GATE | GATE-CS-2006 | Question 49

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

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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);
}

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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: Same as http://quiz.geeksforgeeks.org/data-structures-queue-question-10/

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