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 remaining elements in the stack are {8, 19}.

Step-by-step solution

Understanding Stack Operation

Stack operates on the principle of "Last in, First out" (LIFO). "push" is an operation which inserts an element into the stack. On the other hand, "pop" is an operation that removes the most recently added element that's not yet been removed. An empty stack is the initial condition in this problem.

Perform First Push Operation

The first operation provided in the exercise is push(8). This operation places the number 8 onto the stack.

Perform Second Push Operation

The next operation is push(7). This places the number 7 on top of number 8 in the stack.

Perform First Pop Operation

The next operation is pop(). This will remove the most recently added number from the stack. In this case, it will remove the number 7.

Perform Third Push Operation

Afterwards, push(19) is conducted. This operation adds number 19 on top of the stack which only includes number 8 before.

Perform Fourth Push Operation

Afterwards, push(21) is conducted. This operation places number 21 on top of the number 19 in the stack.

Perform Second Pop Operation

The final operation is pop(). This operation will remove the most recently added number from the stack which is 21. After all of these operations, the elements left in the stack, from bottom to top, will be {8, 19}.

Key concepts

Stack Operations

A stack is a fundamental data structure in computer science, resembling a collection of items that follows the principle of "Last In, First Out" or LIFO.
It functions similarly to a stack of plates: you add, or "push," new plates onto the top and remove, or "pop," the top plates first.

• A stack can hold any kind of data, such as numbers, strings, or objects.
• All operations occur at one end, known as the "top" of the stack.
• The primary operations include pushing and popping items.
• One can also "peek" at the top item without removing it, but this is not part of the operations in our exercise.

Its simplicity and utility make it crucial in daily computing tasks such as function call management, parsing expressions, and more.
Understanding stack operations lays the groundwork for numerous programming concepts and applications.

Push and Pop

The core operations of a stack are "push" and "pop."
These define how elements are added and removed from the stack. Let's explore these operations more fully: The Push Operation:

• "Push" adds an element to the top of the stack.
• It increases the stack's size by one.
• The newly added element becomes the topmost item on the stack.
• For instance, performing push(8) on an empty stack will have 8 as the top element.

The Pop Operation:

• "Pop" removes the element at the top of the stack.
• This operation decreases the stack's size by one.
• The element popped is the most recently pushed that hasn't been removed yet.
• After a pop operation, the next element becomes the new top of the stack.
• If we pop after push(7) following push(8), the element 7 is removed, leaving 8 as the top element.

These operations are the backbone of stack functionality and make stacks suitable for any operation requiring ordered data management.

Last In First Out (LIFO)

The principle of Last In, First Out (LIFO) is fundamental to stacks. This means the last item added to the stack is the first one to be removed.
It's as if you were piling up books one by one; you can only take off the top book without disturbing the ones below it.

• LIFO ensures that each time an element is "popped," it is the most recent addition, preserving an order where new elements temporarily overshadow older ones.
• This behavior makes stacks useful for scenarios like undo mechanisms in software, where the last change needs to be reversed first.
• With LIFO, stacks serve effectively in managing recursive function calls in programming, ensuring the most recent call completes before earlier calls.

In understanding stack operations, appreciating the LIFO concept helps clarify why certain element arrangements occur, like in the example where pushing a series of numbers results in altering their order when popped.