L4_02 二维数组/多维数组

一、C++ 二维数组的定义与使用

1.1 定义方式

#include <iostream>
using namespace std;

int main() {
    // 方法1：指定行数和列数
    int arr1[3][4];
    
    // 方法2：初始化时指定元素
    int arr2[3][4] = {
        {1, 2, 3, 4},
        {5, 6, 7, 8},
        {9, 10, 11, 12}
    };
    
    // 方法3：省略内层大括号
    int arr3[3][4] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12};
    
    return 0;
}

1.2 访问元素

int arr[3][4] = {{1,2,3,4}, {5,6,7,8}, {9,10,11,12}};

// 访问第2行第3列的元素（索引从0开始）
cout << arr[1][2] << endl;  // 输出7

1.3 遍历二维数组

int arr[3][4] = {{1,2,3,4}, {5,6,7,8}, {9,10,11,12}};

for (int i = 0; i < 3; i++) {
    for (int j = 0; j < 4; j++) {
        cout << arr[i][j] << " ";
    }
    cout << endl;
}

---

二、C++ 多维数组

2.1 三维数组

int arr[2][3][4];  // 2个3x4的二维数组

// 初始化
int arr[2][3][4] = {
    {
        {1, 2, 3, 4},
        {5, 6, 7, 8},
        {9, 10, 11, 12}
    },
    {
        {13, 14, 15, 16},
        {17, 18, 19, 20},
        {21, 22, 23, 24}
    }
};

2.2 访问三维数组元素

cout << arr[1][2][3] << endl;  // 输出24

---

三、Python 复合类型的嵌套使用

3.1 列表的嵌套

# 创建二维列表
matrix = [
    [1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]
]

# 访问元素
print(matrix[0][0])  # 1
print(matrix[1][2])  # 6

# 遍历二维列表
for row in matrix:
    for element in row:
        print(element, end=" ")
    print()

3.2 列表推导式创建矩阵

# 创建3x3的单位矩阵
identity = [[1 if i == j else 0 for j in range(3)] for i in range(3)]
print(identity)
# [[1, 0, 0], [0, 1, 0], [0, 0, 1]]

3.3 字典的嵌套

students = {
    "Alice": {
        "age": 20,
        "grades": {"math": 95, "english": 88}
    },
    "Bob": {
        "age": 19,
        "grades": {"math": 87, "english": 92}
    }
}

# 访问嵌套字典
print(students["Alice"]["grades"]["math"])  # 95

3.4 列表中包含字典

books = [
    {"title": "Python", "author": "Guido"},
    {"title": "C++", "author": "Stroustrup"}
]

for book in books:
    print(f"{book['title']} by {book['author']}")

---

四、二维数组的应用

4.1 矩阵加法

#include <iostream>
using namespace std;

int main() {
    int A[2][3] = {{1,2,3}, {4,5,6}};
    int B[2][3] = {{7,8,9}, {10,11,12}};
    int C[2][3];
    
    for (int i = 0; i < 2; i++) {
        for (int j = 0; j < 3; j++) {
            C[i][j] = A[i][j] + B[i][j];
        }
    }
    
    // 输出结果
    for (int i = 0; i < 2; i++) {
        for (int j = 0; j < 3; j++) {
            cout << C[i][j] << " ";
        }
        cout << endl;
    }
    
    return 0;
}

4.2 矩阵转置

matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]

# 转置矩阵
transposed = [[row[i] for row in matrix] for i in range(3)]

for row in transposed:
    print(row)

---

五、示例程序

5.1 C++ 二维数组操作

#include <iostream>
using namespace std;

int main() {
    int matrix[3][3] = {{1,2,3}, {4,5,6}, {7,8,9}};
    
    // 计算对角线元素之和
    int sum = 0;
    for (int i = 0; i < 3; i++) {
        sum += matrix[i][i];
    }
    cout << "对角线元素之和: " << sum << endl;
    
    // 打印矩阵
    cout << "矩阵内容:" << endl;
    for (int i = 0; i < 3; i++) {
        for (int j = 0; j < 3; j++) {
            cout << matrix[i][j] << "\t";
        }
        cout << endl;
    }
    
    return 0;
}

5.2 Python 嵌套数据结构

# 学生成绩管理
students = [
    {"name": "Alice", "scores": [90, 85, 95]},
    {"name": "Bob", "scores": [80, 75, 85]},
    {"name": "Charlie", "scores": [95, 90, 88]}
]

# 计算每个学生的平均分
for student in students:
    avg = sum(student["scores"]) / len(student["scores"])
    print(f"{student['name']}: {avg:.2f}")