/* Selection sort (quadratic)
 * Frank Pfenning, Fall 2010
 */

bool beloweq(int x, int[] A, int lower, int upper)
//@requires 0 <= lower && lower <= upper && upper <= \length(A);
{ int i;
  for (i = lower; i < upper; i++)
    //@loop_invariant lower <= i && i <= upper;
    if (!(x <= A[i])) return false;
  return true;
}

bool is_sorted(int[] A, int lower, int upper)
//@requires 0 <= lower && lower <= upper && upper <= \length(A);
{ int i;
  for (i = lower; i < upper-1; i++)
    //@loop_invariant lower == upper || (lower <= i && i <= upper-1);
    if (!(A[i] <= A[i+1])) return false;
  return true;
}

void swap(int[] A, int i, int j)
//@requires 0 <= i && i < \length(A);
//@requires 0 <= j && j < \length(A);
// modifies A[i], A[j];
//@ensures A[i] == \old(A[j]) && A[j] == \old(A[i]);
{ int tmp = A[i];
  A[i] = A[j];
  A[j] = tmp;
}

/* Selection sort (in place)
 * Result is permutation because we only swap elements of A
 * Complexity is quadratic
 */
void selsort(int[] A, int lower, int upper)
//@requires 0 <= lower && lower <= upper && upper <= \length(A);
//@ensures is_sorted(A, lower, upper);
{ int i; int j;
  for (i = lower; i < upper; i++) // i = upper-1 is redundant, but inv's are easier..
    //@loop_invariant lower <= i && i <= upper;
    //@loop_invariant is_sorted(A, lower, i);
    //@loop_invariant i == lower || beloweq(A[i-1], A, i, upper);
    { int min = i;
      for (j = i+1; j < upper; j++)
	//@loop_invariant i+1 <= j && j <= upper;
	//@loop_invariant beloweq(A[min], A, i, j);
	if (A[j] < A[min]) min = j;
      // swap A[i] and A[min]
      swap(A, i, min);
    }
}