Chapter 6.1
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., \(\lfloor n/2 \rfloor + 1, \lfloor n/2 \rfloor + 2,\ldots,n\).