Heapsort 6.1-1
2008-11-01 20:46
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Problem:
What are the minimum and maximum numbers of elements in a heap of height h?
My answer:
The height of a node in a heap is the number of edges of the longest simple path from the node downward to a leaf, so the height of a heap is the height of its root.
When a heap of height h is a full binary tree, it has the maximum number of elements, which is 2^(h+1)-1.
And the minimum number of a heap with height h is 2^(h).
What are the minimum and maximum numbers of elements in a heap of height h?
My answer:
The height of a node in a heap is the number of edges of the longest simple path from the node downward to a leaf, so the height of a heap is the height of its root.
When a heap of height h is a full binary tree, it has the maximum number of elements, which is 2^(h+1)-1.
And the minimum number of a heap with height h is 2^(h).
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