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Chapter 6.1

Table of Contents

ch6.1

6.1-1

In a heap of height \(h\), the minimum numbers of elements is \(2^h\), the maximum numbers of elements is \(2^{h+1} - 1\).

6.1-2

We know that \(2^h \leq n \leq 2^{h+1} - 1\), so that the height is \(h = \lfloor \lg n \rfloor\).

6.1-3

All the nodes in the subtree derive from the root, so that the root has the largest value in the subtree.

6.1-4

The smallest elements only resides in the leaves.

6.1-5

Certainly it is.

6.1-6

No, because the parent of 7 is 6.

6.1-7

The leaves are the nodes indexed by \(\{i\ |\ n < 2i, i\leq n\}\), i.e., \(\lfloor n/2 \rfloor + 1, \lfloor n/2 \rfloor + 2,\ldots,n\).

Author: pedh

Created: 2023-08-17 Thu 10:35

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