Question

Suppose the following operations are performed on an empty stack: push(8); push(7); pop(); push(19); push(21); pop(); Insert numbers in the following diagram to show what will be stored in the static stack after the operations above have executed.

Short answer

Answer: The final state of the stack is [8, 19].

Step-by-step solution

Understanding the stack and initial state

A stack is a linear data structure in which elements are stored and removed according to the last-in, first-out (LIFO) principle. Initially, the stack is empty, i.e. there are no elements present.

Performing push(8) operation

The push operation adds an element to the top of the stack. Therefore, after the push(8) operation, the stack will contain only the element 8. Stack: [8]

Performing push(7) operation

After the push(7) operation, the stack will have two elements - 8 and 7, with 7 being on top of 8. Stack: [8, 7]

Performing pop() operation

The pop operation removes the topmost element from the stack. After the pop() operation, the top element (7) will be removed, leaving only the element 8 in the stack. Stack: [8]

Performing push(19) operation

After the push(19) operation, the stack will have two elements - 8 and 19, with 19 being on top of 8. Stack: [8, 19]

Performing push(21) operation

After the push(21) operation, the stack will have three elements - 8, 19, and 21, with 21 being on top of 19. Stack: [8, 19, 21]

Performing pop() operation and final stack

After the pop() operation, the top element (21) will be removed, leaving the elements 8 and 19 in the stack. Final Stack: [8, 19]

Key concepts

Linear Data Structures

In computer science, linear data structures are crucial for organizing and managing data efficiently. A linear data structure arranges data in a sequential order, which means each element is connected to the previous and next element. This order allows for efficient traversal, meaning you can go through each element one by one with ease. Common linear data structures include arrays, queues, and stacks.
Stacks are a particularly interesting type of linear data structure because they follow a specific order for adding and removing elements. Understanding linear data structures provides the foundation for grasping more complex structures, making them a valuable tool in both programming and algorithm design.

Last-in First-out (LIFO)

The last-in first-out (LIFO) principle is the fundamental rule of how a stack operates. This means that the last item added to the stack will be the first one to be removed. Imagine a stack of plates; the plate you placed last is the one you will take out first. This behavior is especially useful in certain programming algorithms where you need to reverse operations or remember the state of the last operations performed.
In the original exercise, understanding LIFO is essential because each operation, whether it is pushing or popping an element, adheres to this principle, affecting which element is next to be removed. Recognizing and practicing LIFO principles will greatly improve your problem-solving skills in computer science and software development.

Push Operation

The push operation is a fundamental action in managing stacks. When you perform a push operation, you add a new element to the top of the stack.
For example, in the given exercise, when the push(8) operation was conducted, the stack transitioned from an empty state to holding the element 8. A subsequent push of 7 adds 7 on top, now stacking 8 at the bottom and 7 at the top. It is through the push operation that new elements can be introduced to the stack, and it is important to note that a push always occurs at the top, ensuring that earlier elements remain undisturbed until they become the topmost item. This operation is a critical component in implementing the stack efficiently.

Pop Operation

The pop operation is the counterpart to the push operation, and it is just as critical in stack management. Performing a pop operation will remove the element currently at the top of the stack. It follows the LIFO principle by making sure that the most recently added element is the one removed. For instance, in the problem's exercise, when a pop operation is carried out after push(7), the element 7 is removed, leaving 8 as the topmost item.
Understanding how the pop operation works is essential when you need to revert changes or backtrack in your operations, as it ensures that you can efficiently manage and access the most recent elements in a controlled manner.