CLRS Chapter 6 solutions

Exercises

6.1-1

What are the minimum and maximum numbers of elements in a heap of height \(h?\)

Sol’n

rough draft:

\[ \begin{align*} \sum_{k = 1}^{h - 1} 2^k & < \# \text{ of elements in heap} \le \sum_{k = 1}^h 2^k. \end{align*} \]

Sol’n

6.1-2

Show that an \(n\)-element heap has height \(\lfloor \lg n \rfloor.\)

Sol’n

6.1-3

Show that in any subtree of a max-heap, the root of the subtree contains the largest value occurring anywhere in that subtree.

Sol’n