Complexity Analysis: What's the Cost?

Time Complexity: A Closer Look

Our choice to employ the built-in sorting methods contributes the most to our time complexity. Sorting operations generally have a time complexity of $O\left(n\log n\right)$. All other operations we've performed—such as string manipulation and array joining—are more or less constant time operations, leaving sorting as the primary driver of computational cost.

Space Complexity: How Roomy?

In terms of space, we've created additional arrays or lists to hold the sorted characters from each string. This memory allocation grows linearly with the size of the input strings, resulting in a space complexity of $O\left(n\right)$.

The Final Tally

So, there you have it: the complete breakdown of our anagram detection algorithm. It's efficient in terms of space, but the sorting step does add a logarithmic factor to the time complexity. Keep these considerations in mind when weighing this method against alternatives for your specific use case.