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Learn Data Structures and Algorithms in Java

Big-O Practice Questions II

Explore advanced Big-O notation patterns by analyzing loops and recursive functions. Learn to evaluate algorithm efficiency involving logarithmic, square root, and exponential growth, deepening your understanding of performance scaling.

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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.

Java 25
for (int i = 0; i < n; i++) {
    int j = 1;
    while (j < i) {
        j *= 2;
    }
}

Explanation

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