CSIS 0250B Design and Analysis of Algorithms
Assignment 1
Due: 10:30 AM, Feb 11, 2009
Warmup (no need to turn in)
1. Show how you would modify depth ﬁrst search to report a cycle of a given undirected graph,
if it exists. The running time of your algorithm should be
O
(
m
+
n
) for a graph with
n
nodes
and
m
edges.
2. The following algorithm attempts to detect whether an undirected graph contains a cycle:
Sum the number of entries in the adjacent lists of all vertices. If the sum is at least twice the
number of vertices, report that the graphs contains a cycle. Is this algorithm correct?
3. You are given an array of
n
elements. Some of the elements are duplicates. Given an
O
(
n
log
n
)
time algorithm to remove all duplicates from the array.
4. Claim: Let G be a graph on n nodes, where n is an even number. If every node of G has
degree at least n/2, then G is connected.
Is the claim true or false?
Problems
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 Spring '10
 Chan
 Algorithms, Graph Theory, Planar graph, undirected graph, time algorithm

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