//  supporting functions - for ordinary heaps

void child (int i, int & lc, int & rc)
//  find the two children of i
//  return their positions in the two reference parameters
{  lc = 2 * i + 1;
   rc = 2 * i + 2;
}

int parent (int i)
//  return the position of the parent of i
{  return (i-1)/2;
}