How efficient is the collection.sort() function?

Question

How fast is the collection.sort() function in Java? What algorithm was used? I came across this function in this answer that sorts a list in descending order:

public static void main(String arg[])
{
    List<Double> testList=new ArrayList();

   /*Adding The values to the List*/

    testList.add(0.5);
    testList.add(0.2);
    testList.add(0.9);
    testList.add(0.1);
    testList.add(0.1);
    testList.add(0.1);
    testList.add(0.54);
    testList.add(0.71);
    testList.add(0.71);
    testList.add(0.71);
    testList.add(0.92);
    testList.add(0.12);
    testList.add(0.65);
    testList.add(0.34);
    testList.add(0.62);

    /*Declare a new List for storing sorted Results*/

    List<Double> finalList=new ArrayList();


    while(!testList.isEmpty()) //perform operation until all elements are moved to new List
    {
        double rank=0;
        int i=0;
            for(double d: testList)
            {
                if(d>=rank)
                {
                    rank=d;
                }

            }
            finalList.add(rank);

            testList.remove(testList.indexOf(rank));

     }
    for(double d : finalList) {
        System.out.println(d);
    }

}

I think this runs in O(n(n-1)) time and it would be pretty inefficient for a large list. I don't believe this is how Collections.sort() was created considering how inefficient it is.

Answer 1

From the Documentation on Collection's method 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.

It means that is O(n log n) in the worst case. So YES it's very fast (even in the worst case), much faster than a O(n^2) sorting algorithm.