Let Q denote a queue containing sixteen numbers and S be an empty stack. Head(Q) returns the element at the head of the ...

Question

Let Q denote a queue containing sixteen numbers and S be an empty stack. Head(Q) returns the element at the head of the queue Q without removing it from Q. Similarly Top(S) returns the element at the top of S without removing it from S. Consider the algorithm given below:

while Q is not Empty do
  if S is Empty OR Top(S) <= Head(Q) then
    x = Dequeue(Q);
    Push(S, x);
  else
    x = Pop(S);
    Enqueue(Q, x);
end

The maximum possible number of iterations of the while loop in the algorithm is ___.

Accepted Answer

The maximum possible number of iterations of the while loop is 256. We have a queue Q with 16 numbers and an empty stack S. The algorithm repeatedly either moves the front of Q onto S (if S is empty or the top of S is <= head of Q), or pops S back into Q (if top of S > head of Q). We need to find the worst-case number of loop iterations.