5258 Goodrich, Michael.6377, arXiv : 1110.4428, CiteSeerX.7812, doi :.1007/ X_5, isbn Fredman, Michael Lawrence (July 1999).

Fredman, Michael Lawrence ; Tarjan, Robert.The next two elements of the array contain its children.Since logn/2(logn)1displaystyle log n/2(log n)-1, a constant factor (half) of these insertions are within a constant factor of the maximum, so asymptotically we can assume kndisplaystyle kn ; formally the time is nO(log n)-O(n)O(nlog n).

(2012 "Elementary Yet Precise Worst-Case Analysis of Floyd's Heap-Construction Program Fundamenta Informaticae, IOS Press, 120 (1 7592, doi :.3233/FI.Different types of heaps implement the operations in different ways, but notably, insertion is often done by adding the new element at the end of the heap in the first available free space.K-way merge : A heap data structure is useful to merge many already-sorted input streams into a single sorted output stream.