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CS 473: Algorithms, Fall 2010
HW 7 (due Tuesday, October 26)
This homework contains four problems.
Read the instructions for submitting homework on
the course webpage
. In particular,
make sure
that you write the solutions for the problems on
separate sheets of paper; the sheets for each problem should be stapled together. Write your name
and netid on each sheet.
Collaboration Policy:
For this home work, Problems 13 can be worked in groups of up to 3
students each.
Problem 0 should be answered in Compass as part of the assessment HW6Online and
should be done individually.
0. (10 pts) HW7Online on Compass.
1. (25 pts) Let
G
= (
V,E
) be an undirected graph with edge costs
c
e
. Given an integer
k
where
1
≤
k
≤
n

1, describe an algorithm that ﬁnds the minimumcost forest in
G
that contains
k
edges.
2. (25 pts) Recall from class the idea of PathCompression in the UnionFind data structure
for maintaining disjoint sets. Prove that if PathCompression is used then the total time
for
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 Fall '08
 Chekuri,C
 Algorithms

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