Step 1: Understanding the Question:
The question asks to calculate the remaining number of elements in a stack of capacity $N$, after inserting $M$ elements and then popping out $M/2$ of those elements. We are given the condition $M < N$.
Step 2: Stacks and their Operations:
- A stack is a linear data structure that operates under the Last-In, First-Out (LIFO) model.
- Push: Adds an element to the stack, increasing its size by 1.
- Pop: Removes the top element from the stack, decreasing its size by 1.
Step 3: Detailed Explanation:
Let us keep track of the count of elements in the stack:
- Initially, the stack is empty, meaning the element count is 0.
- We insert (push) $M$ elements into the stack. Since the stack size is $N$ and we are given $M < N$, no overflow occurs.
\[ \text{Count after insertion} = M \]
- Next, we remove (pop) $M/2$ elements from the stack. Each pop decreases the active count by 1.
\[ \text{Elements remaining} = \text{Initial insertions} - \text{Popped elements} \]
\[ \text{Elements remaining} = M - \frac{M}{2} = \frac{M}{2} \]
- Note that the maximum stack capacity $N$ is only a boundary constraint. It does not affect the calculation of active elements as long as $M < N$ is satisfied.
Step 4: Final Answer:
The remaining number of elements inside the stack is $M/2$.
Hence, option (B) is the correct choice.