What techniques do you apply when analyzing the complexity of an algorithm?

When analyzing the complexity of an algorithm, I start with Big O notation to assess the worst-case scenario. For example, at my last internship, I had to optimize a sort function and realized it was O(n^2). I managed to refine it to O(n log n) by switching to merge sort. I also look into best and average cases for a fuller understanding. Moreover, I use tools like profilers to gather runtime information to see the impact of the algorithm in practice, especially memory usage, which I found quite beneficial on a previous project where we had to process large datasets without overloading the server.

In my previous roles, I've employed several techniques to assess algorithm complexity. Starting with Big O notation, I evaluate the time and space complexity as in my last project, where I reduced a search algorithm from O(n^2) to O(log n) using binary search principles. I make sure to consider empirical analysis too, by implementing code profiling to track execution time, particularly useful in my past experience with an image processing task. Besides, I've used domain knowledge to tailor algorithms to specific problems, like optimizing a path-finding algorithm in a game I worked on by applying heuristic approaches. I've learned that collaborating with peers is crucial for refining these analyses, and I regularly participate in code reviews to both learn and contribute insights on algorithm efficiency.

Throughout my career, rigorous analysis of algorithm complexity has been a cornerstone of my approach. For instance, I start with theoretical analysis, using Big O to gauge worst-case scenarios, as I did when refactoring a critical module's algorithm, reducing its complexity from O(n^2) to O(n log n), thus enhancing performance significantly. I support this with empirical techniques, such as time profiling in real-world scenarios, which proved invaluable when I optimized a video encoding algorithm under memory constraints at my last job. To get a nuanced understanding, I also explore Big Omega and Theta for best and average cases respectively, which was pivotal when working on a machine learning data sorting task. I engage with peers for insights, optimizing through collective expertise as in our project retrospectives that delved into performance trade-offs. I'm proactive in upskilling, having learned new profiling tools to keep abreast of emerging best practices, which has readied me for adapting algorithms to diverse and evolving technological landscapes.