## Stack-and-Queue

 Question 1

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?

 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
Data-Structures       Stack-and-Queue       GATE 2006
Question 1 Explanation:
Let's first consider for push, i.e., x.
Best case:
First push m elements in S1 then pop m elements from S1 and push them in S2 and then pop all m elements from S2. Now push remaining (n-m) elements to S1.
So total push operation
= m + m + (n-m)
= n+m
Worst Case:
First push all n elements in S1. Then pop n elements from S1 and push them into S2. Now pop m elements from S2.
So total push operation
= n+n
= 2n
Now lets consider for pop operation, i.e., y.
For best case:
First push m elements in S1, then pop m elements and push them in S2. Now pop that m elements from S2. Now push remaining (n-m) elements in S1.
So total pop operation
= m+m
= 2m
For worst case:
First push n elements in S1, then pop them from S1 and push them into S2. Now pop m elements fro m S2.
So total pop operation
= n+m
Therefore, option A is correct answer.
There is 1 question to complete.

Register Now