I read somewhere that the C++ STL parital_sort function (used to find k smallest numbers) has a running time complexity of O(n.logk).

It achieves this by going through the entire data, maintaining a k-sized max-heap, throwing away the top whenever size exceeds k, and in the end printing the k remaining elements from the heap.

Can't an n-sized min-heap be used instead and then the first k smallest numbers simply extracted from it. I understand it won't remain in-place and would require additional memory.

But time complexity wise, it would take O(n+k.logn) which is better than O(n.logk), right? (assuming k to be any number smaller than n)

Then why is the O(n.logk) version preferred? Why is it mentioned everywhere and used by the std template?