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

void merge(int[] A, int lo, int mid, int hi)
//@requires 0 <= lo && lo < mid && mid < hi && hi <= \length(A);
//@requires is_sorted(A, lo, mid) && is_sorted(A, mid, hi);
//@ensures is_sorted(A, lo, hi);
{ 
  int[] B = alloc_array(int, hi-lo);
  int i = lo; 
  int j = mid; 
  int k = 0;

  while (i < mid && j < hi)
  //@loop_invariant lo <= i && i <= mid;
  //@loop_invariant mid <= j && j <= hi;
  //@loop_invariant k == (i - lo) + (j - mid);
  {
    if (A[i] <= A[j]) {
      B[k] = A[i]; i++;
    } else {
      B[k] = A[j]; j++;
    }
    k++;
  }

  //@assert i == mid || j == hi;
  // Warning, loop invariants for these loops have been omitted!
  while (i < mid) { B[k] = A[i]; i++; k++; }
  while (j < hi) { B[k] = A[j]; j++; k++; }
  for (k = 0; k < hi-lo; k++) { A[lo+k] = B[k]; }
}


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 mid = lo + (hi-lo)/2;
  sort(A, lo, mid); //@assert is_sorted(A, lo, mid);
  sort(A, mid, hi); //@assert is_sorted(A, mid, hi);
  merge(A, lo, mid, hi);
  return;
}