/**
 * Quicksort
 *
 * 15-122 Principles of Imperative Computation
 */

int partition(int[] A, int lo, int pi, int hi)
//@requires 0 <= lo && lo <= pi && pi < hi && hi <= \length(A);
//@ensures lo <= \result && \result < hi;
//@ensures ge_seg(A[\result], A, lo, \result);
//@ensures le_seg(A[\result], A, \result, hi);
{
  int pivot = A[pi];
  swap(A, pi, lo);
  int left = lo + 1;
  int right = hi;

  while (left < right)
  //@loop_invariant lo <= left && left <= right && right <= hi;
  //@loop_invariant ge_seg(pivot, A, lo, left);
  //@loop_invariant le_seg(pivot, A, right, hi);
  //@loop_invariant pivot == A[lo];
  {
    if (A[left] <= pivot) { 
      left++;
    } else {
      //@assert A[left] > pivot;
      swap(A, left, right-1);
      right--;
    }
  }

  //@assert left == right;
  swap(A, lo, left-1);
  return left-1;
}

void sort(int[] A, int lo, int hi)
//@requires 0 <= lo && lo <= hi && hi <= \length(A);
//@ensures is_sorted(A, lo, hi);
{
  if (hi - lo <= 1) return;
  int pi = lo + (hi - lo)/2;
  //@assert lo <= pi && pi < hi;
  int mid = partition(A, lo, pi, hi);
  sort(A, lo, mid);
  sort(A, mid+1, hi);
  return;
}