Quicksort Algorithm (Cormen) gives Stackoverflow

Question

i implemented the Quick Sort Algorithm which given pseudo code in Introduction to Algorithms (Cormen, 3rd Edition) 7.1

When i tried algorithm with small sized arrays, result is true. But when i tried with N=50000 and array is already sorted like this; N = {1, 2, 3, ..., 50000};

It gives StackOverflowError. I think it's happening because the function recurse itself 50000 times. QuickSort(A, 0, 49999) => QuickSort(A, 0, 49998) => QuickSort(A, 0, 49997)... so go on.

Can i solve this problem? Or should i use different pivot position?

Here is my code;

public void sort(int[] arr){ QuickSort(arr, 0, arr.length - 1); }

private void QuickSort(int[] A, int left, int right){
    if(left < right){
        int index = Partition(A, left, right);
        QuickSort(A, left, index - 1);
        QuickSort(A, index + 1, right);
    }
}

private int Partition(int[] A, int left, int right){
    int pivot = A[right];
    int wall = left-1;
    for(int i=left; i<right; i++){
        if(A[i] <= pivot){
            Swap(A, ++wall, i);
        }
    }
    Swap(A, wall + 1, right);
    return wall + 1;
}

private void Swap(int[] A, int x, int y){
    int keeper = A[x];
    A[x] = A[y];
    A[y] = keeper;
}

Answer 1

Yes, this pivot scheme is not right choice for sorted array. It causes very unbalanced partition, leads to O(N^2) complexity and very deep recursion level, as you noticed.
There are some approaches to improve this behavior. For example, you can use random index for pivot like pivotIdx = start + rand() % (end-start+1);, or choose median-of-three method (median of the first, last and middle elements in index range).

P.S. An option to avoid stack overflow - call recursion for shorter segment at first, then for longer one.

https://en.wikipedia.org/wiki/Quicksort#Choice_of_pivot