Question

Assume that the stack s contains the sequence of values 302544 , and that 44 is at the top. Write the values contained in the queue \(q\) after they are removed from the stack and added to the queue (the queue is empty before this process is run). The value at the left of the queue is at its front.

Short answer

The queue is [44, 4, 4, 25, 30].

Step-by-step solution

- Understand the Stack Sequence

The stack contains the sequence of values 30, 25, 4, 4, and 44, with 44 being at the top.

- Removing from Stack

Remove elements from the stack one by one. Start with the topmost element, which is 44.

- Adding to Queue

Add each removed element to the queue. The queue will be built from the removed elements in the order they are taken from the stack.

- Process Sequence

Remove 44 and add to the queue, then continue removing 4, 4, 25, and finally 30, adding each to the queue after removal.

- Final Queue Order

The queue, after all elements are transferred from the stack, is [44, 4, 4, 25, 30].

Key concepts

Understanding Stack Operations

Stacks are a type of data structure that follow the Last In, First Out (LIFO) principle. This means the last element added to the stack is the first one to be removed. In Java, the Stack class contains methods like `push`, `pop`, and `peek` to manage elements.

The `push` method adds an element to the top of the stack. The `pop` method removes the top element, reducing the stack size by one. Finally, the `peek` method returns the top element without removing it.

For example, given a stack with values 30, 25, 4, 4, and 44 (with 44 at the top), removing elements (using `pop`) would retrieve them in reverse order: 44, 4, 4, 25, 30.

Knowing how to manipulate stacks is fundamental to understanding how data structures manage and organize data.

Exploring Queue Operations

Queues are another essential data structure but operate on a First In, First Out (FIFO) principle. This means the first element added will be the first to be removed. In Java, one can use interfaces such as `Queue` with implementations like `LinkedList` or `PriorityQueue`.

Queues primarily use the `add` or `offer` method to insert elements and the `remove` or `poll` method to retrieve and remove the front element. The `peek` method can be used to obtain the front element without removing it.

For example, if you initially have an empty queue and add elements sequentially (as we did from the stack: 44, 4, 4, 25, 30), the queue will provide these elements in the same order when you start removing them. The resulting queue will be `[44, 4, 4, 25, 30]`.

Mastering queue operations is fundamental for tasks like scheduling processes or managing tasks in order.

Element Transfer between Stack and Queue

Transferring elements between a stack and a queue involves understanding how each data structure manages order. Starting with a stack containing 30, 25, 4, 4, and 44, our goal is to move and reorder these elements into a queue.

Follow these steps to perform the transfer:
1. Initialize both a stack (with elements) and an empty queue.
2. Use the `pop` method on the stack to remove the top element.
3. Immediately `add` this element to the queue.
4. Repeat for all elements until the stack is empty.

Finally, the queue will contain `[44, 4, 4, 25, 30]`. Note how the order has been maintained from the stack's LIFO to the queue's FIFO.

Understanding this transfer operation is critical, especially when converting data between different structures, ensuring correct data handling across various applications.