C Programming: Pointer arithmetics instead of index operations

Array index access a[i] equals pointer arithmetic *(a + i).

First why do want to do pointer arithmetic? Pointer arithmetic is simply a[i] = *(a + i) which gives no performance improvement for your program

I think for performance improvement what you need is references because that is the best practice to do so. Check the revised code.

#include<stdio.h>
#define N 10

void quicksort(int a[], int low, int high);
int split(int a[], int low, int high);

int main(void)
{
  int a[N], i;

  printf("Enter %d numbers to be sorted: ", N);
  for (i = 0; i < N; i++)
    scanf("%d", &a[i]);

  quicksort(&a[0], 0, N - 1);

  printf("In sorted order: ");
  for (i = 0; i < N; i++)
    printf("%d ", a[i]);
  printf("\n");

  return 0;
}

void quicksort(int *a, int low, int high)
{
  int middle;

  if (low >= high) return;
  middle = split(a, low, high);
  quicksort(a, low, middle - 1);
  quicksort(a, middle + 1, high);
}

int split(int *a, int low, int high)
{
  int part_element = a[low];

  for (;;) {
    while (low < high && part_element <= a[high])
      high--;
    if (low >= high) break;
    a[low++] = a[high];

    while (low < high && a[low] <= part_element)
      low++;
    if (low >= high) break;
    a[high--] = a[low];
  }

  a[high] = part_element;
  return high;
}

I'm wondering if the goal here is to redefine the sort function:

quicksort(int *low, int *high)
{
int *middle;
    if((high - low) == 0)
        return;
    middle = low + ((high - low)/2);
    /* ... */
}