GATE CS 2026 Set 2 — Question 50
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Programming & Data Structures → Stacks & Queues → Queue & Circular Queue
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Question
Consider a stack and a queue . 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 (pushed on ) or to (enqueued to ). 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 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 or .
Which of the following options is/are possible valid assignment(s) of the elements?Note: In the options, the notation denotes that element was assigned to and denotes that element was assigned to .
Given the output, the objective is to predict whether an element was assigned to or .
Which of the following options is/are possible valid assignment(s) of the elements?Note: In the options, the notation denotes that element was assigned to and denotes that element was assigned to .
Correct answer
(A) 1S, 2Q, 3S, 4S, 5Q; (B) 1Q, 2Q, 3S, 4S, 5Q
Solution
The input sequence is 1, 2, 3, 4, 5. The output sequence is generated by first popping all elements from stack , then dequeueing all elements from queue . The final output is 4, 3, 1, 2, 5.Let the sequence of elements pushed to be and the sequence of elements enqueued to be .
The output from will be the reverse of (LIFO).
The output from will be (FIFO).The total output is Reverse() concatenated with .
We need to find a split point in the output sequence 4, 3, 1, 2, 5 such that the first part is the reverse of a subsequence of the input (1, 2, 3, 4, 5) and the second part is the remaining subsequence in increasing order.Let's test the options:Option (A):
. Output from = Reverse() = .
. Output from = .
Total Output = . This matches the given output. So, (A) is correct.Option (B):
. Output from = Reverse() = .
. Output from = .
Total Output = . This matches the given output. So, (B) is correct.Option (C):
. Output from = .
. Output from = .
Total Output = . Mismatch.Option (D):
. Output from = .
. Output from = .
Total Output = . Mismatch.Thus, both (A) and (B) are valid assignments.
The output from will be the reverse of (LIFO).
The output from will be (FIFO).The total output is Reverse() concatenated with .
We need to find a split point in the output sequence 4, 3, 1, 2, 5 such that the first part is the reverse of a subsequence of the input (1, 2, 3, 4, 5) and the second part is the remaining subsequence in increasing order.Let's test the options:Option (A):
. Output from = Reverse() = .
. Output from = .
Total Output = . This matches the given output. So, (A) is correct.Option (B):
. Output from = Reverse() = .
. Output from = .
Total Output = . This matches the given output. So, (B) is correct.Option (C):
. Output from = .
. Output from = .
Total Output = . Mismatch.Option (D):
. Output from = .
. Output from = .
Total Output = . Mismatch.Thus, both (A) and (B) are valid assignments.
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