Greetings! Today, we're unveiling the concept of Stacks in Ruby, a fundamental data structure. Imagine a stack as a pile of dishes: you add a dish to the top (Last In) and take it from the top (First Out). This Last-In, First-Out (LIFO) principle exemplifies the stack. Ruby handles stacks effortlessly with Arrays. This lesson will illuminate the stack data structure, operations, and their Ruby applications. Are you ready to start?

A stack is a storage structure that allows Push (addition) and Pop (removal) operations. It's akin to a stack of plates in a cafeteria, where plates are added (pushed) and removed (popped) from the top. No plate can be taken from the middle or the bottom, exemplifying a Last-In, First-Out (LIFO) operation.

To create a stack, Ruby employs a built-in data structure known as an Array. For the Push operation, we use push, which adds an element at the end of the array. For the Pop operation, there's the pop method that removes the last element, simulating the removal of the 'top' element in a stack. Here's how it looks:

In the example provided, we push 'John', 'Mary', and 'Steve' into the stack and then pop 'Steve' from the stack.

Stack operations go beyond merely push and pop. For example, to verify if a stack is empty, you can use the empty? method. If it returns true, that means the stack is empty. Conversely, if it returns false, we can infer the stack is not empty. To peek at the top element of the stack without popping it, indexing with -1 is handy.

Here's an example:

In this example, 'Sam' is added (pushed), and then the topmost stack element, which is 'Sam', is peeked.

Practical applications of stacks in Ruby are plentiful. Here is one of them — reversing a string.

We will push all characters into a stack and then pop them out to get a reversed string!

A stack can be utilized to verify if parentheses in an expression are well-matched, i.e., every bracket has a corresponding pair. For example, parentheses in the string "()[{}]" are well-matched, while in the strings "([]()", ")()[]{}", "([)]", and "[{})" they are not.

Let's break down the solution into simple steps:

We start by creating a hash that maps each closing bracket to its corresponding opening bracket and an empty stack. Then, we iterate over each character paren in the string paren_string:

• If paren is an opening bracket, it gets appended to the stack.
• If paren is a closing bracket and the top element in the stack is the corresponding opening bracket, we remove the top element from the stack.
• If neither of the above conditions is met, we return false.

Finally, if the stack is empty (all opening brackets had matching closing brackets), we return true. If there are some unmatched opening brackets left, we return false.

Great job! Having covered the stack data structure, operations, and their Ruby applications is a commendable feat. Next up, you'll encounter practice exercises that will solidify your newly acquired knowledge. Dive into them and master Stacks in Ruby!