$2^h-1$ is the inner nodes and also that is construed according to the understood fact. But since nowhere except CLRS mentions heaps to it is in a **Nearly finish Binary Tree** anywhere it is pointed out as a complete Binary Tree.

You are watching: What are the minimum and maximum number of elements in a heap of height h?

The maximum number of elements have the right to be quickly computed:$$sum_i=0^h 2^i = 2^h+1-1$$

But i cannot get the allude of computing the minimum number of elements:Should the be:$$2^h+1$$ because that $0$ or $2$ youngsters property

Or need to it be:$$2^h$$ for $0$ or $1$ children property

Reference1: https://walkccc.github.io/CLRS/Chap06/6.1/#61-1

Reference2: HeapSort

Thank you.

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asked Jun 19 "20 in ~ 9:20

Sachin BahukhandiSachin Bahukhandi

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A heap of elevation $h$ is complete up to the level in ~ depth $h-1$ and also needs to have at least one node ~ above level $h$.

Therefore the minimum total number of nodes have to be at least$sum_i=0^h-1 2^i + 1 = 2^h-1 + 1= 2^h.$, and this tight due to the fact that an heap with $2^h$ nodes has height $h$.

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reply Jun 19 "20 in ~ 11:32

StevenSteven

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I know there"s currently an welcomed answer, yet for those who"ve got the exact same question and also are still a little bit perplexed (as i was), or sth is unclear, clock this crystal clearexplanation till the end.

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answered might 12 in ~ 17:44

Aarush AggarwalAarush Aggarwal

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