I am studying for heap data structure and in my textbook, it says,
"bottom up heap construction is asymptotically faster than incrementally inserting n entries into an initially empty heap. Intuitively, we are performing a single downheap operation at each position in the tree, rather than a single up-heap operation from each. Since more nodes are closer to the bottom of a tree than the top, the sum of the downward paths is linear, as shown in the following proposition."
But, I am not sure how this is intuitive.
I searched single down heaps and single up heaps but I cannot really find the differences between those two and I cannot see the one is better than the other one.
Can someone clarify this, please?
Thank you