Question

In a stack of Size 'N', if there are 'M' elements inserted into the stack and then 'M/2' are popped out. What is the remaining number of elements left in the stack? Assume 'M' $<$ 'N'.

• A. N-M/2
• B. M/2
• C. N/2
• D. 1

Hint:

The total capacity ($N$) of a stack only determines when the stack becomes full (overflow check).
The actual active count is determined purely by tracking the number of pushes and pops:
\[ \text{Final Count} = \text{Pushed} - \text{Popped} \]

Answer 1

The Correct Option is B

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.