GATE CS 2022 Set 1 — Question 62
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Programming & Data Structures → Stacks & Queues → Queue & Circular Queue
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Question
Consider the queues containing four elements and 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 required to place the elements of in in reverse order (shown as the Final State in the figure) without using any additional storage is ___________.Correct answer
0 to 0
Solution
To reverse the elements of into without using any additional explicit storage (like an auxiliary queue or array), we can utilize the implicit stack of a recursive function. The procedure is as follows:Execution Trace:
void reverse(Queue Q1, Queue Q2) {
if (isEmpty(Q1))
return;
// Remove element from Q1 and hold it in the recursion stack
int x = Dequeue(Q1);
// Recursive call to process the rest
reverse(Q1, Q2);
// Enqueue the held element into Q2 as the recursion unwinds
Enqueue(Q2, x);
}
1.
Dequeue(Q1) removes 1. Recurse.2.
Dequeue(Q1) removes 2. Recurse.3.
Dequeue(Q1) removes 3. Recurse.4.
Dequeue(Q1) removes 4. Recurse.5. is empty. Return.
6.
Enqueue(Q2, 4) (4 is added to ).7.
Enqueue(Q2, 3) (3 is added to ).8.
Enqueue(Q2, 2) (2 is added to ).9.
Result: contains and is empty.During this entire process, we only perform Enqueue(Q2, 1) (1 is added to ).Dequeue on and Enqueue on . We never perform an Enqueue operation on . Thus, the minimum number of Enqueue operations on is 0.Continue learning with Success Tracker
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