1. 引言

什么是向量（Vector）？

向量（Vector）是 C++ 标准模板库（STL）中的一种序列容器，能够动态地管理可变大小的数组。与传统的固定大小的数组不同，向量可以根据需要随时调整其大小，提供更高的灵活性和便利性。

向量与数组的比较

2. std::vector 基础

2.1 包含头文件

使用 std::vector 需要包含 <vector> 头文件：

#include <vector>

2.2 定义与初始化

定义一个整数向量：

std::vector<int> numbers;

定义一个字符串向量：

#include <vector>
#include <string>

std::vector<std::string> words;

初始化向量：

• 默认初始化：

  std::vector<int> vec1; // 空向量
  

• 指定大小和默认值：

  std::vector<int> vec2(5, 10); // 5个元素，值均为10
  

• 使用初始化列表：

  std::vector<int> vec3 = {1, 2, 3, 4, 5};
  

• 拷贝构造：

  std::vector<int> vec4(vec3); // 复制vec3
  

• 移动构造：

  std::vector<int> vec5(std::move(vec4)); // 移动vec4到vec5
  

示例代码：

#include <iostream>
#include <vector>

int main() {
    // 默认初始化
    std::vector<int> vec1;

    // 指定大小和默认值
    std::vector<int> vec2(5, 10);

    // 使用初始化列表
    std::vector<int> vec3 = {1, 2, 3, 4, 5};

    // 拷贝构造
    std::vector<int> vec4(vec3);

    // 移动构造
    std::vector<int> vec5(std::move(vec4));

    // 输出vec2
    std::cout << "vec2: ";
    for(auto num : vec2) {
        std::cout << num << " ";
    }
    std::cout << std::endl;

    // 输出vec3
    std::cout << "vec3: ";
    for(auto num : vec3) {
        std::cout << num << " ";
    }
    std::cout << std::endl;

    // 输出vec5
    std::cout << "vec5: ";
    for(auto num : vec5) {
        std::cout << num << " ";
    }
    std::cout << std::endl;

    return 0;
}

输出：

vec2: 10 10 10 10 10 
vec3: 1 2 3 4 5 
vec5: 1 2 3 4 5

2.3 向量的大小与容量

• size()：返回向量中元素的数量。
• capacity()：返回向量目前为止分配的存储容量。
• empty()：检查向量是否为空。

示例代码：

#include <iostream>
#include <vector>

int main() {
    std::vector<int> vec = {1, 2, 3};

    std::cout << "Size: " << vec.size() << std::endl;       // 输出: 3
    std::cout << "Capacity: " << vec.capacity() << std::endl; // 输出: 3（或更大，取决于实现）

    std::cout << "Is empty? " << (vec.empty() ? "Yes" : "No") << std::endl; // 输出: No

    vec.reserve(10); // 预留容量
    std::cout << "After reserve(10), Capacity: " << vec.capacity() << std::endl; // 输出: 10

    vec.shrink_to_fit(); // 收缩到适合大小
    std::cout << "After shrink_to_fit(), Capacity: " << vec.capacity() << std::endl; // 输出: 3

    return 0;
}

输出示例：

Size: 3
Capacity: 3
Is empty? No
After reserve(10), Capacity: 10
After shrink_to_fit(), Capacity: 3

注意： capacity() 并不一定精确匹配 size()，它表示在需要重新分配内存之前，向量可以容纳的元素数量。

3. 向量的基本操作

3.1 添加与删除元素

• push_back()：在向量末尾添加一个元素。
• pop_back()：移除向量末尾的元素。
• insert()：在指定位置插入元素。
• erase()：移除指定位置的元素或范围内的元素。
• clear()：移除所有元素。

示例代码：

#include <iostream>
#include <vector>

int main() {
    std::vector<int> vec;

    // 使用push_back添加元素
    vec.push_back(10);
    vec.push_back(20);
    vec.push_back(30);

    std::cout << "After push_back: ";
    for(auto num : vec) {
        std::cout << num << " ";
    }
    std::cout << std::endl; // 输出: 10 20 30 

    // 使用pop_back移除最后一个元素
    vec.pop_back();

    std::cout << "After pop_back: ";
    for(auto num : vec) {
        std::cout << num << " ";
    }
    std::cout << std::endl; // 输出: 10 20 

    // 在第二个位置插入25
    vec.insert(vec.begin() + 1, 25);

    std::cout << "After insert: ";
    for(auto num : vec) {
        std::cout << num << " ";
    }
    std::cout << std::endl; // 输出: 10 25 20 

    // 删除第二个元素（25）
    vec.erase(vec.begin() + 1);

    std::cout << "After erase: ";
    for(auto num : vec) {
        std::cout << num << " ";
    }
    std::cout << std::endl; // 输出: 10 20 

    // 清空向量
    vec.clear();
    std::cout << "After clear, size: " << vec.size() << std::endl; // 输出: 0

    return 0;
}

输出：

After push_back: 10 20 30 
After pop_back: 10 20 
After insert: 10 25 20 
After erase: 10 20 
After clear, size: 0

3.2 访问元素

• operator[]：通过索引访问元素。
• at()：通过索引访问元素，带边界检查。
• front()：访问第一个元素。
• back()：访问最后一个元素。

示例代码：

#include <iostream>
#include <vector>

int main() {
    std::vector<std::string> fruits = {"Apple", "Banana", "Cherry"};

    // 使用operator[]访问元素
    std::cout << "First fruit: " << fruits[0] << std::endl; // 输出: Apple

    // 使用at()访问元素
    try {
        std::cout << "Second fruit: " << fruits.at(1) << std::endl; // 输出: Banana
        std::cout << "Invalid fruit: " << fruits.at(5) << std::endl; // 抛出异常
    }
    catch(const std::out_of_range& e) {
        std::cerr << "Exception: " << e.what() << std::endl;
    }

    // 使用front()和back()
    std::cout << "Front: " << fruits.front() << std::endl; // 输出: Apple
    std::cout << "Back: " << fruits.back() << std::endl;   // 输出: Cherry

    return 0;
}

输出：

First fruit: Apple
Second fruit: Banana
Exception: vector::_M_range_check: __n (which is 5) >= this->size() (which is 3)
Front: Apple
Back: Cherry

3.3 遍历向量

• 使用范围 for 循环
• 使用传统 for 循环
• 使用迭代器

示例代码：

#include <iostream>
#include <vector>

int main() {
    std::vector<int> numbers = {1, 2, 3, 4, 5};

    // 使用范围 for 循环
    std::cout << "Using range-based for loop: ";
    for(auto num : numbers) {
        std::cout << num << " ";
    }
    std::cout << std::endl;

    // 使用传统 for 循环
    std::cout << "Using traditional for loop: ";
    for(size_t i = 0; i < numbers.size(); ++i) {
        std::cout << numbers[i] << " ";
    }
    std::cout << std::endl;

    // 使用迭代器
    std::cout << "Using iterators: ";
    for(auto it = numbers.begin(); it != numbers.end(); ++it) {
        std::cout << *it << " ";
    }
    std::cout << std::endl;

    return 0;
}

输出：

Using range-based for loop: 1 2 3 4 5 
Using traditional for loop: 1 2 3 4 5 
Using iterators: 1 2 3 4 5

3.4 修改元素

• 通过索引或迭代器修改
• 使用 assign() 重新赋值
• 替换整个向量内容

示例代码：

#include <iostream>
#include <vector>

int main() {
    std::vector<int> vec = {10, 20, 30, 40, 50};

    // 通过索引修改元素
    vec[2] = 35;

    // 使用 at() 修改元素
    vec.at(4) = 55;

    // 使用迭代器修改元素
    for(auto it = vec.begin(); it != vec.end(); ++it) {
        if(*it == 20) {
            *it = 25;
        }
    }

    // 输出修改后的向量
    std::cout << "Modified vector: ";
    for(auto num : vec) {
        std::cout << num << " ";
    }
    std::cout << std::endl; // 输出: 10 25 35 40 55 

    return 0;
}

输出：

Modified vector: 10 25 35 40 55

4. 向量的高级用法

4.1 嵌套向量（二维向量）

向量可以包含其他向量，形成多维数组结构。

示例代码：二维向量

#include <iostream>
#include <vector>

int main() {
    // 定义一个3x4的二维向量，初始化为0
    std::vector<std::vector<int>> matrix(3, std::vector<int>(4, 0));

    // 填充矩阵
    for(int i = 0; i < 3; ++i) {
        for(int j = 0; j < 4; ++j) {
            matrix[i][j] = i * 4 + j + 1;
        }
    }

    // 输出矩阵
    std::cout << "Matrix:" << std::endl;
    for(auto row : matrix) {
        for(auto elem : row) {
            std::cout << elem << "\t";
        }
        std::cout << std::endl;
    }

    return 0;
}

输出：

Matrix:
1    2    3    4    
5    6    7    8    
9    10    11    12

4.2 向量与其他数据结构结合

向量可以与结构体、类等其他数据结构结合使用，增强数据组织能力。

示例代码：向量与结构体结合

#include <iostream>
#include <vector>
#include <string>

// 定义学生结构体
struct Student {
    int id;
    std::string name;
    float grade;
};

int main() {
    // 定义一个学生向量
    std::vector<Student> students;

    // 添加学生
    students.push_back({1001, "Alice", 89.5});
    students.push_back({1002, "Bob", 92.0});
    students.push_back({1003, "Charlie", 85.0});

    // 遍历并输出学生信息
    for(const auto& student : students) {
        std::cout << "ID: " << student.id 
                  << ", Name: " << student.name 
                  << ", Grade: " << student.grade << std::endl;
    }

    return 0;
}

输出：

ID: 1001, Name: Alice, Grade: 89.5
ID: 1002, Name: Bob, Grade: 92
ID: 1003, Name: Charlie, Grade: 85

4.3 使用迭代器操作向量

迭代器是一种指针类型，用于遍历和操作容器中的元素。

示例代码：使用迭代器

#include <iostream>
#include <vector>

int main() {
    std::vector<int> vec = {10, 20, 30, 40, 50};

    // 使用迭代器遍历并修改元素
    for(auto it = vec.begin(); it != vec.end(); ++it) {
        *it += 5;
    }

    // 输出修改后的向量
    std::cout << "After modifying: ";
    for(auto it = vec.begin(); it != vec.end(); ++it) {
        std::cout << *it << " ";
    }
    std::cout << std::endl; // 输出: 15 25 35 45 55 

    return 0;
}

输出：

After modifying: 15 25 35 45 55

5. 常用算法与向量

5.1 排序

可以使用 <algorithm> 头文件中的 sort() 函数对向量进行排序。

示例代码：对整数向量排序

#include <iostream>
#include <vector>
#include <algorithm>

int main() {
    std::vector<int> numbers = {50, 20, 40, 10, 30};

    // 排序前
    std::cout << "Before sorting: ";
    for(auto num : numbers) {
        std::cout << num << " ";
    }
    std::cout << std::endl;

    // 使用sort()排序
    std::sort(numbers.begin(), numbers.end());

    // 排序后
    std::cout << "After sorting: ";
    for(auto num : numbers) {
        std::cout << num << " ";
    }
    std::cout << std::endl;

    return 0;
}

输出：

Before sorting: 50 20 40 10 30 
After sorting: 10 20 30 40 50

自定义排序规则：降序

#include <iostream>
#include <vector>
#include <algorithm>

int main() {
    std::vector<int> numbers = {50, 20, 40, 10, 30};

    // 使用sort()并传入lambda表达式进行降序排序
    std::sort(numbers.begin(), numbers.end(), [](int a, int b) {
        return a > b;
    });

    // 输出排序后的向量
    std::cout << "After sorting in descending order: ";
    for(auto num : numbers) {
        std::cout << num << " ";
    }
    std::cout << std::endl;

    return 0;
}

输出：

After sorting in descending order: 50 40 30 20 10

5.2 反转

使用 reverse() 函数可以反转向量中的元素顺序。

示例代码：

#include <iostream>
#include <vector>
#include <algorithm>

int main() {
    std::vector<char> letters = {'A', 'B', 'C', 'D', 'E'};

    std::cout << "Before reversing: ";
    for(auto c : letters) {
        std::cout << c << " ";
    }
    std::cout << std::endl;

    // 反转向量
    std::reverse(letters.begin(), letters.end());

    std::cout << "After reversing: ";
    for(auto c : letters) {
        std::cout << c << " ";
    }
    std::cout << std::endl;

    return 0;
}

输出：

Before reversing: A B C D E 
After reversing: E D C B A

5.3 查找

使用 find() 函数可以在向量中查找特定元素。

示例代码：

#include <iostream>
#include <vector>
#include <algorithm>

int main() {
    std::vector<std::string> fruits = {"Apple", "Banana", "Cherry", "Date"};
    std::string target = "Cherry";

    // 使用find()查找元素
    auto it = std::find(fruits.begin(), fruits.end(), target);

    if(it != fruits.end()) {
        std::cout << target << " found at position " << std::distance(fruits.begin(), it) << std::endl;
    }
    else {
        std::cout << target << " not found." << std::endl;
    }

    return 0;
}

输出：

Cherry found at position 2

6. 向量的性能与优化

6.1 内存管理

向量会动态地管理内存，自动调整其容量以适应新增或删除的元素。频繁的内存分配可能会影响性能。

6.2 预留空间

使用 reserve() 可以提前为向量分配足够的内存，减少内存重新分配的次数，提高性能。

示例代码：

#include <iostream>
#include <vector>

int main() {
    std::vector<int> vec;

    // 预留空间
    vec.reserve(1000);
    std::cout << "Capacity after reserve(1000): " << vec.capacity() << std::endl;

    // 添加元素
    for(int i = 0; i < 1000; ++i) {
        vec.push_back(i);
    }

    std::cout << "Size after adding elements: " << vec.size() << std::endl;
    std::cout << "Capacity after adding elements: " << vec.capacity() << std::endl;

    return 0;
}

输出示例：

Capacity after reserve(1000): 1000
Size after adding elements: 1000
Capacity after adding elements: 1000

6.3 收缩容量

使用 shrink_to_fit() 可以请求收缩向量的容量以匹配其大小，释放多余的内存。

示例代码：

#include <iostream>
#include <vector>

int main() {
    std::vector<int> vec;

    // 预留较大的空间
    vec.reserve(1000);
    std::cout << "Capacity before adding: " << vec.capacity() << std::endl;

    // 添加少量元素
    vec.push_back(1);
    vec.push_back(2);
    vec.push_back(3);
    std::cout << "Size after adding: " << vec.size() << std::endl;
    std::cout << "Capacity after adding: " << vec.capacity() << std::endl;

    // 收缩容量
    vec.shrink_to_fit();
    std::cout << "Capacity after shrink_to_fit: " << vec.capacity() << std::endl;

    return 0;
}

输出示例：

Capacity before adding: 1000
Size after adding: 3
Capacity after adding: 1000
Capacity after shrink_to_fit: 3

7. 示例项目

示例项目1：学生信息管理系统

需求分析：

创建一个程序，管理学生的信息，包括添加、删除、显示和查找学生。每个学生包含ID、姓名和成绩。

代码实现：

#include <iostream>
#include <vector>
#include <string>
#include <algorithm>

// 定义学生结构体
struct Student {
    int id;
    std::string name;
    float grade;
};

// 打印学生信息
void printStudent(const Student& student) {
    std::cout << "ID: " << student.id 
              << ", Name: " << student.name 
              << ", Grade: " << student.grade << std::endl;
}

// 添加学生
void addStudent(std::vector<Student>& students) {
    Student s;
    std::cout << "Enter Student ID: ";
    std::cin >> s.id;
    std::cout << "Enter Student Name: ";
    std::cin.ignore(); // 忽略之前输入的换行符
    std::getline(std::cin, s.name);
    std::cout << "Enter Student Grade: ";
    std::cin >> s.grade;
    students.push_back(s);
    std::cout << "Student added successfully.\n";
}

// 删除学生
void deleteStudent(std::vector<Student>& students) {
    int id;
    std::cout << "Enter Student ID to delete: ";
    std::cin >> id;

    auto it = std::find_if(students.begin(), students.end(), [id](const Student& s) {
        return s.id == id;
    });

    if(it != students.end()) {
        students.erase(it);
        std::cout << "Student deleted successfully.\n";
    }
    else {
        std::cout << "Student with ID " << id << " not found.\n";
    }
}

// 显示所有学生
void displayStudents(const std::vector<Student>& students) {
    if(students.empty()) {
        std::cout << "No students available.\n";
        return;
    }
    std::cout << "Student List:\n";
    for(const auto& s : students) {
        printStudent(s);
    }
}

// 查找学生
void findStudent(const std::vector<Student>& students) {
    int id;
    std::cout << "Enter Student ID to find: ";
    std::cin >> id;

    auto it = std::find_if(students.begin(), students.end(), [id](const Student& s) {
        return s.id == id;
    });

    if(it != students.end()) {
        std::cout << "Student Found:\n";
        printStudent(*it);
    }
    else {
        std::cout << "Student with ID " << id << " not found.\n";
    }
}

int main() {
    std::vector<Student> students;
    int choice;

    do {
        std::cout << "\n=== Student Management System ===\n";
        std::cout << "1. Add Student\n";
        std::cout << "2. Delete Student\n";
        std::cout << "3. Display All Students\n";
        std::cout << "4. Find Student by ID\n";
        std::cout << "5. Exit\n";
        std::cout << "Enter your choice (1-5): ";
        std::cin >> choice;

        switch(choice) {
            case 1:
                addStudent(students);
                break;
            case 2:
                deleteStudent(students);
                break;
            case 3:
                displayStudents(students);
                break;
            case 4:
                findStudent(students);
                break;
            case 5:
                std::cout << "Exiting the system.\n";
                break;
            default:
                std::cout << "Invalid choice. Please choose between 1-5.\n";
        }

    } while(choice != 5);

    return 0;
}

运行示例：

=== Student Management System ===
1. Add Student
2. Delete Student
3. Display All Students
4. Find Student by ID
5. Exit
Enter your choice (1-5): 1
Enter Student ID: 1001
Enter Student Name: Alice
Enter Student Grade: 89.5
Student added successfully.

=== Student Management System ===
1. Add Student
2. Delete Student
3. Display All Students
4. Find Student by ID
5. Exit
Enter your choice (1-5): 1
Enter Student ID: 1002
Enter Student Name: Bob
Enter Student Grade: 92
Student added successfully.

=== Student Management System ===
1. Add Student
2. Delete Student
3. Display All Students
4. Find Student by ID
5. Exit
Enter your choice (1-5): 3
Student List:
ID: 1001, Name: Alice, Grade: 89.5
ID: 1002, Name: Bob, Grade: 92

=== Student Management System ===
1. Add Student
2. Delete Student
3. Display All Students
4. Find Student by ID
5. Exit
Enter your choice (1-5): 4
Enter Student ID to find: 1001
Student Found:
ID: 1001, Name: Alice, Grade: 89.5

=== Student Management System ===
1. Add Student
2. Delete Student
3. Display All Students
4. Find Student by ID
5. Exit
Enter your choice (1-5): 5
Exiting the system.

代码解析：

1. 结构体定义： 定义了一个 Student 结构体，包含 id、name 和 grade。
2. 功能函数：
   • addStudent：添加新学生。
   • deleteStudent：根据 ID 删除学生。
   • displayStudents：显示所有学生的信息。
   • findStudent：根据 ID 查找并显示学生信息。
3. 主函数： 提供一个菜单驱动的用户界面，允许用户选择不同的操作。

示例项目2：动态库存管理系统

需求分析：

创建一个程序，管理库存中的商品信息，包括添加、删除、更新和显示商品。每个商品包含商品ID、名称和数量。

代码实现：

#include <iostream>
#include <vector>
#include <string>
#include <algorithm>

// 定义商品结构体
struct Product {
    int id;
    std::string name;
    int quantity;
};

// 打印商品信息
void printProduct(const Product& product) {
    std::cout << "ID: " << product.id 
              << ", Name: " << product.name 
              << ", Quantity: " << product.quantity << std::endl;
}

// 添加商品
void addProduct(std::vector<Product>& products) {
    Product p;
    std::cout << "Enter Product ID: ";
    std::cin >> p.id;
    std::cout << "Enter Product Name: ";
    std::cin.ignore(); // 忽略之前输入的换行符
    std::getline(std::cin, p.name);
    std::cout << "Enter Product Quantity: ";
    std::cin >> p.quantity;
    products.push_back(p);
    std::cout << "Product added successfully.\n";
}

// 删除商品
void deleteProduct(std::vector<Product>& products) {
    int id;
    std::cout << "Enter Product ID to delete: ";
    std::cin >> id;

    auto it = std::find_if(products.begin(), products.end(), [id](const Product& p) {
        return p.id == id;
    });

    if(it != products.end()) {
        products.erase(it);
        std::cout << "Product deleted successfully.\n";
    }
    else {
        std::cout << "Product with ID " << id << " not found.\n";
    }
}

// 更新商品数量
void updateProductQuantity(std::vector<Product>& products) {
    int id, newQty;
    std::cout << "Enter Product ID to update: ";
    std::cin >> id;

    auto it = std::find_if(products.begin(), products.end(), [id](const Product& p) {
        return p.id == id;
    });

    if(it != products.end()) {
        std::cout << "Enter new quantity: ";
        std::cin >> newQty;
        it->quantity = newQty;
        std::cout << "Product quantity updated successfully.\n";
    }
    else {
        std::cout << "Product with ID " << id << " not found.\n";
    }
}

// 显示所有商品
void displayProducts(const std::vector<Product>& products) {
    if(products.empty()) {
        std::cout << "No products available.\n";
        return;
    }
    std::cout << "Product List:\n";
    for(const auto& p : products) {
        printProduct(p);
    }
}

int main() {
    std::vector<Product> products;
    int choice;

    do {
        std::cout << "\n=== Inventory Management System ===\n";
        std::cout << "1. Add Product\n";
        std::cout << "2. Delete Product\n";
        std::cout << "3. Update Product Quantity\n";
        std::cout << "4. Display All Products\n";
        std::cout << "5. Exit\n";
        std::cout << "Enter your choice (1-5): ";
        std::cin >> choice;

        switch(choice) {
            case 1:
                addProduct(products);
                break;
            case 2:
                deleteProduct(products);
                break;
            case 3:
                updateProductQuantity(products);
                break;
            case 4:
                displayProducts(products);
                break;
            case 5:
                std::cout << "Exiting the system.\n";
                break;
            default:
                std::cout << "Invalid choice. Please choose between 1-5.\n";
        }

    } while(choice != 5);

    return 0;
}

运行示例：

=== Inventory Management System ===
1. Add Product
2. Delete Product
3. Update Product Quantity
4. Display All Products
5. Exit
Enter your choice (1-5): 1
Enter Product ID: 2001
Enter Product Name: Laptop
Enter Product Quantity: 50
Product added successfully.

=== Inventory Management System ===
1. Add Product
2. Delete Product
3. Update Product Quantity
4. Display All Products
5. Exit
Enter your choice (1-5): 1
Enter Product ID: 2002
Enter Product Name: Smartphone
Enter Product Quantity: 150
Product added successfully.

=== Inventory Management System ===
1. Add Product
2. Delete Product
3. Update Product Quantity
4. Display All Products
5. Exit
Enter your choice (1-5): 4
Product List:
ID: 2001, Name: Laptop, Quantity: 50
ID: 2002, Name: Smartphone, Quantity: 150

=== Inventory Management System ===
1. Add Product
2. Delete Product
3. Update Product Quantity
4. Display All Products
5. Exit
Enter your choice (1-5): 3
Enter Product ID to update: 2001
Enter new quantity: 45
Product quantity updated successfully.

=== Inventory Management System ===
1. Add Product
2. Delete Product
3. Update Product Quantity
4. Display All Products
5. Exit
Enter your choice (1-5): 4
Product List:
ID: 2001, Name: Laptop, Quantity: 45
ID: 2002, Name: Smartphone, Quantity: 150

=== Inventory Management System ===
1. Add Product
2. Delete Product
3. Update Product Quantity
4. Display All Products
5. Exit
Enter your choice (1-5): 5
Exiting the system.

代码解析：

1. 结构体定义： 定义了一个 Product 结构体，包含 id、name 和 quantity。
2. 功能函数：
   • addProduct：添加新商品。
   • deleteProduct：根据 ID 删除商品。
   • updateProductQuantity：根据 ID 更新商品数量。
   • displayProducts：显示所有商品的信息。
3. 主函数： 提供一个菜单驱动的用户界面，允许用户选择不同的操作。