Data Structures and Algorithms in Java[1].pdf - Fulvio Frisone

visited in a preorder traversal of H? What about an inorder traversal of H? What
about a postorder traversal of H?
R-8.15
Show that the sum
which appears in the analysis of heap-sort, is Ω(nlogn).
R-8.16
Bill claims that a preorder traversal of a heap will list its keys in nonde creasing
order. Draw an example of a heap that proves him wrong.
R-8.17
Hillary claims that a postorder traversal of a heap will list its keys in non
increasing order. Draw an example of a heap that proves her wrong.
R-8.18
Show all the steps of the algorithm for removing key 16 from the heap of Figure
8.3.
R-8.19
Show all the steps of the algorithm for replacing key 5 with 18 in the heap of
Figure 8.3.
R-8.20
Draw an example of a heap whose keys are all the odd numbers from 1 to 59
(with no repeats), such that the insertion of an entry with key 32 would cause
up-heap bubbling to proceed all the way up to a child of the root (replacing that
child's key with 32).
R-8.21
Complete Figure 8.9 by showing all the steps of the in-place heap-sort
algorithm. Show both the array and the associated heap at the end of each step.
R-8.22
Give a pseudo-code description of a nonrecursive in-place heap-sort algorithm.
R-8.23
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