Comparing algorithms with big O

Tip: When comparing time complexities, it is important to consider the growth rates as the input size approaches infinity. This is called asymptotic analysis. While it may be tempting to compare the running times for specific values of $n$, this can sometimes lead to misleading conclusions. For example, there may arise some confusion between $O(3^n)$ and $O(n^4)$ depending on the value you use to test.

Instead, focus on the highest order term that contributes the most to the growth rate. Keep in mind that time complexity provides an upper bound on the growth rate, and exceptions or edge cases with specific values of $n$ may not accurately represent the overall trend. So, analyze the dominant terms and consider how they scale for large input sizes to determine the relative speeds of algorithms.