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GO Classes DPP | PYTHON & DSA |STACK

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Consider a scenario where you have an empty stack $S$ and an empty queue $Q$. You are given a sequence of $n$ distinct integers. You perform the following operations in order:

  1. ENQUEUE all $n$ integers into $Q$.
     
  2. DEQUEUE $\lfloor n / 2\rfloor$ elements from $Q$ and PUSH them onto $S$.
     
  3. POP all elements from $S$ and ENQUEUE them back into $Q$.
     
  4. DEQUEUE the remaining $n$ elements from $Q$ one by one and PUSH them onto $S$.

Which of the following statements is/are CORRECT?

  1. The final order of elements in $S$ is the exact reverse of the initial input sequence.
     
  2. If the initial sequence was $[1,2,3,4,5]$, the element at the TOP of $S$ at the end is $3$.
     
  3. The first $k=\lfloor n / 2\rfloor$ elements of the initial sequence appear at the top of the final stack $S$ in their original relative order when popped one by one.
     
  4. The total number of DEQUEUE operations performed is $n+\lfloor n / 2\rfloor$.

1 Answer

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Let $n=5$ and sequence be $[1,2,3,4,5]$.

  • Step $2:$ $Q=[1,2,3,4,5] \rightarrow S=[1,2], Q=[3,4,5]$.
     
  • Step $3:$ Pop $S$ to $Q \rightarrow Q=[3,4,5,2,1]$.
     
  • Step $4:$ Dequeue $Q$ to $S \rightarrow S=[3,4,5,2,1]$ $($Top is $1 )$.

(A) is false $(S$ is $[3,4,5,2,1]$, not $[5,4,3,2,1])$.

(B) is false (Top is $1)$.

(C) TRUE: As discussed, the "double reversal" of the first $k$ elements means they are popped in their original $1^{\text {st }}, 2^{\text {nd }}, \ldots, k^{\text {th }}$ order.

(D) is TRUE: $\lfloor n / 2\rfloor$ dequeues in Step 2, and $n$ dequeues in Step $4$.

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