QuickSort stack overflow for sorted arrays (works for other data sets)

Question

So I tried my best to optimize my Quicksort algorithm to run as efficiently as possible, even for sorted or nearly sorted arrays, using a pivot that is the median of three values, and also using insertion sort for small partition sizes. I have tested my code for large arrays of random values and it works, but when I pass an already sorted array I get a stack overflow error(ironic because it led me to find this website). I believe this to be a problem with my recursive calls(I know that the partitioning works for other data sets at least), but I can't quite see what to change.

This is part of my first semester data structures class so any code review will help as well. Thanks.

public void quickSort(ArrayList<String> data, int firstIndex, int numberToSort) {
    if (firstIndex < (firstIndex + numberToSort - 1))
        if (numberToSort < 16) {
            insertionSort(data, firstIndex, numberToSort);
        } else {
            int pivot = partition(data, firstIndex, numberToSort);
            int leftSegmentSize = pivot - firstIndex;
            int rightSegmentSize = numberToSort - leftSegmentSize - 1;
            quickSort(data, firstIndex, leftSegmentSize);
            quickSort(data, pivot + 1, rightSegmentSize);
        }
}



public int partition(ArrayList<String> data, int firstIndex, int numberToPartition) {
    int tooBigNdx = firstIndex + 1;
    int tooSmallNdx = firstIndex + numberToPartition - 1;

    String string1 = data.get(firstIndex);
    String string2 = data.get((firstIndex + (numberToPartition - 1)) / 2);
    String string3 = data.get(firstIndex + numberToPartition - 1);
    ArrayList<String> randomStrings = new ArrayList<String>();
    randomStrings.add(string1);
    randomStrings.add(string2);
    randomStrings.add(string3);
    Collections.sort(randomStrings);
    String pivot = randomStrings.get(1);
    if (pivot == string2) {
        Collections.swap(data, firstIndex, (firstIndex + (numberToPartition - 1)) / 2);
    }
    if (pivot == string3) {
        Collections.swap(data, firstIndex, firstIndex + numberToPartition - 1);
    }
    while (tooBigNdx < tooSmallNdx) {
        while ((tooBigNdx < tooSmallNdx) && (data.get(tooBigNdx).compareTo(pivot) <= 0)) {
            tooBigNdx++;
        }
        while ((tooSmallNdx > firstIndex) && (data.get(tooSmallNdx).compareTo(pivot) > 0)) {
            tooSmallNdx--;
        }
        if (tooBigNdx < tooSmallNdx) {// swap
            Collections.swap(data, tooSmallNdx, tooBigNdx);
        }
    }
    if (pivot.compareTo(data.get(tooSmallNdx)) >= 0) {
        Collections.swap(data, firstIndex, tooSmallNdx);
        return tooSmallNdx;
    } else {
        return firstIndex;
    }
}

Answer 1

You can avoid stack overflows without changing your algorithm too much. The trick is to tail-call optimize on the largest partition and only use recursion on the smallest one. This usually means your have to change your if to a while . I can't really test java code right now, but it should look something like:

public void quickSort(ArrayList<String> data, int firstIndex, int numberToSort) {
    while (firstIndex < (firstIndex + numberToSort - 1))
        if (numberToSort < 16) {
            insertionSort(data, firstIndex, numberToSort);
        } else {
            int pivot = partition(data, firstIndex, numberToSort);
            int leftSegmentSize = pivot - firstIndex;
            int rightSegmentSize = numberToSort - leftSegmentSize - 1;

            //only use recursion for the smallest partition
            if (leftSegmentSize < rightSegmentSize) {
                quickSort(data, firstIndex, leftSegmentSize);
                firstIndex = pivot + 1;
                numberToSort = rightSegmentSize;
            } else {
                quickSort(data, pivot + 1, rightSegmentSize);
                numberToSort = leftSegmentSize;
            }
        }
}

This ensures that the call stack size will be at most O(log n) , because on each call you only use recursion on an array of at most n/2 size.

Answer 2

In your partition method you sometimes use a element outside the range:

String string1 = data.get(firstIndex);
String string2 = data.get((firstIndex + (numberToPartition - 1)) / 2);
String string3 = data.get(firstIndex + numberToPartition - 1);

(firstIndex + (numberToPartition - 1)) / 2 is not index of the middle element. That would be (firstIndex + (firstIndex + (numberToPartition - 1))) / 2

= firstIndex + ((numberToPartition - 1) / 2) .

In fact if firstIndex > n/2 (where n is the number of elements in the input) you're using a element with an index smaller than firstIndex . For sorted arrays that means you choose the element at firstIndex as pivot element. Therefore you get a recursion depth in

,

which causes the stack overflow for large enough inputs.