程控制', link: `/notes/01_c-basic/09_${commonDirectoryName}/` }, - { text: '内存泄漏和内存溢出', link: `/notes/01_c-basic/10_${commonDirectoryName}/` }, - { text: '数组一', link: `/notes/01_c-basic/11_${commonDirectoryName}/` }, - { text: '数组二', link: `/notes/01_c-basic/12_${commonDirectoryName}/` }, + { text: '变量和常量', link: `/notes/01_c-basic/04_${commonDirectoryName}/` }, + { text: '进制', link: `/notes/01_c-basic/05_${commonDirectoryName}/` }, + { text: '数据类型', link: `/notes/01_c-basic/06_${commonDirectoryName}/` }, + { text: '运算符', link: `/notes/01_c-basic/07_${commonDirectoryName}/` }, + { text: 'C 语言中的字符集', link: `/notes/01_c-basic/08_${commonDirectoryName}/` }, + { text: '格式化输入输出', link: `/notes/01_c-basic/09_${commonDirectoryName}/` }, + { text: '虚拟地址空间', link: `/notes/01_c-basic/10_${commonDirectoryName}/` }, + { text: '流程控制', link: `/notes/01_c-basic/11_${commonDirectoryName}/` }, + { text: '内存泄漏和内存溢出', link: `/notes/01_c-basic/12_${commonDirectoryName}/` }, + { text: '数组一', link: `/notes/01_c-basic/13_${commonDirectoryName}/` }, + { text: '数组二', link: 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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 + +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: + +![](./assets/1.png) + +* 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;那么,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。 + +![](./assets/2.png) + +## 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 + +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。 + +> [!TIP] +> +> 在 CLion 中开启`嵌入提示(形参名称-->显示数组索引的提示)`功能,即: +> +> ![](./assets/3.png) +> +> 这样,在 CLion 中,将会显示数组初始化时每个元素对应的索引,即: +> +> ![](./assets/4.png) + + + +* 示例:静态部分初始化 + +```c +#include + +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 + +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 + +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; +} +``` + +### 2.1.4 静态初始化 3 + +* 在 C 语言中,也可以只给部分元素赋值。当 {} 中的值少于元素的个数的时候,只会给前面的部分元素赋值,至于剩下的元素就会自动初始化为 0 。 + +```c +int arr[10] = {1,2,3,4,5}; +``` + +> [!NOTE] +> +> * ① 数组 `arr` 在内存中开辟了 `10` 个连续的内存空间,但是只会给前 `5` 个内存空间赋值初始化值,即:`arr[0] ~ arr[4]` 分别是 `1`、`2`、`3`、`4`、`5`,而 `arr[5] ~ arr[9]` 就会被自动初始化为 `0` 。 +> * ② 当赋值的元素少于数组总体元素的时候,剩余的元素自动初始化为 `0`,其规则如下: +> * 对于 `short`、`int`、`long`,就是整数 `0`。 +> * 对于 `char`,就是字符 `'\0'`。需要注意的是,`'\0'` 的十进制数就是 `0` 。 +> * 对于 `float`、`double`,就是小数 `0.0`。 + + + +* 示例: + +```c +#include +int main() { + int arr[10] = {1, 2, 3, 4, 5}; + + 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[5] = %d \n", arr[5]); // arr[5] = 0 + printf("arr[6] = %d \n", arr[6]); // arr[6] = 0 + printf("arr[7] = %d \n", arr[7]); // arr[7] = 0 + printf("arr[8] = %d \n", arr[8]); // arr[8] = 0 + printf("arr[9] = %d \n", arr[9]); // arr[9] = 0 + + 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 + +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 + +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 + +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 + +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。 + +![](./assets/5.png) + +> [!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 + +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 `。 + +![](./assets/6.png) + +> [!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 + +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 + +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 + +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: + +![](./assets/7.png) + +> [!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 + +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} ; // [!code error] +``` + + + +* 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}; // [!code error] +``` + + + +* 示例:错误演示 + +```c +int num[5]; + +// 报错,需要和 Java 区别一下,在 C 中不可以 +num = NULL; // [!code error] +``` + + + +* 示例:错误演示 + +```c +int a[] = {1,2,3,4,5} + +// 报错,需要和 Java 区别一下,在 C 中不可以 +int b[5] = a ; // [!code error] +``` + +## 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 + +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 + +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 + +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 + +#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 + +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 + +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 + +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 + +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; +} +``` + +### 2.7.8 应用示例 + +* 需求:数组中的元素是从小到大排列的,现在要求根据指定的元素获取其在数组中的位置。 + +> [!NOTE] +> +> 二分查找(折半查找)的前提条件是:数组中的元素必须是`有序`的(从小到大或从大到小)。其基本步骤,如下所示: +> +> * ① 确定初始范围:定义数组的起始索引 `min = 0` 和结束索引 `max = len - 1` 。 +> * ② 计算中间索引:在每次迭代中,计算中间位置 `mid = (min + right) / 2`。 +> * ③ 比较中间值: +> * 如果`目标值`比 `arr[mid]` 小,则继续在`左`半部分查找,那么 `min` 不变,而`max = mid - 1` 。 +> * 如果`目标值`比 `arr[mid]` 大,则继续在`右`半部分查找,那么 `max` 不变,而`min = mid + 1` 。 +> * 如果`目标值`和 `arr[mid]` 相等,则找到了目标,返回该索引。 +> * ④ 结束条件:当 `min > max` 的时候,表示查找范围为空,即:元素不存在,返回 `-1`。 + + + +* 示例: + +```c +#include + +/** + * 二分查找 + * + * @param arr 数组 + * @param len 数组长度 + * @param num 要查找的数据 + * @return 返回数据的下标,没有找到返回-1 + */ +int search(int arr[], int len, int num) { + int min = 0; + int max = len - 1; + while (min <= max) { + int mid = (min + max) / 2; + if (num < arr[mid]) { // 说明要查找的数据在左半边 + max = mid - 1; + } else if (num > arr[mid]) { // 说明要查找的数据在右半边 + min = mid + 1; + } else { // 说明找到了 + return mid; + } + } + return -1; +} + +int main() { + + int arr[] = {1, 2, 3, 4, 5, 6}; + + int len = sizeof(arr) / sizeof(arr[0]); + + int index = search(arr, len, -1); + + printf("index = %d\n", index); + + 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。 + + ![](./assets/8.png) + + * **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。 + + ![](./assets/9.png) + + * **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。 + + ![](./assets/10.jpg) + +* 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。 + + ![](./assets/11.png) + + * **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](./assets/12.png) + + * **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。 + + ![](./assets/13.png) + + * **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。 + + ![](./assets/14.jpg) + +* 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。 + + ![](./assets/15.png) + + * **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。 + + ![](./assets/16.png) + + * **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。 + + ![](./assets/17.png) + + * **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。 + + ![](./assets/18.png) + +* 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: + +![](./assets/19.png) + +> [!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 如果数组中嵌套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 + +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 + +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; +} +``` + +### 3.2.3 静态初始化 2 + +* 语法: + +```c +数据类型 数组名[][列数] = {{元素1,元素2,...},{元素3,...},...} +``` + +> [!NOTE] +> +> * ① 列数 = 每个⼀维数组中有几个具体的数据元素。 +> * 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 + +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: + +![](./assets/20.png) + +## 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 + +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,如下所示: + +![](./assets/21.png) + +> [!NOTE] +> +> * ① 这就是 `C` 语言的二维数组在进行静态初始化的时候,`可以`忽略`行数`的原因所在(底层的`内存结构`是`线性`的),因为可以根据 `元素的总数 ÷ 每列元素的个数 = 行数`的公式计算出`行数`。 +> * ② 如果你学过 `Java` 语言,可能会感觉困惑,Java 语言中的二维数组在进行静态初始化,是`不能`忽略`行数`的,是因为 Java 编译器会根据`行数`去堆内存空间先开辟出一维数组,然后再继续...,所以当然`不能`忽略`行数`。 + +## 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 + +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; +} +``` + + diff --git a/docs/notes/01_c-basic/12_xdx/assets/1.png b/docs/notes/01_c-basic/14_xdx/assets/1.png similarity index 100% rename from docs/notes/01_c-basic/12_xdx/assets/1.png rename to docs/notes/01_c-basic/14_xdx/assets/1.png diff --git a/docs/notes/01_c-basic/12_xdx/assets/10.svg b/docs/notes/01_c-basic/14_xdx/assets/10.svg similarity index 100% rename from docs/notes/01_c-basic/12_xdx/assets/10.svg rename to 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