Big-O Practice Questions II
Explore advanced Big-O notation patterns involving loops and recursion to understand how different growth rates affect algorithm time complexity. Learn to analyze nested logarithmic loops, shrinking inputs, square root behaviors, and various recursive structures. This lesson sharpens your ability to evaluate algorithm efficiency and scalability with practical examples.
In this lesson, we’ll practice applying Big-O notation to more advanced patterns involving loops and recursion, focusing on how different growth rates impact time complexity. Instead of guessing, we analyze how many times operations run, especially in cases like logarithmic growth, shrinking inputs, and recursive calls.
We’ll explore patterns such as log-based loops, square root behavior, fast-growing loops, and different types of recursion. These concepts help develop a deeper understanding of algorithm efficiency and how algorithms scale with input size.
Question 1: Increasing inner loop (Log inside loop)
This question analyzes a loop where the inner loop grows exponentially. It focuses on how logarithmic behavior appears inside nested loops.
Explanation
The inner loop doubles j each time. So for a given