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An implementation of a queue Q, using two stacks S1 and S2 is given below
void insert (Q, x) {
push (S1, x);
}
void delete (Q) {
if (stack-empty (S2)) then
if (stack-empty (S1)) then {
print (“Q is empty”);
return;
}
else while (! (stack-empty (S1))) {
x = pop (S1);
push (S2, x);
}
x = pop (S2);
}
Let n insert and m(≤ n) delete operations be performed in an arbitrary order on an empty queue Q. Let x and y be the number of push and pop operations performed respectively in the process. Which one of the following is true for all m and n?
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- n + m ≤ x < 2n and 2m ≤ y ≤ n + m
- n + m ≤ x ≤ 2n and 2m ≤ y ≤ 2n
- 2m ≤ x ≤ 2n and 2m ≤ y ≤ n + m
- 2m ≤ x < 2n and 2m ≤ y ≤ 2n
- n + m ≤ x < 2n and 2m ≤ y ≤ n + m
Correct Option: A
The order in which insert and delete operations are performed matters here.
The best case : Insert and delete operations are performed alternatively. In every delete operation, 2 pop and 1 push operations are performed. So, total m+ n push (n push for insert() and m push for delete()) operations and 2m pop operations are performed.
The worst case : First n elements are inserted and then m elements are deleted. In first delete operation, n + 1 pop operations and n push operation are performed. Other than first, in all delete operations, 1 pop operation is performed. So, total m + n pop operations and 2n push operations are performed (n push for insert() and m push for delete())
