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/***ITERATIVE VERSION*****/
int binarySearch(int [] a, int x){
  //set limits and midpoint.
  int low = 0;
  int high = a.length-1;
  int mid;
  while(low <= high){//too small
    mid(low+high) / 2;
    if(a[mid] < x){
      low = mid + 1;
    }else if(a[mid] > x){//too large
      high = mid - 1;
    }else{//FOUND!!
      return mid;
    }
  }
  return -1; //Error
}

/***RECURSIVE VERSION*****/
int binarySearchRecursive(int[] a, int x, int low, int high) {
  if(low > high) return -1; // Error
  int mid = (low + high) / 2;
  if(a[mid] < x){//too small
    return binarySearchRecursive(a, x, mid+1, high);
  }else if(a[mid] > x){//too large
    return binarySearchRecursive(a, x, low, mid-1);
  }else{//FOUND!!
    return mid;
  }
}