Sparse Arrays, take three

Recall the sparse arrays of HW 4. Re-implement the SparseArray class of that homework but this time use a binary search tree rather than a linked list, in order to improve performance. Other than that the requirements are still the same:

• Program a constructor and destructor and a read_element and write_element method to allow the user to access parts of the array. A read on a position where the user has not written anything should return a 0.
• Overload the [] operator so that the user can use this class as if it were an array. (This requires some thought to decide what the proper behavior should be. Include a detailed comment explaining what your implementation does and why)
• The memory used in your implementation should be proportional to the number of non-zero elements the user currently has in the array. It should not depend on the positions where the user is writing. In particular, it would be nice if you removed elements that contain a 0, since this is the default value of the array, in order to save space.