Can someone plz explain me max-heap building in O(n) time?

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I am learning data structure & algorithm. I want to understand how to build max-heap in O(n) time complexity. I have read several articles, still it is not clicking in my mind. I am looking for something in plain english & less technicality. Please share any useful resource you have. Or if you have time, plz explain here.

What I have tried:

Read several articles, but still it looks to me as O(n log n).

Posted 21-Aug-22 4:08am

Member 15743445

Updated 21-Aug-22 6:50am

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2 solutions

Solution 1

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Can someone plz explain me max-heap building in O(n) time?

Extremely simple, you don't. It does not exist.
Technically, it is O(n)=n, and this means that you need a fixed amount of work/time to get the final position in the heap.
For O(n)=n log n, this means that the amount of work/time needed to get the final position depends on the amount of data already in heap.

[Update]
In fact, it is possible for the very restricted conditions as explained in solution 3.

Posted 21-Aug-22 6:50am

Patrice T

Updated 22-Aug-22 23:33pm

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lalnu · Accepted Answer · 2022-08-22T01:22:00

O(n) time binary heap building is possible using bottom-up approach. But heap elements should be predefined & fixed. If new elements keep coming, then bottom-up approach won't work with same complexity. You can try StackOverFlow site. It contains similar questions & answers I believe. Or you can also try this article Building Binary Heap In O(n) Worst Time Complexity Explained – W3 Spot[^] . It compares both top-down & bottom-up approaches with time complexity analysis. There are diagrams & examples in the post which should be simple enough to understand.