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CMPT 307 — Data Structures and Algorithms
Exercises on Heaps and Stable Matchings. Due: Thursday, Septem
ber 24th (at the beginning of the class)
Reminder: the work you submit must be your own. Any collaboration and consulting outside
resourses must be explicitely mentioned on your submission.
1. Describe a Θ(
n
log
n
) time algorithm that, given a set
S
of
n
integers and another integer
x
,
determines whether or not there exist two elements in
S
whose sum is exactly
x
.
2. Suppose that in the MergeSort algorithm the input sequence split into
k
subsequences (
k >
2,
but ﬁxed). Determine the running time of such algorithm. Does it have any advantages
comparing to the standard MergeSort? (You may wish to look into Chapter 4 of CLR.)
3. We explore the issue of truthfulness in the Stable Matching problem and speciﬁcally in the
GaleShapley algorithm. The basic question is: Can a man or a woman end up better oﬀ
lying about his or her preferences? More concretely, we suppose each participant has a true
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 Fall '09
 A.BULATOV
 Algorithms, Data Structures

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