Welcome to the course on Data Structures and Algorithms. We begin by defining the primary goal of this subject: transforming you from a functioning coder into an efficient problem-solver.
- The primary objective is to master the concept of scale—how an algorithm's performance changes as the input size, $n$, grows. A solution that works for $n=10$ may crash for $n=10,000,000$.
- The DSA Goal: To design algorithms $f(n)$ that minimize resource consumption (time, memory) relative to the input size $n$.
- This pursuit of efficiency directly impacts real-world applications like Search Engines, GPS Routing, and Databases.
- We use Big O notation, $O(...)$, to formally analyze this relationship and determine the worst-case time complexity of any solution.
- Mastering DSA means choosing the $O(1)$ or $O(\log_2 n)$ solution over the $O(n^2)$ solution whenever possible.
Big O Notation Summary
| Notation | Name | Scalability |
|---|---|---|
| $O(1)$ | Constant | Excellent |
| $O(\log n)$ | Logarithmic | Excellent |
| $O(n)$ | Linear | Good |
| $O(n^2)$ | Quadratic | Poor |