Question

Preface: This is not a homework question. I’m going through an algos book in Python.

If I have the following code to solve an anagram.

Public bool anagram (string a, string b) {
    return sort(a) == sort(b);
}

Let’s say the sorting algorithm is merge sort which is O(n log n). Since I have to do it twice does the time complexity become O(n^2 log n)?

Answer 1

No, since you need to do it a constant number of times, the complexity remains O(n log n).

Note that there is one more operation that you need to perform – namely, comparing strings. However, it’s O(n), and O(n + n log n) remains O(n log n).

Also note that your n is “underdefined”: you should say that n is max(a.length, b.length)