GATE CSE 2026 Session 2 Q50: Stack/queue assignments that produce the output 4 3 1 2 5

Consider a stack $S$ and a queue $Q$. Both of them are initially empty and have the capacity to store ten elements each. The elements 1, 2, 3, 4, and 5 arrive one by one, in that order. When an element arrives, it is assigned either to $S$ (pushed on $S$) or to $Q$ (enqueued to $Q$). Once all the five elements are stored, the output is generated in two steps. First, stack $S$ is emptied by popping all elements. Then queue $Q$ is emptied by dequeueing all elements. The output obtained by following this process is 4 3 1 2 5.

Given the output, the objective is to predict whether an element was assigned to $S$ or $Q$.

Which of the following options is/are possible valid assignment(s) of the elements?

Note: In the options, the notation $x_S$ denotes that element $x$ was assigned to $S$ and $y_Q$ denotes that element $y$ was assigned to $Q$.