带插入的Quicksort排序完成-我在哪里出错？

Question

I am working on a project for a class. We are to write a quick-sort that transitions to a insertion sort at the specified value. Thats no problem, where I am now having difficulty is figuring out why I am not getting the performance I expect.

One of the requirements is that it must sort an array of 5,00,000 ints in under 1,300 ms (this is on standard machines, so CPU speed is not an issue). First of all, I can't get it to work on 5,000,000 because of a stack overflow error (too many recursive calls...). If I increase the heap size, I am still getting a lot slower than that.

Below is the code. Any hints anyone?

Thanks in advance

public class MyQuickSort {

    public static void sort(int [] toSort, int moveToInsertion)
    {
        sort(toSort, 0, toSort.length - 1, moveToInsertion);
    }

    private static void sort(int[] toSort, int first, int last, int moveToInsertion)
    {
        if (first < last)
        {
            if ((last - first) < moveToInsertion)
            {
                insertionSort(toSort, first, last);
            }
            else
            {
                int split = quickHelper(toSort, first, last);
                sort(toSort, first, split - 1, moveToInsertion);
                sort(toSort, split + 1, last, moveToInsertion);
            }
        }
    }

    private static int quickHelper(int[] toSort, int first, int last)
    {
        sortPivot(toSort, first, last);
        swap(toSort, first, first + (last - first)/2);
        int left = first;
        int right = last;
        int pivotVal = toSort[first];
        do
        {
            while ( (left < last) && (toSort[left] <= pivotVal)) 
            {
                left++;
            }

            while (toSort[right] > pivotVal) 
            {
                right--;
            }

            if (left < right) 
            { 
                swap(toSort, left, right); 
            }

        } while (left < right);

        swap(toSort, first, right);


        return right;
    }

    private static void sortPivot(int[] toSort, int first, int last)
    {
        int middle = first + (last - first)/2;

        if (toSort[middle] < toSort[first]) swap(toSort, first, middle);

        if (toSort[last] < toSort[middle]) swap(toSort, middle, last);

        if (toSort[middle] < toSort[first]) swap(toSort, first, middle);

    }

    private static void insertionSort(int [] toSort, int first, int last)
    {
         for (int nextVal = first + 1; nextVal <= last; nextVal++)
            {
                int toInsert = toSort[nextVal];
                int j = nextVal - 1;
                while (j >= 0 && toInsert < toSort[j])
                {
                    toSort[j + 1] = toSort[j];
                    j--;
                }
                toSort[j + 1] = toInsert;
            }
    }

    private static void swap(int[] toSort, int i, int j)
    {
        int temp = toSort[i];
        toSort[i] = toSort[j];
        toSort[j] = temp;
    }

}

Answer 1

I haven't tested this with your algorithm, and I don't know what kind of data set you're running with, but consider choosing a better pivot than the leftmost element. From Wikipedia on Quicksort:

Choice of pivot In very early versions of quicksort, the leftmost element of the partition would often be chosen as the pivot element. Unfortunately, this causes worst-case behavior on already sorted arrays, which is a rather common use-case. The problem was easily solved by choosing either a random index for the pivot, choosing the middle index of the partition or (especially for longer partitions) choosing the median of the first, middle and last element of the partition for the pivot

Answer 2

Figured it out.

Actually, not my sorts fault at all. I was generating numbers between the range of 0-100 (for testing to make sure it was sorted). This resulted in tons of duplicates, which meant way to many partitions. Changing the range to min_int and max_int made it go a lot quicker.

Thanks for your help though :D

Answer 3

When the input array is large, its natural to expect that recursive functions run into stack overflow issues. which is what is happening here when you try with the above code. I would recommend you to write iterative Quicksort using your own stack. It should be fast because there is no stack frame allocations/deallocations done at run time. You won't run into stack overflow issues also. Performance also depends on at what point you are running insertion sort. I don't have a particular input size where insertion sort performs badly compared to quicksort. I would suggest you to try with different sizes and I'm sure you will notice difference.

You might also want to use binary search in insertion sort to improve performance. I don't know how much it improves when you run on smaller input but its a nice trick to play.

I don't want to share code because that doesn't make you learn how to convert recursive quicksort to iterative one. If you have problems in converting to iterative one let me know.