Lesson 1: Introduction to Computational Thinking: A New Way to Solve Problems

Learning Objectives Analyze a complex problem and decompose it using recursive thinking. Define and identify the base case and recursive step in a recursive algorithm. Explain the concept of algorithmic efficiency and compare two simple algorithms for the same task. Apply a heuristic approach to find an approximate solution to a complex problem. Model a problem's state space to visualize potential solutions. Differentiate between an optimal solution and a heuristic solution. How does a GPS find a fast route in a huge city almost instantly, even if it's not the absolute shortest one? 🗺️ It's not magic, it's advanced computational thinking! In this lesson, we'll move beyond the four basic pillars of computational thinking. You will learn advanced stra...

TermDefinitionExample RecursionA problem-solving technique where a function calls itself to solve smaller, identical versions of the same problem until it reaches a simple 'base case' that can be solved directly.To calculate a factorial (e.g., 5!), you can define factorial(n) as n * factorial(n-1), with the base case being factorial(1) = 1. The function calls itself with a smaller number until it hits 1. Algorithmic EfficiencyA measure of how many resources (like time or memory) an algorithm uses in relation to the size of its input. It helps us compare which algorithm is 'better' for a given task.Finding a name in a sorted phone book by checking every single page from the start (linear search) is much less efficient than opening to the middle and repeatedly narrowing...

The Recursive Pattern function solve(problem): if problem is a base case: return solution to base case else: break problem into subproblem sub_solution = solve(subproblem) return combine sub_solution with remaining work Use this pattern for problems that can be broken down into smaller, self-similar versions, like calculating factorials, traversing tree data structures, or the Tower of Hanoi puzzle. The Greedy Algorithm Strategy 1. Start with an empty solution. 2. At each step, examine all available choices. 3. Make the choice that looks best at the current moment (the 'locally optimal' choice). 4. Add this choice to your solution and repeat until the problem is solved. Use this when you need a fast, 'good enough' solution and finding...