I have a max binary heap implemented based on a complete binary tree. I need to insert multiple elements into the heap, where the current heap array has a length of n and the new elements array has a length of m.

I have two methods to consider:

1.Merge the new elements array directly with the heap array and then perform Floyd’s heap construction, which has a time complexity of O(m+n).

2.Insert each new element one by one into the heap, which results in a time complexity proportional to log(n) + log(n+1) + … + log(n+m).

When m is small, the second method is preferable, but when m is large, the first method is more efficient.

How can I determine a threshold or critical point to decide which method to use?