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Data Structures | Queue | Question 11

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An implementation of a queue Q, using two stacks S1 and S2, is given below: 

C

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?

(A)

n+m <= x < 2n and 2m <= y <= n+m

(B)

n+m <= x < 2n and 2m<= y <= 2n

(C)

2m <= x < 2n and 2m <= y <= n+m

(D)

2m <= x <2n and 2m <= y <= 2n



Answer: (A)

Explanation:

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 n push for delete())

Hence Option (A) is the correct answer.



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Last Updated : 28 Jun, 2021
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