From f4fb5a79e021688d7656d9cca3c3852cde6b5db1 Mon Sep 17 00:00:00 2001 From: Zengtudor Date: Tue, 22 Oct 2024 16:59:42 +0800 Subject: [PATCH] update --- README.md | 54 +- senior/2.C++程序设计.md | 1058 ++++++++++++++++++ senior/image/2.C++程序设计/1729576522156.png | Bin 0 -> 225549 bytes senior/image/2.C++程序设计/1729578565293.png | Bin 0 -> 102801 bytes senior/image/2.C++程序设计/1729579349732.png | Bin 0 -> 76010 bytes senior/image/2.C++程序设计/1729579712646.png | Bin 0 -> 60214 bytes senior/image/2.C++程序设计/1729579725048.png | Bin 0 -> 60214 bytes 7 files changed, 1085 insertions(+), 27 deletions(-) create mode 100644 senior/2.C++程序设计.md create mode 100644 senior/image/2.C++程序设计/1729576522156.png create mode 100644 senior/image/2.C++程序设计/1729578565293.png create mode 100644 senior/image/2.C++程序设计/1729579349732.png create mode 100644 senior/image/2.C++程序设计/1729579712646.png create mode 100644 senior/image/2.C++程序设计/1729579725048.png diff --git a/README.md b/README.md index 37f688f..e4201e2 100644 --- a/README.md +++ b/README.md @@ -8,30 +8,30 @@ ### 优先撰写提高组内容,会录制视频,这里放一个大纲内容 -1. 大纲 - 1. 入门级(暂未开始) - 2. 提高级 - 1. [基础知识与编程环境](./senior/1.%E5%9F%BA%E7%A1%80%E7%9F%A5%E8%AF%86%E4%B8%8E%E7%BC%96%E7%A8%8B%E7%8E%AF%E5%A2%83.md) - 2. C++程序设计 - 1. 类 - 2. STL模板 - 3. 数据结构 - 1. 线性结构 - 2. 集合与森林 - 3. 常见图 - 4. 哈希表 - 4. 算法 - 1. 复杂度分析 - 2. 算法策略(离散化) - 3. 基础算法(分治算法) - 4. 排序算法 - 5. 字符串相关算法(KMP) - 6. 搜索算法 - 7. 图论算法 - 8. 动态规划 - 5. 数学与其它 - 1. 初等数学 - 2. 初等数论 - 3. 离散与组合数学 - 4. 线性代数 - 3. NOI级(暂未开始) \ No newline at end of file +1. 大纲 + 1. 入门级(暂未开始) + 2. 提高级 + 1. [基础知识与编程环境](./senior/1.%E5%9F%BA%E7%A1%80%E7%9F%A5%E8%AF%86%E4%B8%8E%E7%BC%96%E7%A8%8B%E7%8E%AF%E5%A2%83.md) + 2. [C++程序设计](./senior/2.C++程序设计.md) + 1. 类 + 2. STL模板 + 3. 数据结构 + 1. 线性结构 + 2. 集合与森林 + 3. 常见图 + 4. 哈希表 + 4. 算法 + 1. 复杂度分析 + 2. 算法策略(离散化) + 3. 基础算法(分治算法) + 4. 排序算法 + 5. 字符串相关算法(KMP) + 6. 搜索算法 + 7. 图论算法 + 8. 动态规划 + 5. 数学与其它 + 1. 初等数学 + 2. 初等数论 + 3. 离散与组合数学 + 4. 线性代数 + 3. NOI级(暂未开始) diff --git a/senior/2.C++程序设计.md b/senior/2.C++程序设计.md new file mode 100644 index 0000000..4e7ff41 --- /dev/null +++ b/senior/2.C++程序设计.md @@ -0,0 +1,1058 @@ +# 类 + +## 类的概念及简单应用 + +1. [官方文档解释](https://zh.cppreference.com/w/cpp/language/classes) + + 1. > 比较复杂,有些东西用不到,想要深入了解时可以自行学习 + > ![1729576522156](image/2.C++程序设计/1729576522156.png) + > +2. 通俗的说: + + > C++类就像是“模具”,用来创建“物体”。比如,如果你要建造很多房子,先做一个房子的模具,里面规定了房子有几扇门、几扇窗户。这个模具就是“类”。每次用模具做出来的具体房子就是“对象”。 + > + + > 类里面可以有“属性”(就像房子的面积、颜色)和“方法”(像开门、关窗的操作)。通过这个类,你可以快速制造出多个相似的对象,而不用每次重新定义所有细节。 + > +3. 关于struct 与 class + + 1. C++ 中 struct与class没有本质区别,只不过class中默认private,struct中默认public + +## 成员函数和运算符重载 + +1. 程序 + +```cpp +#include +#include +#include +#include + +class Student{ +private: + std::string name; + int age; +public: + Student(const std::string &name, const int &age):name(name), age(age){ //重定义构造函数 + std::cout<<"Student "<name = that.name; + this->age = that.age; + } + Student(Student&&that){//移动构造函数 + std::cout<<"Move constructor\n"; + this->name = that.name; + this->age = that.age; + that.name.clear(); + that.age = -1; + } + friend std::ostream& operator<<(std::ostream &os,const Student &s){ // 友元函数与运算符重载 + os<<"Student { name:'"<name+that.name, this->age+that.age); + } + void say_hello()const{ //打招呼,成员函数 + std::cout<<"Hello, my name is "<name<<" .\n"; + } +}; + +int main(){ + Student Zengtudor("Zengtudor",18);//构造函数 + Zengtudor.say_hello();//成员函数 + Student Alice("Alice",18);//构造函数 + Student fake_Zengtudor = Zengtudor;//拷贝构造函数 + Student new_Zengtudor = std::move(Zengtudor);//移动构造函数,数据移动到新的,销毁旧的 + std::cout< +#include + +#define NV(v)#v<<" :\t"<<(v) +int main(){ + std::set s; + s.insert({1,2,3}); + auto it = s.find(2); + std::cout<输出 +``` +*s.begin() : 1 +*s.rbegin() : 3 +*it : 2 +*--it : 1 +*(++ ++it) : 3 +``` + +## 对(pair) + +>在C++中,`std::pair` 是一个模板类,可以将两个数据组合成一个单一的对象,常用于需要将两个相关的数据项捆绑在一起的时候,例如键值对、坐标对等。下面是`std::pair`的重点用法: + +### 1. 定义和初始化 +`std::pair` 可以通过多种方式进行初始化: + +```cpp +#include +#include + +int main() { + // 直接构造 + std::pair p1(1, "apple"); + + // 使用make_pair构造(推荐) + auto p2 = std::make_pair(2, "banana"); + + // 列表初始化(C++11及之后) + std::pair p3 = {3, 4.5}; + + // 复制构造 + std::pair p4 = p1; + + std::cout << p1.first << ", " << p1.second << std::endl; + std::cout << p2.first << ", " << p2.second << std::endl; + std::cout << p3.first << ", " << p3.second << std::endl; + std::cout << p4.first << ", " << p4.second << std::endl; + + return 0; +} +``` + +### 2. 成员变量 +`std::pair`有两个公开的成员变量: + +- `first`:存储第一个数据 +- `second`:存储第二个数据 + +使用示例: + +```cpp +std::pair p = {10, "hello"}; +std::cout << p.first << std::endl; // 输出 10 +std::cout << p.second << std::endl; // 输出 hello +``` + +### 3. 使用`std::make_pair` +`std::make_pair` 可以自动推导类型,简化构造`std::pair`的过程: + +```cpp +auto p = std::make_pair(42, "example"); +std::cout << p.first << ", " << p.second << std::endl; +``` + +### 4. 比较操作 +`std::pair` 支持字典序比较,即先比较 `first`,如果 `first` 相等,则再比较 `second`: + +```cpp +std::pair p1 = {1, 5}; +std::pair p2 = {1, 10}; + +if (p1 < p2) { + std::cout << "p1 is less than p2" << std::endl; +} +``` + +上面的代码中,`p1 < p2` 是 `true`,因为 `1 == 1`,然后 `5 < 10`。 + +### 5. 作为容器的元素 +`std::pair` 可以用于标准容器(如`std::vector`, `std::map`)中。例如,`std::map` 的键值对本质上就是 `std::pair`: + +```cpp +#include + +std::map m; +m.insert(std::make_pair(1, "one")); +m[2] = "two"; + +for (const auto& item : m) { + std::cout << item.first << " -> " << item.second << std::endl; +} +``` + +### 6. 结构化绑定(C++17) +在C++17中,可以使用结构化绑定直接从 `std::pair` 中解构出两个值: + +```cpp +auto [id, name] = std::make_pair(3, "C++"); +std::cout << id << ", " << name << std::endl; +``` + +### 7. 应用场景 +`std::pair` 主要用于以下场景: +- 返回多个值:如果函数需要返回多个值,可以使用 `std::pair`。 +- 键值对:在 `std::map` 中使用。 +- 组合相关的数据:如坐标 `(x, y)`、范围 `(start, end)`等。 + +### 示例:使用`std::pair`返回多个值 + +```cpp +std::pair getMinMax(const std::vector& nums) { + int min = *std::min_element(nums.begin(), nums.end()); + int max = *std::max_element(nums.begin(), nums.end()); + return {min, max}; +} + +int main() { + std::vector numbers = {5, 7, 2, 9, 1}; + auto [minValue, maxValue] = getMinMax(numbers); + std::cout << "Min: " << minValue << ", Max: " << maxValue << std::endl; +} +``` + +在上面的例子中,`getMinMax` 函数使用 `std::pair` 返回了最小值和最大值。 + +## 元组(tuple) +在C++中,`std::tuple` 是一个可以包含多个不同类型元素的容器。它类似于结构体,但更灵活,因为不需要预先定义类型和数量。`std::tuple` 是在 C++11 中引入的,它在 `` 头文件中定义。 + +### 1. 创建和初始化 `std::tuple` + +可以使用 `std::make_tuple` 或直接构造一个 `std::tuple` 来创建: + +```cpp +#include +#include +#include + +int main() { + // 使用std::make_tuple + auto person = std::make_tuple("Alice", 25, 1.75); + + // 直接构造一个std::tuple + std::tuple person2("Bob", 30, 1.80); + + return 0; +} +``` + +### 2. 访问 `std::tuple` 元素 + +可以使用 `std::get` 来访问 `tuple` 的元素。需要注意的是,索引是从 `0` 开始的: + +```cpp +std::string name = std::get<0>(person); +int age = std::get<1>(person); +double height = std::get<2>(person); + +std::cout << "Name: " << name << ", Age: " << age << ", Height: " << height << std::endl; +``` + +### 3. 修改 `std::tuple` 元素 + +`std::get` 也可以用于修改元素的值: + +```cpp +std::get<1>(person) = 26; // 将age改为26 +``` + +### 4. 获取 `std::tuple` 的元素数量 + +可以使用 `std::tuple_size` 来获取 `tuple` 的元素数量: + +```cpp +std::cout << "Tuple size: " << std::tuple_size::value << std::endl; +``` + +### 5. 使用 `std::tie` 解构 `tuple` + +`std::tie` 可以将 `tuple` 的内容分解为多个变量: + +```cpp +std::string name; +int age; +double height; + +std::tie(name, age, height) = person; +std::cout << "Name: " << name << ", Age: " << age << ", Height: " << height << std::endl; +``` + +还可以忽略不需要的元素,用 `std::ignore`: + +```cpp +std::tie(name, std::ignore, height) = person; +``` + +### 6. 比较 `std::tuple` + +`std::tuple` 支持比较运算符(`==`, `!=`, `<`, `<=`, `>`, `>=`),按照字典顺序进行比较: + +```cpp +std::tuple t1(1, 2, 3); +std::tuple t2(1, 3, 2); + +if (t1 < t2) { + std::cout << "t1 is less than t2" << std::endl; +} +``` + +### 7. 合并 `std::tuple` + +可以使用 `std::tuple_cat` 将多个 `tuple` 合并: + +```cpp +auto t1 = std::make_tuple(1, 2); +auto t2 = std::make_tuple(3.5, "hello"); +auto t3 = std::tuple_cat(t1, t2); + +std::cout << std::get<0>(t3) << ", " << std::get<1>(t3) << ", " + << std::get<2>(t3) << ", " << std::get<3>(t3) << std::endl; +``` + +### 8. 使用结构化绑定 (C++17) + +在 C++17 中,引入了结构化绑定,可以更加方便地解构 `tuple`: + +```cpp +auto [name, age, height] = person; +std::cout << "Name: " << name << ", Age: " << age << ", Height: " << height << std::endl; +``` + +### 总结 + +`std::tuple` 非常适合在需要返回多个不同类型的值、或处理不同类型的数据集合时使用。它的灵活性和便捷的接口使得它成为 C++ 中一种非常实用的工具。 + +## 集合(set) +`std::set` 是 C++ 标准库中的一种关联容器,主要用于存储不重复的元素,并且会自动按照元素的顺序进行排序。常见的用法包括插入、删除、查找元素等。`std::set` 的底层实现通常是基于红黑树,因此它的操作(插入、删除、查找)时间复杂度都是 O(log n)。 + +下面是 `std::set` 的一些基本用法和示例。 + +### 1. 引入头文件 +要使用 `std::set`,需要包含头文件: +```cpp +#include +``` + +### 2. 定义 `std::set` +```cpp +std::set s; // 定义一个存储 int 类型元素的集合 +std::set strSet; // 定义一个存储字符串的集合 +``` + +### 3. 插入元素 +使用 `insert` 函数来插入元素。如果元素已经存在,则不会插入。 +```cpp +s.insert(5); +s.insert(10); +s.insert(5); // 重复插入无效,set 中仍然只有一个 5 + +for (int x : s) { + std::cout << x << " "; // 输出: 5 10 +} +``` + +### 4. 删除元素 +- `erase(value)`: 删除指定值的元素。 +- `erase(iterator)`: 删除指定位置的元素。 +- `erase(begin, end)`: 删除指定范围内的元素。 +```cpp +s.erase(5); // 删除元素 5 + +auto it = s.find(10); +if (it != s.end()) { + s.erase(it); // 删除迭代器位置上的元素 10 +} +``` + +### 5. 查找元素 +- `find(value)`: 返回一个指向找到元素的迭代器,如果找不到则返回 `end()`。 +- `count(value)`: 返回元素出现的次数,对于 `set` 来说,要么是 `0` 要么是 `1`。 +```cpp +if (s.find(5) != s.end()) { + std::cout << "5 is in the set" << std::endl; +} + +if (s.count(10) > 0) { + std::cout << "10 is in the set" << std::endl; +} +``` + +### 6. 大小与清空 +- `size()`: 返回集合中元素的个数。 +- `empty()`: 判断集合是否为空。 +- `clear()`: 清空集合中的所有元素。 +```cpp +std::cout << "Size: " << s.size() << std::endl; // 输出集合的大小 + +if (!s.empty()) { + std::cout << "The set is not empty." << std::endl; +} + +s.clear(); // 清空集合 +``` + +### 7. 遍历 `std::set` +可以使用迭代器或者基于范围的 for 循环进行遍历。 +```cpp +for (auto it = s.begin(); it != s.end(); ++it) { + std::cout << *it << " "; +} + +// 或者 +for (const auto &x : s) { + std::cout << x << " "; +} +``` + +### 8. 自定义排序规则 +默认情况下,`std::set` 按照元素的 `<` 运算符排序。如果需要自定义排序规则,可以使用比较函数或仿函数。 +```cpp +// 降序排序 +std::set> s_desc; +s_desc.insert(3); +s_desc.insert(1); +s_desc.insert(2); + +for (int x : s_desc) { + std::cout << x << " "; // 输出: 3 2 1 +} +``` + +### 9. 其它常用操作 +- `lower_bound(value)`: 返回第一个大于或等于 `value` 的迭代器。 +- `upper_bound(value)`: 返回第一个大于 `value` 的迭代器。 +```cpp +s.insert(1); +s.insert(3); +s.insert(5); + +auto lb = s.lower_bound(3); // 指向 3 +auto ub = s.upper_bound(3); // 指向 5 +``` + +### 示例代码 +```cpp +#include +#include + +int main() { + std::set s; + + // 插入元素 + s.insert(1); + s.insert(5); + s.insert(3); + + // 遍历集合 + for (int x : s) { + std::cout << x << " "; // 输出: 1 3 5 + } + std::cout << std::endl; + + // 查找元素 + if (s.find(3) != s.end()) { + std::cout << "Found 3" << std::endl; + } + + // 删除元素 + s.erase(3); + + // 检查大小 + std::cout << "Size: " << s.size() << std::endl; + + return 0; +} +``` +## 多重集合(multiset) +`std::multiset` 是 C++ 标准库中的一个容器,用于存储可以重复的元素,且元素会自动按照特定的顺序排列。`std::multiset` 是一个关联容器,底层通常使用红黑树实现,因此支持高效的插入、删除和查找操作。 + +### 主要特性 + +1. **元素可以重复**:与 `std::set` 不同,`std::multiset` 允许插入重复元素。 +2. **自动排序**:插入的元素会根据给定的比较函数(默认是 `operator<`)自动排序。 +3. **性能**:查找、插入和删除操作的平均时间复杂度为 O(log n)。 + +### 常用操作 + +以下是一些 `std::multiset` 的常用操作: + +1. **包含头文件**: + ```cpp + #include + ``` + +2. **定义和初始化**: + ```cpp + std::multiset ms; // 定义一个整型的multiset + std::multiset ms2 = {1, 2, 2, 3, 4}; // 初始化 + ``` + +3. **插入元素**: + ```cpp + ms.insert(5); + ms.insert(3); + ms.insert(3); // 允许重复 + ``` + +4. **删除元素**: + ```cpp + ms.erase(3); // 删除一个值为3的元素,若存在多个3,删除一个 + ``` + +5. **查找元素**: + ```cpp + auto it = ms.find(2); // 查找值为2的元素 + if (it != ms.end()) { + std::cout << "Found: " << *it << std::endl; + } + ``` + +6. **计数元素**: + ```cpp + size_t count = ms.count(2); // 计数值为2的元素个数 + ``` + +7. **遍历元素**: + ```cpp + for (const auto& val : ms) { + std::cout << val << " "; + } + ``` + +8. **大小和清空**: + ```cpp + std::cout << "Size: " << ms.size() << std::endl; // 返回元素个数 + ms.clear(); // 清空multiset + ``` + +### 示例代码 + +以下是一个使用 `std::multiset` 的简单示例: + +```cpp +#include +#include + +int main() { + std::multiset ms; + + // 插入元素 + ms.insert(5); + ms.insert(3); + ms.insert(3); + ms.insert(7); + ms.insert(1); + + // 遍历元素 + std::cout << "Elements in multiset: "; + for (const auto& val : ms) { + std::cout << val << " "; + } + std::cout << std::endl; + + // 查找元素 + auto it = ms.find(3); + if (it != ms.end()) { + std::cout << "Found: " << *it << std::endl; + } + + // 计数 + std::cout << "Count of 3: " << ms.count(3) << std::endl; + + // 删除元素 + ms.erase(3); // 删除一个3 + std::cout << "After erasing one 3, elements: "; + for (const auto& val : ms) { + std::cout << val << " "; + } + std::cout << std::endl; + + return 0; +} +``` +## 双端队列(deque) +`deque`(双端队列)是C++标准库中提供的一种序列容器,它支持从两端高效地插入和删除元素。与`vector`不同,`deque`允许在头部和尾部都进行高效的操作,适合需要频繁在两端插入和删除的场景。 + +### 1. 引入头文件 +使用`deque`之前,需要包含头文件: +```cpp +#include +``` + +### 2. 创建`deque` +可以使用默认构造函数或指定初始值来创建一个`deque`: +```cpp +std::deque dq; // 创建一个空的 deque +std::deque dq2(5, 10); // 创建一个包含5个10的 deque +``` + +### 3. 常用操作 +以下是一些常用的`deque`操作: + +#### 3.1 插入元素 +- 在头部插入元素:`push_front()` +- 在尾部插入元素:`push_back()` + +```cpp +dq.push_front(1); // 在头部插入 1 +dq.push_back(2); // 在尾部插入 2 +``` + +#### 3.2 删除元素 +- 从头部删除元素:`pop_front()` +- 从尾部删除元素:`pop_back()` + +```cpp +dq.pop_front(); // 删除头部元素 +dq.pop_back(); // 删除尾部元素 +``` + +#### 3.3 访问元素 +- 使用下标访问元素:`operator[]` +- 使用 `at()` 方法安全访问元素 +- 使用 `front()` 和 `back()` 访问头尾元素 + +```cpp +int first = dq.front(); // 获取头部元素 +int last = dq.back(); // 获取尾部元素 +int second = dq[1]; // 获取第二个元素 +``` + +#### 3.4 大小和容量 +- `size()` 获取元素个数 +- `empty()` 判断是否为空 + +```cpp +size_t size = dq.size(); // 获取 deque 的大小 +bool isEmpty = dq.empty(); // 判断 deque 是否为空 +``` + +#### 3.5 清空容器 +- 使用 `clear()` 清空所有元素 + +```cpp +dq.clear(); // 清空 deque +``` + +### 4. 示例代码 +下面是一个完整的示例,演示如何使用`deque`: + +```cpp +#include +#include + +int main() { + // 创建一个双端队列并添加元素 + std::deque dq; + dq.push_back(10); + dq.push_back(20); + dq.push_front(5); + + // 输出当前元素 + std::cout << "当前 deque 元素: "; + for (const auto& elem : dq) { + std::cout << elem << " "; + } + std::cout << std::endl; + + // 删除头部和尾部元素 + dq.pop_front(); // 删除 5 + dq.pop_back(); // 删除 20 + + std::cout << "删除后 deque 元素: "; + for (const auto& elem : dq) { + std::cout << elem << " "; + } + std::cout << std::endl; + + // 访问头尾元素 + std::cout << "头部元素: " << dq.front() << std::endl; + std::cout << "尾部元素: " << dq.back() << std::endl; + + return 0; +} +``` + +### 5. 注意事项 +- `deque`的底层实现使其在插入和删除时比`vector`更高效,但在随机访问时可能比`vector`慢。 +- `deque`适合用作队列和栈,支持高效的插入和删除操作。 +## 优先队列(priority_queue) +在 C++ 中,`priority_queue` 是一个 STL(标准模板库)容器适配器,用于管理优先队列。优先队列是一种特殊类型的队列,其中每个元素都有一个优先级。优先级较高的元素会被优先处理,而不是按照它们被添加的顺序。 + +### 基本特性 + +1. **元素顺序**:在 `priority_queue` 中,元素会根据优先级进行排序。默认情况下,优先级最高的元素位于队列的顶部(即最前面),并且可以快速访问和移除。 + +2. **底层容器**:`priority_queue` 通常使用堆(heap)作为其底层数据结构,默认是最大堆(max heap)。这意味着最大元素总是位于队列的顶部。 + +3. **模板类**:`priority_queue` 是一个模板类,可以与任意类型的元素一起使用,但需要提供比较函数来确定优先级。 + +### 基本操作 + +以下是 `priority_queue` 的一些基本操作和用法: + +- **定义优先队列**: + + ```cpp + #include + #include + #include + + std::priority_queue pq; // 默认最大堆 + ``` + +- **添加元素**: + + ```cpp + pq.push(10); + pq.push(5); + pq.push(20); + ``` + +- **访问顶部元素**: + + ```cpp + std::cout << "Top element: " << pq.top() << std::endl; // 输出 20 + ``` + +- **移除顶部元素**: + + ```cpp + pq.pop(); // 移除 20 + ``` + +- **检查是否为空**: + + ```cpp + if (!pq.empty()) { + std::cout << "Queue is not empty" << std::endl; + } + ``` + +- **获取队列大小**: + + ```cpp + std::cout << "Size of queue: " << pq.size() << std::endl; + ``` + +### 自定义比较 + +如果你想创建一个最小堆(即优先级最低的元素在顶部),可以使用自定义比较函数。下面是一个示例: + +```cpp +#include +#include +#include + +struct Compare { + bool operator()(int a, int b) { + return a > b; // 小的优先 + } +}; + +int main() { + std::priority_queue, Compare> minHeap; + + minHeap.push(10); + minHeap.push(5); + minHeap.push(20); + + std::cout << "Top element (min-heap): " << minHeap.top() << std::endl; // 输出 5 + + return 0; +} +``` +## 映射(map) +`std::map` 是 C++ 标准库中的一个关联容器,它提供了一种基于键-值对存储数据的方式。`std::map` 内部实现通常是平衡二叉树(例如红黑树),这使得它在插入、删除和查找操作上具有对数时间复杂度。下面是一些关于 `std::map` 的基本用法和特性: + +### 1. 基本特性 + +- **键唯一性**:每个键在 `std::map` 中都是唯一的。如果插入一个已经存在的键,旧的值将被新值覆盖。 +- **有序性**:`std::map` 中的元素是按照键的顺序排列的,默认情况下使用 `<` 运算符进行比较。 +- **支持自定义比较**:可以通过提供自定义比较器来定义排序方式。 + +### 2. 常用操作 + +以下是一些常用的操作及示例代码: + +#### 2.1 包含头文件 + +```cpp +#include +#include +``` + +#### 2.2 创建和初始化 + +```cpp +std::map myMap; // 键为字符串,值为整数 + +// 初始化 +std::map myMap = { + {"apple", 2}, + {"banana", 3}, + {"orange", 5} +}; +``` + +#### 2.3 插入元素 + +```cpp +myMap["grape"] = 4; // 插入新元素 +myMap.insert({"pear", 1}); // 使用 insert 方法插入 +``` + +#### 2.4 查找元素 + +```cpp +auto it = myMap.find("banana"); // 查找键为 "banana" 的元素 +if (it != myMap.end()) { + std::cout << "Found banana: " << it->second << std::endl; // 输出对应的值 +} else { + std::cout << "Banana not found!" << std::endl; +} +``` + +#### 2.5 删除元素 + +```cpp +myMap.erase("apple"); // 删除键为 "apple" 的元素 +``` + +#### 2.6 遍历元素 + +```cpp +for (const auto& pair : myMap) { + std::cout << pair.first << ": " << pair.second << std::endl; // 输出每个键值对 +} +``` + +#### 2.7 其他常用操作 + +- **获取大小**:`myMap.size()` 返回元素个数。 +- **检查是否为空**:`myMap.empty()` 检查 `map` 是否为空。 + +### 3. 示例代码 + +以下是一个完整的示例代码,展示了 `std::map` 的基本用法: + +```cpp +#include +#include + +int main() { + // 创建一个 map + std::map myMap; + + // 插入元素 + myMap["apple"] = 2; + myMap["banana"] = 3; + myMap["orange"] = 5; + + // 查找元素 + auto it = myMap.find("banana"); + if (it != myMap.end()) { + std::cout << "Found banana: " << it->second << std::endl; + } + + // 遍历元素 + for (const auto& pair : myMap) { + std::cout << pair.first << ": " << pair.second << std::endl; + } + + // 删除元素 + myMap.erase("apple"); + + // 检查大小 + std::cout << "Size: " << myMap.size() << std::endl; + + return 0; +} +``` +## 多重映射(multimap) +`std::multimap` 是 C++ STL(标准模板库)中的一个关联容器,用于存储键值对,其中一个键可以对应多个值。与 `std::map` 不同,`std::multimap` 允许相同的键多次出现,因此适合需要重复键的场景。 + +### 主要特点 + +1. **存储键值对**:`std::multimap` 存储的是 `std::pair` 类型的数据。 +2. **自动排序**:插入的元素会根据键自动排序,默认是升序排列。 +3. **键的重复性**:相同的键可以多次插入。 +4. **性能**:插入、删除、查找操作的时间复杂度是 O(log n)。 + +### 常用操作 + +以下是 `std::multimap` 的一些常用操作: + +- **定义和初始化**: + ```cpp + #include + #include + + std::multimap mmap; + mmap.insert(std::make_pair(1, "apple")); + mmap.insert(std::make_pair(1, "banana")); + mmap.insert(std::make_pair(2, "cherry")); + ``` + +- **遍历**: + ```cpp + for (const auto& pair : mmap) { + std::cout << pair.first << ": " << pair.second << std::endl; + } + ``` + +- **查找元素**: + ```cpp + auto range = mmap.equal_range(1); // 获取所有键为1的元素 + for (auto it = range.first; it != range.second; ++it) { + std::cout << it->second << std::endl; // 输出 apple 和 banana + } + ``` + +- **删除元素**: + ```cpp + mmap.erase(1); // 删除所有键为1的元素 + ``` + +### 示例代码 + +以下是一个完整的示例代码,展示 `std::multimap` 的基本用法: + +```cpp +#include +#include + +int main() { + std::multimap mmap; + + // 插入元素 + mmap.insert(std::make_pair(1, "apple")); + mmap.insert(std::make_pair(1, "banana")); + mmap.insert(std::make_pair(2, "cherry")); + mmap.insert(std::make_pair(3, "date")); + + // 遍历并打印元素 + std::cout << "Multimap elements:" << std::endl; + for (const auto& pair : mmap) { + std::cout << pair.first << ": " << pair.second << std::endl; + } + + // 查找特定键的所有值 + std::cout << "\nValues with key 1:" << std::endl; + auto range = mmap.equal_range(1); + for (auto it = range.first; it != range.second; ++it) { + std::cout << it->second << std::endl; // 输出 apple 和 banana + } + + // 删除键为1的所有元素 + mmap.erase(1); + + // 打印删除后的元素 + std::cout << "\nAfter erasing key 1:" << std::endl; + for (const auto& pair : mmap) { + std::cout << pair.first << ": " << pair.second << std::endl; + } + + return 0; +} +``` + +### 注意事项 + +- **键的唯一性**:虽然同一个键可以有多个值,但键本身在容器中仍然是唯一的。 +- **性能**:对于需要频繁插入和删除的场景,`std::multimap` 提供了相对较高的性能,但在需要大量查找时,`std::unordered_multimap`(基于哈希表实现)可能会提供更好的性能。 +## 算法模板库中的常用函数 +C++ STL(标准模板库)中提供了丰富的算法函数,这些算法函数可以极大地简化编程任务并提高代码的可读性和效率。以下是一些常用且实用的算法函数,按类别进行分类: + +### 1. **排序和排列算法** +- **`std::sort`**: 对容器中的元素进行排序,支持自定义比较函数。 + ```cpp + std::vector vec = {5, 2, 9, 1}; + std::sort(vec.begin(), vec.end()); + ``` + +- **`std::stable_sort`**: 稳定排序,保持相等元素的相对顺序。 + +- **`std::partial_sort`**: 对部分元素进行排序,前n个元素会被排好序。 + +- **`std::next_permutation`**: 生成下一个字典序排列。 + +### 2. **查找算法** +- **`std::find`**: 在容器中查找特定值。 + ```cpp + auto it = std::find(vec.begin(), vec.end(), 2); + ``` + +- **`std::binary_search`**: 在已排序的容器中查找某个值,使用二分查找,时间复杂度为O(log n)。 + +- **`std::lower_bound`** 和 **`std::upper_bound`**: 在已排序容器中查找第一个不小于(或大于)给定值的元素位置。 + +### 3. **修改算法** +- **`std::copy`**: 将元素从一个容器复制到另一个容器。 + +- **`std::transform`**: 对容器中的每个元素应用给定的函数,并将结果存储到另一个容器。 + ```cpp + std::vector squares; + std::transform(vec.begin(), vec.end(), std::back_inserter(squares), [](int x) { return x * x; }); + ``` + +- **`std::remove`**: 移除容器中的特定元素,实际上是标记,需结合 `erase` 使用。 + +- **`std::fill`**: 将指定值填充到容器的元素中。 + +### 4. **集合算法** +- **`std::set_union`**: 计算两个集合的并集。 + +- **`std::set_intersection`**: 计算两个集合的交集。 + +- **`std::set_difference`**: 计算两个集合的差集。 + +- **`std::set_symmetric_difference`**: 计算两个集合的对称差集。 + +### 5. **数值算法** +- **`std::accumulate`**: 对容器中的元素进行累加(或其他二元操作)。 + ```cpp + int sum = std::accumulate(vec.begin(), vec.end(), 0); + ``` + +- **`std::inner_product`**: 计算两个容器元素的内积。 + +- **`std::adjacent_difference`**: 计算相邻元素的差。 + +### 6. **其他常用算法** +- **`std::for_each`**: 对容器中的每个元素应用给定的操作。 + +- **`std::count`**: 统计容器中某个值的出现次数。 + +- **`std::all_of`, `std::any_of`, `std::none_of`**: 检查容器中是否所有、任意或没有元素满足特定条件。 + +### 7. **并行算法(C++17及以上)** +- **`std::for_each(std::execution::par, ...)`**: 在并行执行上下文中对元素进行操作。 + +- 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