Given a stack data structure with standard push, pop, and empty operations, the challenge is to delete the element located at the middle position of the stack. The constraint is to accomplish this without utilizing any auxiliary data structures.

Brute force: Popping all elements, finding the middle, and reconstructing the stack without the middle element. This is inefficient due to the double traversal.
Recursive approach: Recursively popping elements until half the stack is removed, deleting the top element (which is now the middle), then recursively pushing back the popped elements. While elegant, this might have space implications due to recursion depth.