Operating Stacks in Python: Practical Problem-Solving Approach

Problem 1: Are Brackets Balanced?

Let's start with a common coding challenge - checking if the brackets in a string are balanced. Imagine that the string is the source code of a software application, and these brackets are the open and close statements for loops, if-else conditions, or function blocks in the source code. For the code to be valid and runnable, every open statement (bracket) must have a corresponding close statement (bracket) in the proper order.

Problem 1: Problem Actualization

To make this problem more relatable, let's consider this real-world scenario. You are part of a team developing a text editor for programming languages. As a value-added feature, you want to provide real-time feedback to the users of your text editor about the number of unbalanced brackets in their code to assist them in avoiding syntax errors. This problem accurately mimics such a feature where we are given a string of code, and our task is to check if all the brackets in the code are balanced.

Problem 1: Naive Approach and Its Limitations

If we consider a simple way to approach this problem, we could initialize a counter variable for each type of bracket (parentheses, braces, and square brackets), increment the counters when we encounter an opening bracket, and decrement it when we get a closing bracket. Although this approach checks whether we have a closing bracket for every opening bracket, it completely misses one critical aspect - the order of brackets. For the brackets to be considered balanced, every closing bracket must correspond to the most recently opened bracket of the same type, which is not checked in this approach.

Problem 1: Efficient Approach Explanation

An efficient way to solve this problem is by using a stack data structure. The stack follows the LIFO (Last In, First Out) principle, which makes it highly suitable when we want to track the opening and closing brackets' order, as the most recently opened bracket needs to be closed first before we move on to the next opening bracket.

Problem 1: Solution

Let's break down the solution into simple steps:

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

• If character is an opening bracket, it gets appended to the stack.
• If character 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.

This way, the stack helps us keep track of all opening brackets and ensures that every one of them gets their closing mate.

def are_brackets_balanced(input_str):
    brackets = set(["(", ")", "[", "]", "{", "}"])
    bracket_map = {"(": ")", "[": "]", "{": "}"}
    open_par = set(["(", "[", "{"])
    stack = []

    for character in input_str:
        if character not in brackets:
            continue

        if character in open_par:
            stack.append(character)
        elif stack and character == bracket_map[stack[-1]]
            stack.pop()
        else:
            return False

    return len(stack) == 0

Problem 2: Reverse a String

Continuing on to the next problem, we have the task of reversing the characters of a string using a Stack. This is quite a common task that you will often see in coding tests or interviews because it is a good demonstration of understanding the rules and principles of the Stack data structure.

Problem 2: Problem Actualization

Imagine you're tasked with building a function in which a user can input a string, and you need to display the reversed string as part of the application features. Or, as a more advanced example, in computer networks, stack buffers are often used to reverse the order of packets that arrive out of order. Understanding how to reverse the order of elements using a Stack is a crucial skill.

Problem 2: Naive Approach and its limitations

A straightforward approach for this problem would be using Python's built-in string slicing: input_str[::-1]. While this is actually an efficient solution, we'll explore using a stack to better understand how the LIFO principle can be applied to solve this problem. This helps build a foundation for more complex problems where stacks are truly the optimal solution.

Problem 2: Efficient Approach Explanation

Using a Stack, we can reverse elements by leveraging its LIFO property. The strategy is straightforward: push all the characters to a stack and then pop them out. As a result, we get the reversed string. This helps demonstrate a practical application of stack operations.

Problem 2: Solution

def reverse_string(input_str):
    stack = list(input_str)
    result = ''

    while len(stack):
        result += stack.pop()

    return result

The list(input_str) breaks the string into characters and simulates a stack where each letter is stacked on top of the previous one. Then result += stack.pop() pops out the characters from the top of the stack (which is the reversed order as they were put in) and appends them to the result string. In the end, we get the string in reverse order.

Problem 3: Postfix Expression Evaluation

Now, let's move on to another classic algorithmic problem - evaluating postfix expressions. In simple terms, a postfix expression is an arithmetic expression where operators are placed after their operands. For example, the expression 2 3 + is a simple postfix expression, which equals 5 when evaluated.

Problem 3: Problem Actualization

You've been given a task at work to build a small calculator application. This calculator should be capable of evaluating postfix expressions, as this form of notation eliminates the need for parentheses to indicate the execution order. This problem perfectly fits into such a scenario where you're given a postfix expression as a string; your task is to evaluate the expression and return the result.

Problem 3: Naive Approach and Its Limitations

One might think of directly parsing the expression from left to right and performing the operations. However, this won't work because it ignores one fundamental aspect of postfix expressions – an operator applies to the most recently seen numbers that haven't been used yet. This basic understanding of postfix expression pushes us to think about a certain data structure that we've encountered before.

Problem 3: Efficient Approach Explanation

The evaluation of postfix expressions can be efficiently done using a stack data structure. The Stack follows the LIFO (Last In, First Out) principle, which is fitting in this scenario because we process the most recently encountered yet unused numbers first.

Problem 3: Solution

The solution process is as follows:

• We create an empty stack.
• Then, we iterate over each character operand in the expression.
  • If operand is a number, we push it onto the stack.
  • If operand is an operator, we pop two numbers from the stack, perform the operation, and push the result back onto the stack.
• After we have processed all characters of the expression, the stack should contain exactly one element, the result of the expression.

def evaluate_postfix(expression):
    stack = []
    for element in expression.split(' '):
        if element.isdigit():
            stack.append(int(element))
            continue

        operand_2 = stack.pop()
        operand_1 = stack.pop()

        if element == '+':
            stack.append(operand_1 + operand_2)
        elif element == '-':
            stack.append(operand_1 - operand_2)
        elif element == '*':
            stack.append(operand_1 * operand_2)
        elif element == '/':
            stack.append(operand_1 / operand_2)

    return stack[0]