Building heaps and heapsort using linked list I know that linked list is not a appropriate data structure for building heaps but I am interested in knowing the time complexity of building heaps and heapsort using linked list.

One of the answers here (https://stackoverflow.com/a/14584517/5841727) says that heap sort can be done in O(nlogn) using linked list which is same as with arrays.

For building a heap, I think that heapify operation would cost  O(n) time in linked list and we would need (n/2) heapify operations leading to time complexity of O(n^2). Is it correct?

Also, can someone please tell how to achieve O(nlogn) complexity (for heap sort ) using linked list ?
doubly linked list can be sorted by heapsort with O(nlogn) time, O(1) space complexity, but not singly linked-list.
merge sort can apply to singly linked list with O(nlogn) time, O(n) space complexity.