A queue $Q$ containing $n$ items and an empty stack $S$ are given. It is required to transfer all the items from the queue to the stack, so that the item at the front of queue is on the TOP of the stack, and the order of all other items are preserved. Show how this can be done in $O(n)$ time using only a constant amount of additional storage. Note that the only operations which can be performed on the queue and stack are Delete, Insert, Push and Pop. Do not assume any implementation of the queue or stack.
We can do this be first extracting items one by one from Q, and inserting them to S. After all items are done, S will contain the items in reverse order. Now, pop the elements from S and insert to Q. After this operation, items in Q will be in reverse order from the starting. Now, extract items from Q and push on to stack and we are done.
Delete an item from Q
Push the item to S
While (! empty Q);
Pop an item from S
Insert the item to Q
While (! empty S);
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