Fall 2001
Fundamental Algorithms
Professor Yap
Homework 6 (MORE HINTS)
Problem 2 (Dijkstra)
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We omitted to mention the source for this
problem -- use vertex A, of course.
Problem 4 (Union Find Problem).
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The cost of Find should be defined as "the number of
nodes along the Find-path" (so this is one more than
then length of the Find-path).
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The data structure we assume here is
what I call the ``compressed tree'' data structure in lectures,
or what the book calls ``disjoint-set forest'' (section 21.3, p.505).
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As in all Union-Find Problems,
the sets are initially singletons.
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In "Link(x,y)", it is assumed that x and y are
the roots of compressed trees. In practice, it
means that you have already performed two Finds to
get x and y before doing a link. Also, you can
either make x or y the new root, unless there
is some other restrictions like the rank heuristic.
Problem 5
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It was confusing to say
that "non-sinks has degree 2". We mean "outdegree 2".