Construct a binary heap of size 2N from two binary heaps each of size N in linear time?

Question

Constructing a binary heap of size N from scratch takes NlogN compares on an average and thus linearithmic time.

Given that two binary heaps of size N are already in place, how to construct a single binary heap containing all 2N keys, in linear time (uses linear number of compares)?

Answer 1

Constructing a binary heap of size N from scratch takes NlogN compares on an average and thus linearithmic time.

If you mean "constructing a binary heap of size N from an array of size N", then this is not necessarily true. You can do it in linear time. See Building a heap here.

So for your problem, if you have your two heaps in two arrays, concatenating the arrays and running the same algorithm on the resulting array will be linear.