排序：计算操作并评估运行时复杂性，

Question

I am trying to use the system clock (in milliseconds) to count operations and assess the run-time complexity, ( O(N) , O(N^2) , O(1) ) for Collections.sort() . I have somehow come to conclusion that Collections.sort() is O. But from what I see in my code, it is not. How can I improve my code below.

public class TestTime {
    public static void main(String[] args) throws FileNotFoundException {
        Random generator = new Random();

        ArrayList<Integer>numbers = new ArrayList<Integer>();

        for (int n = 1000; n < 1000000; n += 2000) {
            numbers.clear();

            for (int i = 0; i < n; i++) {
                numbers.add(generator.nextInt(100) + 1);
            }

            long startTime1 = System.currentTimeMillis();
            Collections.sort(numbers);
            long endTime1 = System.currentTimeMillis();
            System.out.println( n +"," +(endTime1-startTime1));
        }

        System.out.println("Completed Sorting");
    }
}

Answer 1

Look at the implementation note for Collections.sort() . It specifies that Collections.sort implementation should use iterative merge sort :

Implementation note: This implementation is a stable, adaptive, iterative mergesort that requires far fewer than n lg(n) comparisons when the input array is partially sorted, while offering the performance of a traditional mergesort when the input array is randomly ordered. If the input array is nearly sorted, the implementation requires approximately n comparisons. Temporary storage requirements vary from a small constant for nearly sorted input arrays to n/2 object references for randomly ordered input arrays.

This should give you an estimate of the runtime conplexity of Collections.sort(). It will vary depending on how much partially sorted your list is. The upper bound being O(n logn)