Consider a stack 𝑆 and a queue 𝑄. Both of them are initially empty and have…

2026

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 π‘₯𝑆 denotes that element π‘₯ was assigned to 𝑆 and 𝑦𝑄 denotes that element 𝑦 was assigned to 𝑄.

  1. A.

    1𝑆, 2𝑄, 3𝑆, 4𝑆, 5Q

  2. B.

    1𝑄, 2𝑄, 3𝑆, 4𝑆, 5Q

  3. C.

    1𝑄, 2𝑄, 3𝑄, 4𝑆, 5S

  4. D.

    1𝑆, 2𝑆, 3𝑆, 4𝑄, 5𝑄

Attempted by 28 students.

Show answer & explanation

Correct answer: A, B

Step 1: Analyze Output Structure The output 4 3 1 2 5 is generated in two phases. First, Stack S is emptied (popped). Second, Queue Q is emptied (dequeued). Thus, 4 3 1 comes from S, and 2 5 comes from Q.

Step 2: Analyze Stack S Stack is LIFO (Last In First Out). Output 4 3 1 means 4 was pushed last, then 3, then 1. So 1, 3, 4 must be in S.

Step 3: Analyze Queue Q Queue is FIFO (First In First Out). Output 2 5 means 2 was enqueued first, then 5. So 2, 5 must be in Q.

Step 4: Conclusion Valid assignment: 1S, 2Q, 3S, 4S, 5Q.

Explore the full course: Gate Guidance By Sanchit Sir