利用运算符重载技术，实现矩阵与一个常数相乘，两个矩阵相加，两个矩阵相乘，取矩阵的指定下标的元素（m[i][j]）形式并举例验证；当两个矩阵不满足乘法运算的要求时，抛出RequirementMismatch异常；

在C++中，运算符重载是一种强大的特性，可以让我们定义自定义类型的运算符行为。下面是一个示例，展示如何通过运算符重载实现矩阵与常数的乘法、矩阵加法、矩阵乘法以及矩阵元素的访问。我们还会定义一个`DimensionMismatch`异常，用于处理矩阵乘法时的维度不匹配问题。 ```cpp #include <iostream> #include <vector> #include <stdexcept> class DimensionMismatch : public std::exception { public: const char* what() const noexcept override { return "DimensionMismatch: Matrix dimensions do not match for the requested operation."; } }; class Matrix { private: std::vector<std::vector<double>> data; size_t rows; size_t cols; public: Matrix(size_t rows, size_t cols) : rows(rows), cols(cols), data(rows, std::vector<double>(cols, 0.0)) {} size_t getRows() const { return rows; } size_t getCols() const { return cols; } double& operator()(size_t i, size_t j) { if (i >= rows || j >= cols) { throw std::out_of_range("Index out of range"); } return data[i][j]; } const double& operator()(size_t i, size_t j) const { if (i >= rows || j >= cols) { throw std::out_of_range("Index out of range"); } return data[i][j]; } Matrix operator+(const Matrix& other) const { if (rows != other.rows || cols != other.cols) { throw DimensionMismatch(); } Matrix result(rows, cols); for (size_t i = 0; i < rows; ++i) { for (size_t j = 0; j < cols; ++j) { result.data[i][j] = data[i][j] + other.data[i][j]; } } return result; } Matrix operator*(const Matrix& other) const { if (cols != other.rows) { throw DimensionMismatch(); } Matrix result(rows, other.cols); for (size_t i = 0; i < rows; ++i) { for (size_t j = 0; j < other.cols; ++j) { for (size_t k = 0; k < cols; ++k) { result.data[i][j] += data[i][k] * other.data[k][j]; } } } return result; } Matrix operator*(double scalar) const { Matrix result(rows, cols); for (size_t i = 0; i < rows; ++i) { for (size_t j = 0; j < cols; ++j) { result.data[i][j] = data[i][j] * scalar; } } return result; } friend Matrix operator*(double scalar, const Matrix& matrix) { return matrix * scalar; } void print() const { for (const auto& row : data) { for (const auto& elem : row) { std::cout << elem << " "; } std::cout << std::endl; } } }; int main() { Matrix A(2, 3); Matrix B(3, 2); Matrix C(2, 3); // Initialize matrices for (size_t i = 0; i < A.getRows(); ++i) { for (size_t j = 0; j < A.getCols(); ++j) { A(i, j) = i + j; } } for (size_t i = 0; i < B.getRows(); ++i) { for (size_t j = 0; j < B.getCols(); ++j) { B(i, j) = i * j; } } for (size_t i = 0; i < C.getRows(); ++i) { for (size_t j = 0; j < C.getCols(); ++j) { C(i, j) = i * j; } } // Matrix addition try { Matrix D = A + C; std::cout << "Matrix A + C:" << std::endl; D.print(); } catch (const DimensionMismatch& e) { std::cout << e.what() << std::endl; } // Matrix multiplication try { Matrix E = A * B; std::cout << "Matrix A * B:" << std::endl; E.print(); } catch (const DimensionMismatch& e) { std::cout << e.what() << std::endl; } // Matrix-scalar multiplication Matrix F = A * 2.0; std::cout << "Matrix A * 2.0:" << std::endl; F.print(); return 0; } ``` ### 解释 1. **异常类`DimensionMismatch`**: - 继承自`std::exception`，并重写了`what()`方法，返回错误信息。 2. **矩阵类`Matrix`**: - 使用`std::vector`存储矩阵数据。 - 重载了`()`运算符，用于访问矩阵元素。 - 重载了`+`运算符，用于矩阵加法。 - 重载了`*`运算符，用于矩阵乘法和矩阵与常数的乘法。 - 提供了`print()`方法，用于打印矩阵。 3. **主函数`main`**: - 初始化三个矩阵`A`, `B`, `C`。 - 进行矩阵加法和乘法，并处理可能的`DimensionMismatch`异常。 - 进行矩阵与常数的乘法。