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

In the merge-sort tree shown in Figures 11.2 through 11.4, some edges are
drawn as arrows. What is the meaning of a downward arrow? How about an
upward arrow?
R-11.5
Give a complete pseudo-code description of the recursive merge-sort algorithm
that takes an array as its input and output.
R-11.6
Show that the running time of the merge-sort algorithm on an n-element
sequence is O(nlogn), even when n is not a power of 2.
R-11.7
Suppose we are given two n-element sorted sequences A and B that should not
be viewed as sets (that is, A and B may contain duplicate entries). Describe an
O(n)-time method for computing a sequence representing the set A > B (with no
duplicates).
R-11.8
Show that (X − A) (X − B) = X − (A ∩ B), for any three sets X, A, and B.
R-11.9
Suppose we modify the deterministic version of the quick-sort algorithm so that,
instead of selecting the last element in an n-element sequence as the pivot, we
choose the element at index … ln/2…. What is the running time of this version
of quick-sort on a sequence that is already sorted?
R-11.10
Consider again the modification of the deterministic version of the quicksort
algorithm so that, instead of selecting the last element in an n-element sequence
as the pivot, we choose the element at index …ln/2…. Describe the kind of
sequence that would cause this version of quick-sort to run in (n 2 ) time.
R-11.11
Show that the best-case running time of quick-sort on a sequence of size n with
distinct elements is O(nlogn).
R-11.12
Describe a randomized version of in-place quick-sort in pseudo-code.
R-11.13
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