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    $\begingroup$ Taking down the heap is not really the reverse of heapify, it is the reverse of starting with an empty heap and adding elements one by one. Both of these are n log n $\endgroup$ Commented Mar 21, 2020 at 13:28
  • $\begingroup$ @MatthewC building a heap is really O(n). See en.wikipedia.org/wiki/Binary_heap#Building_a_heap $\endgroup$ Commented Mar 21, 2020 at 13:52
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    $\begingroup$ What do you mean by "take down"? Note that building heaps in linear time is not accomplished by repeated "push". $\endgroup$ Commented Mar 21, 2020 at 16:27
  • $\begingroup$ @nonpolarity That is heapify (makeHeap, or whatever you like to call the process of transforming an array into a heap). $\endgroup$ Commented Mar 21, 2020 at 16:51