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Learn Data Structures and Algorithms in JavaScript

Big-O Practice Questions II

Practice analyzing algorithm efficiency using Big-O notation through advanced examples involving loops and recursive functions. Understand various growth patterns such as logarithmic, square root, and exponential, and learn how they influence time complexity. This lesson helps deepen your skills in evaluating how algorithms perform and scale with input size.

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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 ...