/* XXX possibly buggy!  an example for testing.  can you find all the bugs? */

/* Linear and binary search
 * 15-122 Principle of Imperative Computation, Spring 2011
 * Frank Pfenning
 */

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

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

int linsearch(int x, int[] A, int n)
//@requires 0 <= n && n <= \length(A);
//@requires is_sorted(A, n);
/*@ensures (-1 == \result && !is_in(x, A, n))
        || ((0 <= \result && \result < n) && A[\result] == x);
  @*/
{
  for (int i = 0; i < n; i++)
    //@loop_invariant 0 <= i && i <= n;
    //@loop_invariant i == 0 || A[i-1] < x;
    {
      if (A[i] == x) return i;
      else if (A[i] > x) return -1;
    }
  return -1;
}

int binsearch(int x, int[] A, int n)
//@requires 0 <= n && n <= \length(A);
//@requires is_sorted(A, n);
/*@ensures (-1 == \result && !is_in(x, A, n))
        || ((0 <= \result && \result < n) && A[\result] == x);
  @*/
{
  int lower = 0;
  int upper = n - 1;
  while (lower < upper)
    //@loop_invariant 0 <= lower && lower <= upper && upper <= n;
    //@loop_invariant (lower == 0 || A[lower-1] < x);
    //@loop_invariant (upper == n || A[upper] > x);
    {
      int mid = lower + (upper-lower)/2; /* mid = (lower+upper)/2 could overflow! */
      //@assert lower <= mid && mid < upper;
      if (A[mid] == x) return mid;
      else if (A[mid] > x) upper = mid;
      else //@assert A[mid] < x;
	lower = mid+1;
    }
  return -1;
}