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Learn Data Structures and Algorithms in JavaScript

Big-O Practice Questions II

Explore advanced Big-O notation practice by analyzing complex loops and recursive patterns. Learn to accurately determine time complexity, including logarithmic, square root, and exponential growth, enhancing your ability to evaluate algorithm efficiency.

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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.

Javascript (babel-node)
for (let i = 0; i < n; i++) {
    let j = 1;
    while (j < i) {
        j *= 2;
    }
}

Explanation

The inner loop doubles j each time. So for a given ...