下面程序的时间复杂度是多少？

Question

What's the time complexity of this program? We calculate time complexity based on arbitrarily large input. In this example, the input string can be really huge but if it will not have spaces then it's just O(n). In case if the string has spaces it's going to be O(n * numberOfWords), can I consider this as O(n^2) time complexity? Thank you in advance!

    public static String revEachWord(String str) {
        String reversed = "";
        String[] words = str.split(" ");
        
        for(String word : words) {
            String reversedWord = "";
            for(int i = word.length() - 1; i >= 0; i--) {
                reversedWord += word.charAt(i);
            }

            reversed += reversedWord + " ";
        }
        
        return reversed.trim();
    }

Answer 1

Aleksey pointed out that it's O(numberOfWords * averageWordLength) . This is correct (if we ignore += for a moment), but a more general answer would be in terms of the length of the input, n . Since n = numberOfWords * averageWordLength , we can say that it's O(n) , or linear.

But that's not quite right. As chrylis pointed out in a comment, since you're using += to build your string, it would take much longer: O(n) for each copy and numberOfWords total copies, for O(n * numberOfWords) total, or O(n^2) in the worst case. (It might be even worse than that, actually; I haven't factored in the += in the nested loop.) Yikes. Better start using StringBuilder to get that nice O(n) running time.

Answer 2

O(numberOfWords * averageWordLength)