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Consider a sequence $a$ of elements $a_{0}=1, a_{1}=5, a_{2}=7, a_{3}=8, a_{4}=9$, and $a_{5}=2$. The following operations are performed on a stack $S$ and a queue $Q,$ both of which are initially empty.

  1. $\textsf{push}$ the elements of $a$ from $a_{0}$ to $a_{5}$ in that order into $S$.
  2. $\textsf{enqueue}$ the elements of $a$ from $a_{0}$ to $a_{5}$ in that order into $Q$.
  3. $\textsf{pop}$ an element from $S$.
  4. $\textsf{dequeue}$ an element from $Q$.
  5. $\textsf{pop}$ an element from $S$.
  6. $\textsf{dequeue}$ an element from $Q$.
  7. $\textsf{dequeue}$ an element from $Q$ and push the same element into $S$.
  8. Repeat operation $\text{VII}$ three times.
  9. $\textsf{pop}$ an element from $S$.
  10. $\textsf{pop}$ an element from $S$.

The top element of $S$ after executing the above operations is ______________.

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3 Answers

9 votes
9 votes

Given initial elements: $a_0=1,a_1=5,a_2=7,a_3=8,a_4=9,a_5=2$

1)  Push all the elements into the stack $S$ in the same order:

2
9
8
7
5
1

2) Push all the elements into the queue $Q$ in the same order:

1 5 7 8 9 2

 

3) Pop(S):

9
8
7
5
1

 

4) Dequeue(Q):

5 7 8 9 2

 

5) Pop(S):

8
7
5
1

6) Dequeue (Q):

7 8 9 2

7)  Dequeue (Q) and push the same element into S:

8 9 2

 

7
8
7
5
1

 

8) repeat step 7  three times we get:

First time:

9 2

 

 

8
7
8
7
5
1

second time: 

2

 

9
8
7
8
7
5
1

third time:

2
9
8
7
8
7
5
1

9 ) pop (S):

9
8
7
8
7
5
1

 

10 ) pop(S):

8
7
8
7
5
1

from the resultant stack $S$ topmost element is $8$

The correct answer is $8$

0 votes
0 votes

Given initial elements: $a_0=1,a_1=5,a_2=7,a_3=8,a_4=9,a_5=2$

1)  Push all the elements into the stack $S$ in same order:

2
9
8
7
5
1

2) Push all the elements into the queue $Q$ in the same order:

1 5 7 8 9 2

 

3) Pop(S):

9
8
7
5
1

 

4) Dequeue(Q):

5 7 8 9 2

 

5) Pop(S):

8
7
5
1

6) Dequeue (Q):

7 8 9 2

7)  Dequeue (Q) and push the same element into S:

8 9 2

 

7
8
7
5
1

 

8) repeat step 7  three times we get:

First time:

9 2

 

 

8
7
8
7
5
1

second time: 

2

 

9
8
7
8
7
5
1

third time:

2
9
8
7
8
7
5
1

9 ) pop (S):

9
8
7
8
7
5
1

 

10 ) pop(S):

8
7
8
7
5
1

from the resultant stack $S$ topmost element is $8$

The correct answer is $8$

Answer:

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