Question-24
Consider the queues \(Q1\) containing four elements and \(Q2\) containing none (shown as the Initial State in the figure). The only operations allowed on these two queues are \(Enqueue(Q, element)\) and \(Dequeue(Q)\). The minimum number of Enqueue operations on \(Q1\) required to place the elements of \(Q1\) in \(Q2\) in reverse order (shown as the Final State in the figure) without using any additional storage is___________.
Initial State:
Q1: |1|2|3|4|
Q2: | | | | |
Final State:
Q1: | | | | |
Q2: |4|3|2|1| \(0\)
The operations performed demonstrate the reversal of elements between \(Q1\) and \(Q2\) without using additional storage, achieving the Final State with the elements reversed in \(Q2\) from the Initial State of \(Q1\).
| Step | Q1 | Q2 | Operation |
|---|---|---|---|
| 1 | 1,2,3,4 | ||
| 2 | 2,3,4 | 1 | Enqueue(Dequeue(Q1), Q2) |
| 3 | 3,4 | 1,2 | Enqueue(Dequeue(Q1), Q2) |
| 4 | 3,4 | 2,1 | Enqueue(Dequeue(Q2), Q2) |
| 5 | 4 | 2,1,3 | Enqueue(Dequeue(Q1), Q2) |
| 6 | 4 | 1,3,2 | Enqueue(Dequeue(Q2), Q2) |
| 7 | 4 | 3,2,1 | Enqueue(Dequeue(Q2), Q2) |
| 9 | 3,2,1,4 | Enqueue(Dequeue(Q1), Q2) | |
| 9 | 2,1,4,3 | Enqueue(Dequeue(Q2), Q2) | |
| 10 | 1,4,3,2 | Enqueue(Dequeue(Q2), Q2) | |
| 11 | 4,3,2,1 | Enqueue(Dequeue(Q2), Q2) |
From the above table it is clear that no Enqueue operation is performed on \(Q1\). THus The minimum number of Enqueue operations on \(Q1\) required is 0.