在c++中设计一个多维数组

我想为多维数组设计一个c++类。所谓多维，我指的是1d, 2d, 3d等等。该类支持逐个元素的加法和标量乘法运算符。假设A和B是类的实例(具有相同大小&维)。我想在下列表达式中使用对象:

C = A * 2 + B

我想知道的是如何管理内存。在上面的表达式中，A * 2将创建一个类的临时对象，然后将其添加到b中。无论如何，添加完成后临时对象是垃圾。我写了下面的类，它工作得很好，但我很确定它泄漏了内存。现在我的问题是，

1. 如何解决内存问题?设计课程的最佳方式是什么?

2. 是否可以在堆栈上而不是堆上分配所需的内存?

   class XArray
   {
       int num_dim;
       int *dims;
       int *index_helper;
       int table_size;
       double *table;
   
   public:
       XArray(const int n, const int *d):num_dim(n), dims(d)
       {
           int size = 1;
           for (int i = 0; i < n; i++) {
               size *= d[i];
           }
           table_size = size;
           table = new double[size];
           index_helper = new int[n];
       };
       ~XArray()
       {
           delete[] table;
           delete[] index_helper;
       };
       int dim(int d)
       {
           return dims[d];
       }
       double& operator()(int i)
       {
           index_helper[0] = i;
           return get_helper(1, index_helper);
       }
       double& operator()(int i, int j)
       {
           index_helper[0] = i;
           index_helper[1] = j;
           return get_helper(2, index_helper);
       }
       double& operator()(int i, int j, int k)
       {
           index_helper[0] = i;
           index_helper[1] = j;
           index_helper[2] = k;
           return get_helper(3, index_helper);
       }
       XArray operator*(double m)
       {
           XArray *xa = new XArray(num_dim, dims);
           for (int i = 0; i < table_size; i++) {
               xa->table[i] = this->table[i] * m;
           }
           return *xa;
       }
       XArray operator+(const XArray &that)
       {
           if (num_dim != that.num_dim) {
               char *msg = new char[100];
               sprintf(msg, "XArray::dimensions do not match in + operation, expected %d, found %d", num_dim, that.num_dim);
               throw msg;
           }
           for (int i = 0; i < num_dim; i++) {
               if (this->dims[i] != that.dims[i]) {
                   char *msg = new char[100];
                   sprintf(msg, "XArray::dimension %d not mached, %d != %d", i, dims[i], that.dims[i]);
                   throw msg;
               }
           }       
           XArray *xa = new XArray(num_dim, dims);
           for (int i = 0; i < table_size; i++) {
               xa->table[i] = this->table[i] + that.table[i];
           }
           return *xa;
       }
   private:
       double& get_helper(int n, int *indices)
       {
           if (n != num_dim) {
               char *msg = new char[100];
               sprintf(msg, "XArray::dimensions do not match, expected %d, found %d", num_dim, n);
               throw msg;
           }
           int multiplier = 1;
           int index = 0;
           for (int i = 0; i < n; i++) {
               if (indices[i] < 0 || indices[i] >= dims[i]) {
                   char *msg = new char[100];
                   sprintf(msg, "XArray::index %d out of range, %d not in (0, %d)", i, indices[i], dims[i]);
                   throw msg;
               }
               index += indices[i] * multiplier;
               multiplier *= dims[i];
           }
       return table[index];
   }
   

   };