Implement Stack using Queues

Background Knowledge

The problem requires implementing a stack using two queues. A stack is a Last-In-First-Out (LIFO) data structure, meaning the most recently added element is the first one to be removed. On the other hand, a queue is a First-In-First-Out (FIFO) data structure, where the first element added is the first one to be removed. To implement a stack using queues, we need to understand how to manipulate the queues to achieve LIFO behavior.

The key concept here is to use the queues in a way that the most recently added element is always at the front of one of the queues. This can be achieved by using two queues and moving elements between them. We can use one queue to store the main stack elements and the other queue to temporarily hold elements when we need to add or remove an element from the main queue.

Understanding the enqueue and dequeue operations of a queue is crucial. The enqueue operation adds an element to the end of the queue, while the dequeue operation removes an element from the front of the queue. We will use these operations to implement the push, pop, top, and empty operations of the stack.

Algorithm/Approach

The general approach to solve this problem is to use two queues, q1 and q2, to implement the stack. We will use q1 to store the main stack elements and q2 to temporarily hold elements when needed. The algorithm will involve moving elements between q1 and q2 to achieve the LIFO behavior.