/* Search, as developed in class
 * 15-122, Fall 2010, CMU
 */

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

bool is_sorted(int[] A, int n)
//@requires 0 <= n && n <= \length(A);
{ int i;
  for (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;
}

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

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