How does the Minimum Stack approach ensure consistency when the minimum element is popped from the main stack?

The Minimum Stack approach is a method used in data structures, particularly in stack operations, to keep track of the minimum element in the stack at any given time. It uses two stacks: the main stack and a minimum stack. The main stack holds all the elements, while the minimum stack keeps track of the minimum elements.

Here's how it ensures consistency when the minimum element is popped from the main stack:

1. When an element is pushed into the main stack, the algorithm checks if the minimum stack is empty or if the new element is less than or equal to the top element of the minimum stack. If either condition is true, the element is also pushed into the minimum stack.

2. When an element is popped from the main stack, the algorithm checks if the popped element is the same as the top element of the minimum stack. If it is, then the top element of the minimum stack is also popped. This ensures that the minimum stack always holds the minimum element of the main stack.

3. If the popped element is not the same as the top element of the minimum stack, then no operation is performed on the minimum stack. This is because the popped element cannot be the minimum element of the main stack.

4. The minimum element of the main stack is always the top element of the minimum stack. This is ensured by the push and pop operations described above.

So, even when the minimum element is popped from the main stack, the minimum stack will still hold the minimum element of the main stack, ensuring consistency.