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GO Classes DPP | PYTHON & DSA |QUEUE

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A queue $\mathrm{Q}$ can be implemented using two stacks, $\mathrm{S}_{\text {IN }}$ (for $\operatorname{ENQUEUE}$ and $\mathrm{S}_{\text {OUT }}$ (for $\operatorname{DQUEUE}$).

$\operatorname{ENQUEUE}(x)$: Pushes $x$ onto $\mathrm{S}_{\text {IN }}$.

The implementation of the $\operatorname{DQUEUE}$ operation is as follows:
 

IF S_OUT is NOT EMPTY:
    POP element from S_OUT and RETURN it.
ELSE :
    WHILE S_IN is NOT EMPTY:
       POP element from S_IN and PUSH it onto S_OUT.
    POP element from S_OUT and RETURN it.


If the queue is initially empty, and the following sequence of operations is performed:

$\operatorname{ENQUEUE}(10), \operatorname{ENQUEUE}(20), \operatorname{DQUEUE}$

$\operatorname{ENQUEUE}(30), \operatorname{DQUEUE}$

$\operatorname{ENQUEUE}(40)$

What is the total number of $\textbf{POP}$ operations performed on the stack $\mathbf{S}_{\text {IN }}$ ?

1 Answer

1 1 vote
Let \( n \) be the number of elements in stack \( S_{IN} \) at the time when a
{DEQUEUE} operation is performed and stack \( S_{OUT} \) is empty.

During such a {DEQUEUE}, every element in \( S_{IN} \) is popped exactly once
and pushed onto \( S_{OUT} \). Hence, the number of pop operations on \( S_{IN} \) is \( n \).

In the given sequence of operations:

Before the first {DEQUEUE},
\[
S_{IN} = \{10, 20\} \Rightarrow n = 2
\]
Therefore, the number of pop operations on \( S_{IN} \) is:
\[
2
\]

Before the second {DEQUEUE}, \( S_{OUT} \neq \varnothing \), so:
\[
0
\]
pop operations are performed on \( S_{IN} \).

Thus, the total number of pop operations on \( S_{IN} \) is:
\[
2 + 0 = \boxed{2}
\]
 
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